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The questionnaire with the 16 case-scenarios was distributed to all participants. The principal investigator made a brief introduction about the study to each individual participated in the study, explained the six attributes and their assigned levels and also provided instructions about the completion of the ranking exercise. The ranking exercise started by explaining participants the six (6) attributes and their assigned levels. Each participant was handed 16 small cards describing each of the 16 scenarios in a table format. Each card basically represented one hypothetical patient and described its main characteristics (Table 2). Individuals were asked to rank order the 16 cards according to priority of treatment. For ease of use, participants were initially asked to sort the 16 cards in three (3) piles: (a) those with the highest priority, (b) those with the lowest priority and (c) those for which they were unsure. Following this, participants had to rank the 16 cards by assigning numbers: starting with number 1 for the card with the highest priority, ending with number 16 for the card with the lowest priority. They were also asked to write down the number on each card after double-checking their decisions. Demographic characteristics (gender, age and educational level) were also obtained.Table 2Card of a hypothetical patientPatient 1 rank orderAge37 years oldHealthy lifestyleNoType of diseaseAcute diseaseSeverity of diseaseMildHealth improvement after treatmentMediocre improvementCost of treatmentLow
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The study conformed to all the ethical requirements including notification to the authority responsible for the protection of the personal data, the authors secured a permission from the Office of the Commissioner for personal data protection of the Republic of Cyprus to set up and maintain records for this study. Written informed consent was obtained from all participants. Anonymity, confidentiality and voluntary participation were assured and the data were kept in a safe place and used only for the purpose of the study.
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Data analysis was based on the conjoint analysis technique. The attributes that participants took into consideration and assigned relative importance were the following: severity of disease, age, type of disease, health improvement after treatment, cost of treatment and healthy lifestyle. These six (6) attributes were used as discrete variables. Sixteen (16) preference cards were created based on the six (6) abovementioned attributes and participants ranked order those cards in terms of utility (starting with the most preferred hypothetical patient to the least important hypothetical patient). Using conjoint analysis the relative utility of each of the six (6) attributes was elicited along with their relevant values with highest values indicating high utility and high relative value. Utility (Χ) for each patient profile is derived from the following equation :\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm X} \, = {\text{ the model's constant }} + \, {\rm X}_{\text{age}} + \, {\rm X}_{\text{healty lifestyle}} + \, {\rm X}_{\text{type of disease}} + \, {\rm X}_{\text{severity of disease}} + \, {\rm X}_{\text{health improvement}} + \, {\rm X}_{\text{cost of treatment}} .$$\end{document}X=the model's constant+Xage+Xhealty lifestyle+Xtype of disease+Xseverity of disease+Xhealth improvement+Xcost of treatment.
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To test the correlations between various utilities and the gender, age and educational level of the study participants the authors used the t test. Also, we performed analysis of variance and t test in order to assess differences on relative importance ascribed by the participants to the six characteristics of the study, based on their gender, age and educational level. The two-sided significance level was set equal to 0.05. Data analysis was conducted using IBM SPSS 21.0 (Statistical Package for Social Sciences).
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The study sample consisted of 50 women (50%) and 50 men (50%). 23% (n = 23) were secondary school graduates, 38% (n = 38) were high school graduates and the remaining 39% (n = 39) of the study population were University graduates. The mean, standard deviation and median of the participant’s age was 38.9, 14.3 and 36 years of age, respectively. The minimum and the maximum values in terms of age were 18 and 74, respectively.
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Table 3 summarises the utilities and relative importance ascribed by participants to the six (6) attributes of this particular study. It becomes evident that younger patients, unhealthy lifestyle, acute and severe disease, large improvement in health and low cost of treatment are assigned with highest levels of utility.Table 3Utilities and relative importance ascribed by the participants to the six (6) attributes of the studyAttributeCategoriesUtility (standard error)Relative importanceAge16 years old1.427 (0.142)25.537 years old−0.018 (0.167)68 years old−1.408 (0.167)Healthy lifestyleYes−0.249 (0.107)7.9No0.249 (0.107)Type of diseaseChronic−0.388 (0.107)15.2Acute0.388 (0.107)Severity of diseaseMild−2.046 (0.107)27.4Severe2.046 (0.107)Health improvementMediocre−0.198 (0.107)12.1Large0.198 (0.107)Cost of treatmentLow0.223 (0.142)11.9Medium−0.127 (0.167)High−0.097 (0.167)Constant8.088 (0.118)
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Ranking attributes/characteristics according to their relative importance (value), starting with the characteristic with the highest relative importance come down to the following:Severity of diseaseAgeType of diseaseHealth improvement after treatmentCost of treatmentHealthy lifestyle
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The total maximum utility for the above-mentioned patient is calculated as follows:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$maximum \;utitlity = 8.088 + 1.427 + 0.249 + 0.388 + 2.046 + 0.198 + 0.223 = 12.619$$\end{document}maximumutitlity=8.088+1.427+0.249+0.388+2.046+0.198+0.223=12.619
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The total lease utility for the above-mentioned patient is calculated as follows:\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$least\;utility = 8.088 - 1.408 - 0.249 - 0.388 - 2.046 - 0.198 - 0.127 = 3.672$$\end{document}leastutility=8.088-1.408-0.249-0.388-2.046-0.198-0.127=3.672
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Table 4 summarises the relative importance values ascribed by participants to the six (6) attributes of this particular study based on their gender, age and educational level.Table 4Relative importance ascribed by the participants to the six (6) characteristics of the study, based on their gender, age and educational levelCharacteristicRelative importanceAgep valueHealthy lifestylep valueType of diseasep valueSeverity of diseasep valueHealth improvementp valueCost of treatmentp valueGender <0.001 a 0.04 a <0.001 a 0.002 a <0.001 a <0.001 a Women28.38.212.527.813.010.2 Men22.77.717.927.011.213.5Age (years)<0.001 a 0.67a <0.001 a <0.001 a 0.11a <0.001 a ≤3522.78.013.729.612.313.7 >3528.27.916.725.211.910.1Educational level<0.001 b,c <0.001 b,d <0.001 b,e < 0.001 b,d <0.001 b,f <0.001 b,f Secondary school (‘gymnasium’) graduates32.07.411.025.411.412.8 High school graduates23.67.017.128.212.112.0 University graduates23.49.115.927.912.511.2 a t test bAnalysis of variance cStatistical significant difference between secondary school graduates and high school graduates (p = 0.049) dStatistical significant difference between secondary school graduates and high school graduates (p < 0.001) and secondary school graduates and university graduates (p < 0.001) eStatistical significant difference among the three groups (p < 0.001 in all cases) fStatistical significant difference between secondary school graduates and high school graduates (p < 0.001)
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The results indicate that women ascribe the largest relative importance to age, while men opted for the severity of the disease. Both women and men ascribed the lowest level of relative importance to healthy lifestyle. Women gave priority to younger patients, in contrast to men. Men gave priority to a patient with large health improvement after treatment, in contrast to women. All differences according to gender were statistically significant.
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Participants with more than 35 years of age ascribed the highest level of relative importance to age (p < 0.001), while participants less than 35 years of age opted for the severity of the disease (p < 0.001). Both groups, however, ascribed the least relative value to healthy lifestyle (p = 0.67). Moreover, participants older than 35 gave priority to a 16 years old patient, in contrast to those participants with less than 35 years of age (p < 0.001).
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Participants with the lowest educational level assigned high importance to younger patients and to the “health improvement after treatment” attribute, in comparison to the participants with the higher educational level who gave priority to a patient with acute disease (p < 0.001 in all cases). Secondary school graduates ascribed the highest level of importance to age, while high school and University graduates to the severity of the disease. The lowest value in terms of importance was assigned to “healthy lifestyle”, irrespective of the participants’ educational level.
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The purpose of the present study was to investigate preferences and the relative importance of possible criteria that could be taken into consideration for health care priority setting in Cyprus. This is the first attempt on the topic in Cyprus and thus there are no similar data available to benchmark against and compare the results.
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Results from the present study revealed that when the citizens asked to set priorities in health care, they report the “severity of disease”, “age”, “type of disease”, “health improvement after treatment”, “cost of treatment” and “healthy lifestyle” are all possible criteria that should be considered. This is congruent to similar findings of other studies .
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The utilities and relative importance values ascribed by the 100 respondents to the six (6) attributes of the study indicate that high priority and thus high utility is associated with patients that demonstrate young age, unhealthy lifestyle, acute and severe diseases, large expected health improvement after treatment and low cost of treatment. Thus, ranking the patients’ characteristics by their relative importance value, starting with the one with the highest importance, elicits the profile of the hypothetical patients with the highest and the lowest priority.
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The study findings indicate that participants gave the highest priority to a patient of 16 years of age, with unhealthy lifestyle, an acute disease that is also severe, who is expected to have large health improvement after treatment and, the cost of his/hers treatment is low. On the contrary, lowest priority is given to a 68 years old patient, with healthy lifestyle and a chronic disease of mild form expected to have mediocre improvement to his/her health condition after treatment and whose cost of treatment is high.
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Moreover, it was identified that the “severity of disease”, “age” and “type of disease” are the three (3) attributes that have the highest importance values. The first two factors although in different order were also found in the study of Winkelhage and Diederich in Germany to influence public preferences in healthcare priority setting. In their study, the most important was age and then severity of the disease. The finding that the “severity of disease” is an important parameter for priority setting and resource allocation in health care is in line with the findings of other studies [18, 19, 23, 28]. Our findings are in line with previous studies indicated that the severity of the disease was either an important parameter for resource allocation in health [1, 18, 19, 23] or was strongly supported by the public as an important health care priority setting criterion [6, 15, 23, 28, 38]. Moreover, the study findings indicate that priority should be given to patients with a severe disease or urgent conditions. The opinions of people participating in the study chose criteria that are mostly concerned with issues related to the value of life, social justice and equality .
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Having as a starting point the fact that participants gave priority to people in greater need for health care treatment can only lead to the assumption that the ground of this particular choice is based on the principle of necessity. These preferences are rather justified and expected since they raise issues that relate to the ultimate value, that of life itself. In life or death situations, the public is not expected to make choices in favor of the sustainability of the health care system or in favor of value maximization, but are rather expected to make choices that can be explained in terms of the principle of necessity. The principle of necessity actually entails that health care services should be offered to the public according to the actual “need” [28, 29, 39]. This approach defines “need” as the severity of the disease and supports that what should also be taken into consideration is the “urgency of the situation”. Therefore, those who are suffering from severe diseases should be priority ranked for health care treatments. This principle seems to be highly supported in Scandinavian countries. The severity of the situation, in the sense that the person who is in greater need should receive health care treatment first, is actually the first priority criterion in the Swedish and Norwegian laws [7, 41–45].
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In the present study “age” was identified the second most significant attribute in terms of utility and importance. Results indicated that older participants gave priority to younger patients. This decision might be based on internal motives and interests . Our findings are in line with the those of other similar studies [6, 47] which used the same conjoint analysis methodology and support consistently that young people should have priority over others for health care treatment [6, 11, 23, 48–54]. On the other hand, other researchers suggest that age should not be a priority setting criterion or yield small support in its favor [1, 10, 11, 14, 18, 19, 21, 38, 55–60]. This implies that these findings may reflect the fact that the same methodology was used in all these studies. This premise, that the order of the questions and the nationality of the participants seem to affect the research results, is also evident in other studies [5, 14, 15, 20, 51, 61–63].
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The attribute of age in our study was presented with three concrete levels (16, 37 and 68 years), while the others were described rather abstractedly with levels such as “mild” or “severe”. One may suggest that this might have influenced the results. However, it seems that the variables ordering did not impacted the results, since the rank order in terms of utility differs from the ones presented in the 16 scenario cards. The fact that “age” was assigned with the second highest utility level needs further investigation, especially because is in conflict with the European directive for equality in health care that suggests that chronological age is less important than biological age .
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Evidence suggests , elements such as younger patients, patients with larger expected health improvement after treatment and low cost treatments, are associated with the “principle of efficiency”, while supporting healthy lifestyle in terms of health care priority is associated with the “principle of merit”. The hypothesis of their research was that participants with higher educational level would be supportive of the principles of efficiency and merit, in contrast to participants with lower educational background. However, this hypothesis was confirmed neither from their study nor from the present study. Instead, participants with lower education support importance values that are associated with the efficiency principle. It should also be noted that other researchers reached the conclusion that accepting “age” as a criterion for health care resource allocation is not associated with the respondents’ educational level .
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The “healthy lifestyle” attribute in the present study was not supported by participants with higher education, in contrast to other studies [6, 22]. According to Winkelhage and Diederich this criterion corresponds to the principle of merit. Participants assigned the lowest relative importance value to “healthy lifestyle” while at the same time ascribed utility to the “unhealthy lifestyle” variable.
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According to Myllykangas et al. if lower priority is given to people with unhealthy lifestyle this will result to increased social health inequities since these population groups are in greater need for medical treatment. The literature suggests that health care resource allocation based on lifestyle is much debated and rather problematic. The adoption of a healthy lifestyle is also influenced by education which is associated with the socioeconomic status which in turns affects the person’s health status consisting a vicious cycle. It is assumed that people of high educational level are most likely to support the principle of necessity compared to people of low, since this principle actually underlines that individual contributions should be rewarded .
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99.9
Cypriots in the present study gave priority to patients with unhealthy lifestyle as opposed to those with healthy lifestyle, irrespective of age, gender and educational level. A possible explanation is that respondents considered people with an unhealthy lifestyle to be in greater need for medical treatment. Another plausible interpretation is that unhealthy lifestyle is highly associated with risk factors such as smoking, obesity and physical inactivity. Considering that Cyprus ranks high in tobacco consumption between EU countries as well as in physical inactivity and obesity, one may assume that a large proportion of the participants had one or more risk factors and this might have affected their decision-making. Irrespective of these assumptions, this finding may suggest that people of low socio-economic status and poor health should have priority due to social inequalities in health. It seems that participants’ responses were based on the principle of necessity or at least we can pertain that these findings can be partially explained on the grounds of this principle.
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Findings from the present study may assist health policy makers in their effort to strengthen the health system and set priorities. Of course, the list of criteria (“age”, “type of disease”, “health improvement after treatment”, “cost of treatment” and “healthy lifestyle”) is not exhaustive but indicative. The integration of public preferences into health policy decision making processes requires a systematic, reliable and effective strategy of public participation. The contribution of citizens to health policy decision making should be official and continuing: from planning to evaluation of the health services and programs. It should be noted that public preferences is rather complementary than conflicted to evidence based data, since they are based on them and do not apply to every aspect and every area or activity of the healthcare system. For instance, the criterion of “type of disease” may be useful to set priorities in universal screening for non-communicable diseases (e.g. cancer and cardiovascular disease instead of multiple sclerosis) for the general population but perhaps it is not suitable in setting priorities in innovative pharmaceutical therapies and health technology assessment procedures. Thus, specific criteria and strategies should be implemented in the different areas of health policy decision making. Of course, the strategy of public participation is a necessary but not sufficient condition to translate evidence into policies.
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98.1
There are different levels of health policy decision making (local, national, European) and healthcare priority setting requiring different channels of participation. At a local level, the integration of public opinions is more feasible, due to community based non-governmental organizations which advocate for citizens’ health needs and may be beneficial in consulting local committees and authorities in healthcare priorities setting. At a national level, more solid and official methods (e.g. legislation establishing patient participation) are needed in order to incorporate public views and preferences in health policy decision making. To achieve this goal, academic research would be more community oriented without losing its credibility. An important prerequisite is to increase the productive interaction between researchers, policy makers, advocates and general public. Community based research may facilitate this process. Moreover, it is imperative for researchers to present evidence in a way that can be exploited by policy makers and provide continuing support to every step of the integration procedure. On the other hand, policy makers should develop official mechanisms and strategies so as to ensure that the role of other key stakeholders (e.g. general public, researchers) is not just consultative but impacts the development, implementation and evaluation of health policies, programs and services.
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The incorporation of public opinions in health priority setting and health policy decision making is a challenging process. There is a growing body of evidence suggesting that public participation in health policy decision making is associated to health systems performance and sustainability, but the strategy to achieve it remains an under-investigate issue . Results from the present study revealed that the “severity of disease”, “age”, “type of disease”, “health improvement after treatment”, “cost of treatment” and “healthy lifestyle” should be considered as criteria in healthcare priorities setting. Moreover, it was identified that “severity of disease”, “age” and “type of disease” were the attributes with the highest importance. This may be attributed to the fact that the study was carried out during the financial crisis in Cyprus which implies that health care needs limited resources. A critical point for the integration of public preferences in health policy decision making is whether they lead to increase or reduce of inequalities in health . Since vulnerable groups are affected disproportionally by health inequalities they should have a say in healthcare priority setting. Thus, it should be clearly defined what we mean by the term “public participation”. Are vulnerable and disadvantaged groups included or just the general population? On the other hand, we should not be focused only on vulnerable groups, because the healthcare system should be accessible and effective for all. This implies that different sources of information and different strategies of data collection should be implemented in order to ensure that all population’ groups are included and the data collected are representative and reliable.
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The fact that interactions between the various attributes in pairs or in triplets were not analyzed is a methodological limitation of the present study, especially considering that Rodriguez and Pinto revealed that age interacts with health gain associated with medical treatment . Nonetheless, the design of the present study did not allow for the analysis of these interactions because the patient scenarios would increase and become unmanageable for the participants.
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Another study limitation is that participants had rather limited information at their disposal. One can assume that should participants had the opportunity to secure adequate and substantial information and to discuss all relevant parameters of the study they might have reached different decisions. To downsize this limitation, the authors provided all participants with the same information and answered all their questions.
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90.06
Colorectal cancer, as a common malignancy in the world, has accounted for the second and third of cancer related death in male and female respectively . Though the patients with early colorectal cancer reach satisfied survival, the advanced ones always own poor survival attributed to unresectable primary tumor, resistance and recurrence [2–4]. Thus, it is necessary to search for efficacious markers to assess the prognosis of colorectal cancer, especially in advanced stage.
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Increasing evidence has observed aberrant blood coagulation in the patients with cancers [5, 6]. As an established risk factor of blood hypercoagulability, the tumor cells release various cytokines to activate coagulation [7, 8]. D-dimer is a canonical marker of hypercoagulability and a common approach to evaluate the hypercoagulable state in clinical practice . Aberrant D-dimer has been detected in various cancers including colorectal cancer and several studies showed elevated D-dimer was correlated with poor survival of colorectal cancer [10, 11]. However, the inconsistent conclusion of pretreatment plasma D-dimer in colorectal cancer could not be ignored [12, 13]. Up to now, whether the pretreatment plasma D-dimer could be used for a predictive biomarker for the prognosis of colorectal cancer is controversial based on current evidence. Therefore, a comprehensive meta-analysis to combine the published studies is essential in order to reach a more convincing conclusion.
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A total of 713 records were identified from the initial search. Thirty-eight studies were analyzed with full-text after excluding the reduplicated or irrelevant studies. Finally, fifteen studies were used for this comprehensive meta-analysis and detailed information of eligible articles were presented in Table 1 [10–24]. The flow diagram of this meta-analysis was provided in Figure 1.
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Fifteen eligible studies (a total of 2283 cases) which ranged from 2001 to 2017 included patients with colorectal cancer of TNM stage I-IV (Dukes stage A-D) that were accepted surgery and/or chemotherapy. Among the fifteen studies, twelve studies showed positive results of the relationships between elevated D-dimer and overall survival of colorectal cancer, and three studies obtained negative results. The combined HR of the fifteen eligible studies was 2.167 (95% CI = 1.672–2.809, P < 0.001, Figure 2) by a random effect model due to obvious heterogeneity (I2 = 73.3%, P < 0.001).
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Subsequently, the sensitivity analysis was employed to investigate the source of heterogeneity among the eligible studies. We observed that the pooled result varied dramatically after removing a certain article (Kimberly et al.) with distinct cut off value of D-dimer (Figure 3). Therefore, we deleted it and gained a homogeneous pooled result (14 studies with 2179 cases) with fixed effect model which was more convincing (HR = 2.143, 95% CI = 1.922–2.390, P < 0.001; heterogeneity test: I2: 0%, P: 0.549, Figure 4)
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We conducted subgroup analysis according to three factors (region, treatment and statistical method for survival). The results were presented in Table 2. Both in the studies of Asia and non- Asia, high D-dimer could predict poor survival of colorectal cancer, especially in Asia population (Figure 5). Likewise, we gained consist significant results in the rest two subgroup analyses (Figures 6, 7).
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Colorectal cancer, as a malignant neoplasm with high incidence worldwide, owns unsatisfied survival in advanced stage due to metastasis, recurrence and resistance of chemotherapy [1, 25, 26]. Thus, an efficacious biomarker to predict the prognosis of colorectal cancer is necessary, thereby providing potential target for treatment. D-dimer is a clinically common marker of activation of coagulation system. Increasing evidence showed that malignant neoplasm could promote the activation of coagulation, and elevated D-dimer was detected in several cancers which correlated to the prognosis, including in lung cancer, gastric cancer, and colorectal cancer [27–29]. Ma et al. have demonstrated high D-dimer predicted worse survival in lung cancer by a meta-analysis . However, regarding colorectal cancer, the prognostic value of D-dimer was contentious based on the published studies.
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In this current meta-analysis, we performed an integration of the current evidence (14 studies including 2179 cases) and provided a more stable and convincing result. The results of this current meta-analysis indicate high pretreatment plasma D-dimer could predict poor survival of colorectal cancer (HR = 2.143, 95% CI: 1.922–2.390). Subgroup analysis according to region, treatment and statistical method for survival, also showed consistent results: D-dimer could act as a predictive factor of survival both in the patients undergoing surgery, and the ones with metastasis received chemotherapy. The heterogeneity test and publication bias test all demonstrated the conclusion of the meta-analysis was stable.
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In terms of the role of D-dimer in prognosis of patients with colorectal cancer, this following evidence may support our conclusion. At the genetic level, Vossen et al. confirmed that prothrombotic factor polymorphisms increased risk of colorectal cancer . Yu et al. established that hypercoagulability owned a causal link to cancer-related genes (K-ras and p53) in colorectal cancer . Meanwhile, the studies by Kemal et al., Wang et al. and Blackwell et al. revealed elevated D-dimer was associated with advanced T stage, positive lymph node metastasis, metastasis and cell differentiation [14–16]. Due to the close relationships between D-dimer and unfavorable clinicopathologic characteristics of colorectal cancer, the association between D-dimer and poor survival of colorectal cancer was understandable. Moreover, several studies clarified that plasma D-dimer of patents with colorectal cancer reduced obviously after surgery or chemotherapy which indicated the higher tumor burden the higher plasma D-dimer [33–35]. Therefore, the prognostic role of plasma D-dimer in pretreatment colorectal cancer was acceptable based on the aforementioned evidence.
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As Yu et al. reported, we could not assess D-dimer status exactly according to normal reference range in the patients with cancers . Thus, tumor-specific D-dimer reference range should be further investigated with more epidemiological studies and provides a useful standard for clinical practice.
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Though our study provided a more convincing conclusion that D-dimer could act as a predictive biomarker of prognosis for colorectal cancer, some inevitable limitations should be discussed: 1) several included studies did not show the TNM stage or Dukes stages of colorectal cancer and it may cause the heterogeneity among the included patients and affect the application of this meta-analysis; 2) a study with negative result was excluded due to unavailable data for meta-analysis which may lead to an exaggerated positive conclusion; 3) limited sample size of several included articles may give a underpowered HR, and thereby impact the pooled HR; 4) studies only in English or Chinese were included which may lead to incomplete evidence collection. Thus, a prospective study with a large sample to confirm the conclusion of this meta-analysis and cover the above limitations is indispensable.
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Collectively, our meta-analysis showed primary comprehensive insight into the significant role in prognosis of plasma D-dimer in pretreatment colorectal cancer and D-dimer maybe a potential target for the treatment of colorectal cancer. The patients with colorectal cancer may benefit from anticoagulation interaction. Moreover, further prospective investigations with large sample size are demanded to validate the role of D-dimer in colorectal cancer.
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In the present comprehensive meta-analysis, we searched six databases to collect the evidence, containing three databases in English (PubMed, Web of Science and Embase) and three databases in Chinese (database of China National Knowledge Infrastructure (CNKI), VIP and WanFang). The terms for retrieval were: 1) “D dimer” or D-dimer or “D-dimer fibrin” or “D-dimer fragments” or “fibrin fragment D1 dimer”; 2) colorectal or colon or rectal or bowel; 3) cancer or carcinoma or adenocarcinoma or tumour or tumor or malignanc* or neoplas*. The literature retrieval of this current meta-analysis was updated to June 12, 2017.
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The eligible standards of the screen for the initial identified records were that 1) colorectal cancer should be pathological diagnosis, 2) detection of D-dimer was conducted in pretreatment colorectal cancer, 3) exploration of the relationships between D-dimer and prognosis of patients with colorectal cancer, and the data of prognosis was available directly or indirectly, 4) English or Chinese article, and 5) the recent study or study with a largest sample size will be included if the population is repetitive.
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Two authors screened the initial records independently and the final decision would be obtained by the third one if inconsistent conclusion existed. Information of the first authors, publication period, region, sample size, stage of colorectal cancer, cut off value, treatment, and HR were extracted. Moreover, we fellow a preferable order for HR extraction: HR (from multivariate analysis) > HR (from univariate analysis) > HR (extracted from Kaplan-Meier survival curve).
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Newcastle-Ottawa Scale (NOS) was employed to estimate the quality of each eligible studies . A certain study is evaluated from 3 sections for the included cohort: selection, comparability and evaluation for outcome. The quality of a certain article was determined by stars summation of the above 3 sources and the study with star ≥ 5 is acceptable.
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The data combination of this meta-analysis was carried out by Stata 12.0. The prognostic value of plasma D-dimer in pretreatment colorectal cancer patients was evaluated via combined HR together with corresponding 95% CI. Q test as well as I2 statistic was utilized to estimate the heterogeneity of the pooled articles. In the meta-analysis, a model of fixed-effect was selected if heterogeneity of pooled studies was acceptable (P > 0.1 and I2 < 50%) . If not, we used a model of random-effect to combine the HR. The publication bias was examined by Egger's test and P < 0.05 indicates statistical significance.
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Representing a significant economic burden on health care systems worldwide, cancer is associated with a high level of morbidity and mortality in virtually every country (Jonsson et al., 2016). Prevalence is increasing along with incidence (Siegel et al., 2015). In 2012, there were 14 million cases of diagnosed cancer patients, while the number of cancer-related deaths was estimated to be 8.2 million (McGuire, 2016). The global cancer mortality increased by 17% between 2005 and 2015 (Wang et al., 2016). During the same period the global burden of neoplasms measured in Disability Adjusted Life Years (DALYs) increased by 11.6% (Kassebaum et al., 2016). The global cancer burden will further increase in the near future, the number of new cases is projected to achieve 22.2 million by 2030 (Vineis and Wild, 2014). Societies with established health care systems dedicate significant resources to providing access to cancer diagnostics and therapies, resulting in improved life expectancy for many oncological conditions (Jonsson et al., 2016). However, extension of life implies extended use of therapies and other health care services, both being accompanied by growing patient needs (IOM, 2001; van Baal et al., 2008). There still is a large variation among nations when it comes to cancer care and nationally allocated expenditures (Luengo-Fernandez et al., 2013; Kimman et al., 2015).
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Value of cancer care treatments in terms of benefits of increased survival and/or increased quality of life poses a challenge especially in lower income countries, while simultaneously considering their affordability. The evaluation of the benefits derived from cancer therapies is difficult as the extent of the benefit may be highly dependent on the components of the measurement and the individual patient perspective, i.e., a therapy can be valued differently by patients, caregivers, payers, and/or society (Basch, 2016). Nonetheless, assessing health gains should not be done without asking the beneficiaries (i.e., patients) about their needs and expectations of care they receive (Tremblay et al., 2015; King et al., 2016). Nevertheless, heterogeneity of patient preferences and values (PPVs) poses a complex problem, and although seeking a simple population-based solution may seem attractive from a policy perspective, it may not bring the needed tangible real-life benefits.
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99.9
Multiple value frameworks have been recently published with the purpose of combining patients', providers', and payers' priorities, including those developed by the American Society of Clinical Oncology (ASCO) (Schnipper et al., 2015, 2016), the European Society for Medical Oncology (ESMO) (Cherny et al., 2015), the Institute for Clinical and Economic Review (ICER) (ICER, 2017), the Memorial Sloan Kettering Cancer Center (MSKCC) (MSKCC, 2017), the National Comprehensive Cancer Network (NCCN) (NCCN, 2017) and the National Cancer Institute—U.S. Department of Health and Human Services (Epstein and Street, 2011). As stated by Basch (2016), the primary focus of several guidelines is setting up a benchmark for institutional standards by taking into account the clinical evidence and the associated drug costs in order to facilitate treatment choices for payers, providers and patients (Basch, 2016). Nonetheless, these frameworks do not appear to fully address the complex issue of patient heterogeneity and patient preferences.
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Beyond direct health benefits there are other aspects with potential added value to cancer therapies. Molecular diagnostics supported by genomic profiling allow applied novel targeted therapies to effectively treat patients, tailoring the treatment to target their unique tumor characteristics (Al-Rohil et al., 2016). Several patient surveys, including Patient Reported Experience Measures (PREMs), have been developed to identify priorities of patient experiences and preferences (Weldring and Smith, 2013; Taylor et al., 2015; Tremblay et al., 2015; Windham et al., 2015; Burns et al., 2016; Halpern et al., 2016). Alongside this gradual shift toward personalized medicine, importance of patient engagement is also increasingly recognized (Tremblay et al., 2015; King et al., 2016; Schnipper et al., 2016). One driver behind their increased involvement is the recently initiated patient network for “big data” collection on individuals' genetic and therapeutic characteristics (CMBRP, 2016). However, patient representatives often argue that current value frameworks and guidelines have limitations in reflecting or even admitting the importance of patients' preferences (Pitts and Goldberg, 2015).
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The objective of this research was (I) to identify PPVs in cancer care and treatment as indicated by POs surveyed on behalf of their patient population; (II) to determine how these PPVs are captured in the guidelines on both a micro and macro level and finally (III) to review how patient representation in clinical and policy decisions are facilitated by the guidelines. Authors are not aware of studies on PPVs from wide array of Patient Organizations (POs) from countries on different continents.
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An exploratory research was conducted to identify key terms that can be considered as relevant value propositions for patients undergoing cancer treatment based on the review of selected publications (Epstein and Street, 2007, 2011; Pitts and Goldberg, 2015; Schnipper et al., 2015, 2016; Windham et al., 2015). Lead representatives of participant POs selected these papers partly because they had been widely discussed in global conferences and they were recommended by clinical experts. After selection of patient relevant value propositions an electronic survey was developed and completed by leaders of 19 POs from four continents to explore relative importance of these PPVs. Nine of the POs initiated this research project via the Global Action for Cancer Patients platform, and an additional 10 POs—all of them are national leaders in their own respective disease areas—joined the survey. Finally, a systematic literature review—using Pubmed as a research engine—was conducted to evaluate how clinical cancer care guidelines incorporate the identified PPVs.
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The survey filled in by PO leaders intended to explore what patients deem to be of most value to them. The final survey included three groups of items/topics: The first set of questions were focusing on descriptive general characteristics of the POs (way of funding, number of payed and voluntary staff). The second group of items were related to POs perception on PPVs (aspects of care and their importance rated on a 5-point ordinal scale, fields for improvement in cancer care formulated as an open-ended question), while the third group contained open-ended questions on involvement of POs into decision making [involvement of patient representatives to health technology assessment (HTA)]. (For the actual questions, please refer to the headlines of the corresponding tables) POs were informed about the objectives of the survey, including the notion of presenting aggregated results in a scientific manuscript. As the survey was filled in by POs and only general policy questions were surveyed without collecting any clinical personal data, after legal consuelling no ethical approval was considered to be necessary for the study.
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Outcomes of the explotarory research and survey results were used to develop a hierarchical classification and data extraction spreadsheet to collect information on PPVs in the clinical cancer care guidelines. The data extraction focused on the presence of three main categories in guidelines, including: (I) patient empowerment related PPVs, (II) health outcomes related PPVs, and (III) patient management related PPVs in the guidelines (see Table 1). The draft data collection spreadsheet was pre-tested using literature references in the initial exploratory research and appeared to be a relevant tool for further data collection.
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The primary purpose of the systematic review was to give a general overview about the representation of PPVs in guidelines. The following keywords were identified based on the survey and the explotarory research: (malignan*[Title/Abstract] OR oncolog*[Title/Abstract] OR cancer[Title/Abstract]) AND (guideline[Title/Abstract]) AND (patient empowerment OR patient value OR patient perspective OR patient preference OR patient centered OR patient view). Pubmed was used as a search engine; search strategy was finalized on 2nd September 2016. Title and abstract screening was done by two independent reviewers by adapting the PRISMA checklist (Jahan et al., 2016). The PICOS—Population-, Intervention-, Comparison-, Outcome- and Study design-based—criteria, originally developed to randomized clinical trials, were restricted to intervention- and study design-based elements. All oncology guidelines focusing on cancer care-related interventions met our inclusion criteria. Hits were further restricted to English language materials published in the last 5 years designated as guidelines by the Pubmed engine. Guidelines eligible for full text review were subject of data extraction.
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Respondents to the survey were representatives of 19 POs located in 18 countries (Argentina, Belgium, Brazil, Bulgaria, Canada (two POs), Croatia, Ireland, Italy, Japan, Lithuania, Norway, Philippines, Poland, Romania, Spain, United Kingdom, United States and Venezuela). For list of POs involved in the survey, please check Table A1. Typical form of funding for the operation and activities of POs was reported to be dominantly private. Budget constraints resulted in a relatively low number of paid employees (typically fewer than five persons per organization), so the majority of organizations had to rely on non-paid volunteers. The general characteristics of POs are described in Table 2.
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The three most valuable propositions of oncology care (where 1 is most important and 5 is less important) by survey respondents were “extended life” (mean value: 1.16), “treatment-free remission” (mean value: 1.37) and “pain reduction” (mean value: 1.42) (see Table 3). “Radical end-stage treatment with adverse events” (mean value: 3.68) and “possibility to take therapy without food” (mean value: 3.74) were the least preferred value propositions.
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The heterogeneity of cancer PPVs were reflected in the survey results. The variability was the highest related to “return to work” (SD: 1.57), “possibility to take therapy without food” (SD: 1.34) and “using radical end-stage treatment” (SD: 1.19). The relevance of these items seemed to be dependent on the personal preferences of individual patients. The most consistently judged values characterized by the lowest SD were “participating in family events and leisure activities” (SD: 0.43), and “possibility to have dose dispensed once monthly” (SD: 0.68).
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When PO representatives were asked about the desired improvement of cancer care in the survey, side-effect management and quality of life related aspects were the most frequently mentioned categories (see Table 4). More efficient use of biomarkers to determine the adequate treatment was also underlined to achieve the appropriate treatment for the right patient at the right time, leading to better disease control and longer survival.
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According to respondents, one of the most relevant areas where patient engagement should be more intense is HTA. Nevertheless, five of the 19 PO respondents reported limited use of HTA for policy and reimbursement decisions in their country (see Table 5). In some countries patient empowerment in HTA or policy recommendations was only superficial. In three cases POs did not contribute to final HTA recommendations or reimbursement decisions; their role was limited to participation in quality of life surveys. Three respondents who personally participated in HTA or policy discussions reported doubts whether their opinion was taken into account in the final decision.
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Initially 461 articles were identified on Pubmed by our search terms. After restricting the hits to English language guidelines published in the last 5 years, 27 articles were eligible for title/abstract screening. By applying our pre-specified inclusion and exclusion criteria, 20 guidelines remained for full-text review and extraction of content (National Institute for Health and Care Excellence, 2011; Hurkmans et al., 2012; Moss et al., 2012; Watanabe et al., 2012; Carter et al., 2013; Qaseem et al., 2013; Thompson et al., 2013; Andersen et al., 2014; Freedland et al., 2014; Fukukita et al., 2014; Levy et al., 2014; Partridge et al., 2014; Wolff et al., 2014; Lebbe et al., 2015; Min et al., 2015; Steele et al., 2015; Stratigos et al., 2015; Tot et al., 2015; Young et al., 2015; Harris et al., 2016) (see Figure 1 for the full flowchart and Table 6 for study characteristics). The fields of breast, prostate and colorectal cancers dominated the therapeutic areas, while only four publications dealt with cancer in general terms. Half of the guidelines were addressing treatments, some described processes for screening and only a few guidelines covered both screening and treatment.
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Patient involvement in treatment choice and recognition of patient heterogeneity were frequently addressed in the guidelines, such as by Freedland et al. (2014), Levy et al. (2014), Steele et al. (2015), and Harris et al. (2016). PPVs were represented in micro-level type decisions, such as involvement of individual patients in treatment choices (n = 13), rather than in macro-level type decisions, such as guideline development (n = 5). Active involvement of patients or patient representatives to guideline development was mentioned in only three publications (focus group, membership in the expert panel, interview with cancer patients). Two other guidelines only implicitly referred to the importance of the patient perspective. Engagement of POs and quality improvement based on PPVs seemed to be neglected topics in guidelines (n = 2 and n = 2 respectively) (see Figure 2).
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Therapeutic management of side-effects was the most frequently included aspect of health outcomes in the guidelines with a mentioning frequency of 15, while aspects that were not strongly related to clinical treatment, such as palliative care and emotional support were rarely mentioned in the guidelines (n = 6 and n = 3 respectively) (see Figure 3).
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The majority of the reviewed guidelines—such as by Hurkmans et al. (2012), Moss et al. (2012), Watanabe et al. (2012), Qaseem et al. (2013), Min et al. (2015), Young et al. (2015), and (National Institute for Health and Care Excellence, 2011)—highlighted that physicians must take into account the risk profile of therapeutic options (e.g., possible complications, adverse events and serious side-effects) and must inform the patient about all associated risks. However, detailed guidance for side-effect management was not usually provided. Half of the reviewed guidelines—including those by Hurkmans et al. (2012), Watanabe et al. (2012), Qaseem et al. (2013), Thompson et al. (2013), Partridge et al. (2014), Stratigos et al. (2015) and other publications—provided recommendations related to comorbidities. This aspect was addressed mainly from the perspective of how comorbidities influence treatment pathways or how they change the efficacy and benefit of primary therapies. Potential interactions between primary treatment and therapeutic management of comorbidities were also mentioned. Treatment-free remission and extended life were mentioned as patient values roughly in 50% of the cases (n = 9 and n = 10 respectively).
review
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The time window between initial and final diagnosis, and timeliness of treatment initiation as an individual level patient value was mentioned only in one quarter of the guidelines reviewed, highlighting the need for more explicit guidance on shortening waiting times for patients (see Figure 4). The relevance of interpersonal communication as patient value between individual patients and health care professionals was acknowledged in the majority of guidelines, such as in those by Moss et al. (2012), Carter et al. (2013), Andersen et al. (2014), Levy et al. (2014), Partridge et al. (2014) (see Figure 4). Reduced information asymmetry between patients and physicians by using easy-to-understand language and providing a detailed information package was highlighted in many guidelines. In some cases the emotional aspects of communication (n = 3) were also addressed PPVs, such as empathy, or referral to psychologists or support groups. The convenience of care was rarely mentioned as a PPV(n = 3).
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Survey results indicated that the existence of a public HTA agency correlates with patient involvement with an exception of two countries. According to the systematic review, in cases where the process of patient engagement in guideline development was explicitly described, micro level PPVs were represented more significantly. This underscores the importance of including the patient voice in the discussion of a vast number of issues related to cancer care. To ensure effective input from patients and respective POs, both patients and the POs need to be better educated and informed to effectively engage in the evaluation or assessment process. Various ongoing initiatives, such as the European Patients Academy on Therapeutic Innovation (EUPATI) organize seminars to educate patients to participate in scientific and policy discussions and advocacy. Participation of patients and POs must be supported by easy-to use tools that consider the individual perspective of the patient in the development phase of clinical guidelines and policy recommendations. The instances of patient inclusion either at the institutional level (e.g., through patient involvement in the activities of the European Medicines Agency (EMA) in the European Union, the more fragmented approach by the Food and Drug Administration (FDA) in the United States, or the bottom-up approach taken by the National Institute for Health and Care Excellence (NICE) in the United Kingdom) or via ad-hoc participatory models attempted at the national level in certain countries, often lack meaningful participation and expectations from all stakeholders. Among ASCO (Schnipper et al., 2015, 2016), ICER (2017), MSKCC (2017), and NCCN (2017), only ICER included patients directly in the developmental process (Milken Institute, 2017). These value frameworks are the catalysts for addressing evaluation of expensive cancer treatments; however, much work needs to be done for those efforts to provide value to the actual patients, such as: (I) increase the overall document clarity by providing a secondary release of the same documents written in patient-friendly language, presented in a clear manner, (II) include PPVs, which may require inclusion of items outside the clinical realm, (III) meaningfully include the burden of illness on households and (IV) patient heterogeneity in value consideration.
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Frequent referencing of patient heterogeneity in the guidelines correlates well with the survey results; patients have various levels of disease burden, cancer stages, individual values and cultural backgrounds that equally affect their personal choices. There is also a strong consensus that the treatment strategy for each patient has to be determined jointly by the physicians and the patient on micro level, as needs and preferences of individual patients can be different (Elwyn et al., 2012; Martinez et al., 2015). However—contrary to the guidelines—survey findings showed that personalized medicine was not yet perceived as a crucial area of cancer care among survey respondents, which seems to be contradictory to recent trends in cancer care (CMBRP, 2016).
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Based on our survey results, feedback from patients was rarely taken into consideration while aiming at improving quality of cancer care, even though such survey tools had already been developed in the oncology field (Booij et al., 2013; Tremblay et al., 2015; Windham et al., 2015; King et al., 2016). This supports the contention that while patient-centricity is enshrined in global (via World Health Organization), regional (e.g., European Union) and national healthcare policies, it has yet to take shape in practice. In comparison to health care, in the field of consumer products, although fueled by commercial interests, the practice of seeking direct feedback from consumers on what is relevant, appealing, and satisfying to them has been globally established and a recognized model of action for decades. However, such practices are not generally prevalent in the cancer field, despite the fact that the impact of decisions made by health policy makers, experts at HTA level or healthcare professionals directly impact the lives of patients and their families. Quality in cancer care may be improved by further utilization of PREMs. Patient satisfaction measured by PREMs may be an important criterion in performance based reimbursement of health care providers based on current discussion in several countries, including the United States (Weldring and Smith, 2013) and the United Kingdom (Taylor et al., 2015; Burns et al., 2016).
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Based on our survey results we cannot conclude that there is any aspect of cancer care referred to in the survey that is not relevant to the cancer patients. There were no items with >3.8 mean value, indicating the importance of each cancer care related item. Key value propositions (e.g., extended life, treatment-free remission and pain reduction) are in line with current value frameworks developed by ASCO, ESMO, ICER, MSKCC, and NCCN. Paradoxically, around only half of the reviewed guidelines addressed extended life, treatment-free remission and palliative care aspects of the treatment cycle. There are two potential explanations for this: either these objectives are too obvious for cancer care, or guidelines for cancer screening were not dealing with such requirements.
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Survey findings highlighted the necessity of guidance for managing side effects, but clinical guidelines seemingly addressed this need. However, although serious adverse events and acute complications were mentioned, long-term and daily life affecting mild-to-moderate side-effects were usually lacking fields in the reviewed publications. This finding is in line with Basch et al. (Basch, 2016) stating that “chronic low-grade toxicities” are mostly ignored in current value frameworks. Nonetheless, initiatives to assign more importance to such mild-to moderate and daily life-affecting adverse events are on the horizon. ASCO—due to the high volume of comments received after having published their framework (Schnipper et al., 2015)—updated the original version and included also mild-to moderate adverse events in the updated framework.
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Interestingly, timeliness of diagnosis and treatment was rather underrepresented in current guidelines and neither was mentioned in the survey as field for improvement by PO representatives. However, previous survey results indicated the high relevance of these aspects of care according to Booij et al. (2013) who found that the average importance score of “early treatment initiation after diagnosis” and the item of “being referred to hospital as quickly as you would like” were the two most important quality aspects of care, being assigned equally 3.72 points on a 4-point Likert scale by cancer patients. If the diagnosis or treatment is delayed due to waiting lists, the patient may not be able to benefit from the treatment, and so scarce health care resources could have been better spent elsewhere (Rutqvist, 2006).
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The relevance of interpersonal communication was mentioned in 13 guidelines. However, neither the guidelines nor the survey respondents highlighted the need for more efficient emotional support. This is in line with the findings of Booij et al. (2013) and Windham et al. (2015) who both identified psychological and emotional support as being underrated by survey respondents: Booij et al. found that the average importance score of the item entitled “It is regularly checked if you need help dealing with the emotions brought about by the disease and treatment” was only about 2.81 on a 4-point Likert scale. Windham et al. (2015) noted that the mean frequency rating of the item “Having your doctors be sensitive to your emotional reaction when telling you your diagnosis or test results” was only 4.54 on a 5-point Likert scale, being placed 20th on a list of 24 items.
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The generalizability of our exploratory research is limited due to several factors. Search terms in the literature review were primarily focusing on guidelines providing direct therapeutic recommendations; thus the relatively low representation of patient aspects was not unexpected. This exploratory study was based on a limited number of survey respondents from 19 POs from 18 countries, where leaders of POs expressed their own views on the questions. Due to the limited number of included publications we have not assessed the abovementioned issues in different cancer types, therefore we could draw only general conclusions on the importance of patient engagement in cancer care.
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The PPVs in cancer care and treatment indicated by the surveyed POs were in line with current (HTA) practices, in which priority is given to overall and progression-free survival, reduced side-effects and improved quality of life. Patient involvement was mostly represented at micro-level decision-making processes, in the treatment planning phase, compared to the macro-level guideline development period. PPVs in cancer care guidelines were mostly limited to those micro-level aspects that are strictly related to health care provision (e.g., side-effects, comorbidities), or manifested in general terms. Although several validated PREMs exist, patient experience was a relatively neglected field and was mostly limited to emphasing the importance of interpersonal communication. Soft fields of patient aspects, such as emotional support, convenience of care were not considered thoroughly in the reviewed guidelines.
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POs believe that patients should be encouraged to take an active role in their own care. Due to the heterogeneity of cancer patients and PPVs, developers of guidelines should engage patients and the respective POs systematically to ensure that PPVs are taken into account. Even if patient-centricity is a leading paradigm in cancer policy, it is not yet standard practice to include patients and / or POs at all appropriate levels of decision-making processes that are related to their health and well-being. Patient engagement and measurement of patient experience should be an integral part of cancer care decision-making. This complexity must be reflected throughout policy making, avoiding a population level “one-size-fits-all” solution. The situation poses a great need for in-depth collaborative solutions with a tangible inclusion of patients and / or the POs throughout the process.
other
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SN initiated the research and drafted the survey with KY; AI, and TA reviewed the survey. ZK finalized the survey. TA drafted the search query for the literature review. AI and ZK reviewed the search query, SN and KY finalized the search query. TA and AI conducted the literature review. BS, KM, and YM provided input for the survey. TA, AI, ZK, and SN interpreted the literautre review results. TA and AI drafted the manuscript. SN, KY, and ZK finalized the manuscript. BS, KM, and YM reviewed and commented the manuscript. All authors read and approved the revised version of the manuscript.
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Syreon Research Institute received research grant from Lithuanian Cancer Patient Coalition (POLA) to conduct the systematic review part of this study. The content of this paper, as well as the views and opinions expressed therein are those of the Authors and not the organizations that employ them. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
other
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Personalised medicine, in which genetic testing is the basis for informing future health status and determining intervention, is effectively applied for a number of monogenic disorders1. For common complex disorders, which are those that are underlain by multiple genetic and environmental factors2, predictive genetic testing that can discriminate individuals who are most at risk is currently limited, mainly because much of the genetic variation remains poorly understood3,4. The potential of genetic risk prediction to (i) inform early interventions and (ii) aid diagnosis by identifying individuals with an increased genetic risk of disease could be improved substantially by increasing the accuracy of genetic risk predictors5. While genome-wide association studies (GWASs) of increased sample size will continue to unravel the role of genetic factors for complex diseases6, improved prediction models are also required to maximise the accuracy of a risk predictor.
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GWASs use linear regression to independently estimate the effects of single-nucleotide polymorphisms (SNPs) across the genome, and commonly, these estimated SNP effects are then used to create a genetic risk predictor in independent samples7–9. However, this approach is not optimal because it either ignores linkage disequilibrium (LD) between markers or accounts for LD by discarding potentially informative SNPs10. Prediction accuracy of complex phenotypes can be improved by methods that jointly estimate the SNP associations to obtain SNP effect estimates with best linear unbiased predictor (BLUP) properties within a linear mixed model (LMM) approach, a model termed genomic BLUP (GBLUP)7,11,12. A multi-trait extension of the LMM approach, yielding multivariate BLUP (MT-BLUP) predictors of the SNP effects, can further improve prediction accuracy when phenotypes are genetically correlated, because measurements on each trait provide information on the genetic values of the other correlated traits13–16. MT-BLUP has been shown to improve prediction accuracy for genetically correlated common psychiatric disorders when combining individual-level data across independent data sets16,17. However, the application of MT-BLUP to complex common disorders is limited as combining individual-level genotype-phenotype data across case–control studies of all complex diseases is generally not feasible due to data protection concerns and restrictions on data sharing.
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Here we overcome this limitation by developing a framework that combines publically available GWAS summary statistics across multiple studies of different traits together in a weighted index to generate approximate multi-trait summary statistic BLUP (wMT-SBLUP) predictors (Supplementary Table 1). We show through theory and simulation study that MT-BLUP predictors, which traditionally require individual-level phenotype–genotype data for all traits, can be approximated accurately by wMT-SBLUP predictors in a computationally efficient manner using only summary statistic data and an independent genomic reference sample. We also show how multi-trait summary statistic predictors can be created directly from GWAS summary statistics (wMT-GWAS) or from predictors obtained using the software LDPred18 that extends a single-trait summary statistic BLUP model (SBLUP) by assuming that marker effects come from a mixture of distributions. We apply our approach to multiple phenotypes in the Psychiatric Genomics Consortium (PGC) to compare summary statistic approaches to direct estimation on individual-level data. We further apply our approach to summary statistics of several other phenotypes to create predictors that we evaluate using the UK Biobank data. We show that, for most traits, our multi-trait predictors improve prediction accuracy as compared to a single-trait predictors.
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Standard GWAS summary statistics are ordinary least squares (OLS) estimates of the SNP effects and do not have optimal properties for prediction11. Even when LMM association analysis is used, the estimated SNP effects still represent marginal effects and not effects conditional on other SNPs, which is what is desirable for prediction19. Previous studies have shown how OLS summary statistics can be reanalysed in a mixed model framework to produce approximate BLUP predictors (summary statistic BLUP: SBLUP, implemented in the most recent release of GCTA)18,20,21 or approximate mixture model predictors (LDPred). We first extend the SBLUP approach to a multi-trait framework (MT-SBLUP) and find a computational limitation associated with the inversion of a SNP-by-SNP-by-trait matrix. To overcome this, we then derive theory to show how single-trait predictors with BLUP properties can be combined together in a weighted index to generate predictors with equivalent properties to those gained from a MT-BLUP analysis (Fig. 1).Fig. 1Schematic of the methods. a Data and programs used to create predictors. b Terminology to refer to different types of predictors. OLS, ordinary least squares. The most common GWAS methodology to estimate SNP effects is to estimate the effect sizes of one SNP at a time using linear regression. BLUP, best linear unbiased prediction. SNP effects are estimated simultaneously for all SNPs. The estimates depend on the other SNPs included in the analysis, since the contribution from correlated SNPs will be shared between them
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Schematic of the methods. a Data and programs used to create predictors. b Terminology to refer to different types of predictors. OLS, ordinary least squares. The most common GWAS methodology to estimate SNP effects is to estimate the effect sizes of one SNP at a time using linear regression. BLUP, best linear unbiased prediction. SNP effects are estimated simultaneously for all SNPs. The estimates depend on the other SNPs included in the analysis, since the contribution from correlated SNPs will be shared between them
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Consider two genetically correlated traits for which we have individual-level genetic predictors with BLUP properties. For each individual, i, and focal trait of interest, f, we have a genetic prediction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{BLUP}}_{i,k}}} \right)$$\end{document}g^BLUPi,k for each trait, k, that we can combine together using the index weights, wi,k, for each \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{g}}_{{\mathrm{BLUP}}_{i,k}}$$\end{document}g^BLUPi,k effect to produce a weighted multi-trait BLUP genetic predictor:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{g}}_{{\mathrm{wMT}} - {\mathrm{BLUP}}_{i,f}} = \mathop {\sum }\limits_k w_{i,k}{\hat{\bf g}}_{{\mathrm{BLUP}}_{i,k}} = {\bf{w}}_i\prime \widehat {\bf{g}}_{{\mathrm{SBLUP}}_i}$$\end{document}g^wMT-BLUPi,f= ∑kwi,kg^BLUPi,k=wi′g^SBLUPiIn the Methods section, we show that the optimal index weights can be calculated as:2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${w} = \left[ {\begin{array}{*{20}{c}} {w_1} \\ {w_2} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {R_1^2} & {\frac{{r_{\mathrm{G}}R_1^2R_2^2}}{{\sqrt {h_1^2h_2^2} }}} \\ {\frac{{r_{\mathrm{G}}R_1^2R_2^2}}{{\sqrt {h_1^2h_2^2} }}} & {R_2^2} \end{array}} \right]^{ - 1}\left[ {\begin{array}{*{20}{c}} {R_1^2} \\ {r_{\mathrm{G}}\sqrt {\frac{{h_1^2}}{{h_2^2}}} R_2^2} \end{array}} \right]$$\end{document}w=w1w2=R12rGR12R22h12h22rGR12R22h12h22R22-1R12rGh12h22R22where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_k^2$$\end{document}hk2 is the SNP heritability of trait k (proportion of phenotypic variance explained by genome-wide SNPs), rG is the genetic correlation between trait k and the focal trait and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_k^2$$\end{document}Rk2 is the expected squared correlation between a phenotype and a BLUP predictor, calculated as:3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_k^2 = \frac{{h_k^2}}{{1 + M_{{\mathrm{eff}}}\frac{{1 - R_k^2}}{{N_kh_k^2}}}}$$\end{document}Rk2=hk21+Meff1-Rk2Nkhk2where Meff is the effective number of chromosome segments and Nk is the sample size of trait k. These weights will ensure that the contribution of each added trait is approximately proportional to the square root of its sample size, its SNP heritability and its genetic correlation with the focal trait (trait 1), while accounting for different variances of single-trait BLUP predictors.
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Both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_k^2$$\end{document}hk2 and rG can be estimated from GWAS summary statistics using LD score regression22,23. Following20, individual-level genetic predictors with BLUP properties can also be obtained from GWAS summary statistics (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{g}}_{{\mathrm{SBLUP}}_k}$$\end{document}g^SBLUPk, where SBLUP represents summary statistic approximate BLUP). Therefore, for any given trait, genetic predictors with BLUP properties \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {\widehat {\bf{g}}_{{\mathrm{SBLUP}}_k}} \right)$$\end{document}g^SBLUPk can be created from GWAS summary statistics and these can then be placed in a weighted index to produce approximate multi-trait summary statistic BLUP (wMT-SBLUP) predictors, using only LD score regression and an independent reference sample. This approach, provided in the freely available software SMTPred (see Code availability section), approximates MT-BLUP predictors without the need for individual-level phenotype–genotype data for all traits, enabling prediction accuracy to be improved by fully utilising all of the publically available GWAS summary statistic data. We also show how weighted indices can be calculated for GWAS summary statistics (wMT-GWAS) or from predictors obtained using the software LDPred18 (wMT-LDPred), therefore depending upon the genetic architecture of the trait approximate multi-trait summary statistics can be created to maximise genomic prediction accuracy.
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We first conducted a simulation study using observed SNP genotype data to confirm the expectations from our theory. We show through theory (see Methods section) that a wMT-SBLUP genetic predictor has the same expected prediction accuracy as one created from a multivariate mixed-effects model (multi-trait BLUP: MT-BLUP) if the linkage disequilibrium among SNP markers in the individual-level analysis is well approximated by a reference genotype panel (see Methods section). We demonstrate that a wMT-SBLUP predictor increases prediction accuracy over a single-trait predictor, with the magnitude of increase being proportional to the ratio of the SNP heritability of the added traits relative to that of the predicted trait, the sample size of the added traits relative to that of the predicted trait and the genetic correlation between the added traits and the predicted trait (Fig. 2, Supplementary Figs. 1 and 2). We also demonstrate how genetic predictors generated by LDPred18 can be combined in an approximate multi-trait weighting (Supplementary Fig. 3).Fig. 2Improving prediction accuracy using information from multiple traits. a Expected gain from multi-trait vs cross-trait predictors as a function of rG. Two traits are considered. The first trait has a sample size of 20,000 and a SNP heritability of 0.5. The sample size and SNP heritability of the second trait vary between panels. The blue line shows the expected prediction accuracy of a single-trait predictor. The black line shows the expected prediction accuracy of a multi-trait predictor. The purple line shows the expected prediction accuracy of a cross-trait predictor (using only trait 2 to predict trait 1). The advantage of a multi-trait predictor over a cross-trait predictor decreases with increasing rG, h2, and sample size of the second trait. b Simulation results. Prediction accuracy is shown as correlation between simulated genetic value and predicted phenotype of individuals. Genotypes from European individuals in the GERA cohort were used for simulation. Boxplots show results across six replicates. In the left panels, the LD structure was removed by permuting dosage values for each SNP across all individuals. In the right panels, the original genotypes were used for simulation. Expected prediction accuracies were derived for the case of unlinked genotypes and are shown as red horizontal bars. In each section, the prediction accuracy of three predictors is shown: (1) single trait BLUP, (2) multi-trait BLUP (MT-BLUP), and (3) weighted approximate BLUP (summary statistic-based multi-trait predictor: wMT-SBLUP). Simulation in genotypes without LD results in prediction accuracies, which conform to expectations. In the presence of LD, the expected prediction accuracy depends very much on the choice of Meff
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Improving prediction accuracy using information from multiple traits. a Expected gain from multi-trait vs cross-trait predictors as a function of rG. Two traits are considered. The first trait has a sample size of 20,000 and a SNP heritability of 0.5. The sample size and SNP heritability of the second trait vary between panels. The blue line shows the expected prediction accuracy of a single-trait predictor. The black line shows the expected prediction accuracy of a multi-trait predictor. The purple line shows the expected prediction accuracy of a cross-trait predictor (using only trait 2 to predict trait 1). The advantage of a multi-trait predictor over a cross-trait predictor decreases with increasing rG, h2, and sample size of the second trait. b Simulation results. Prediction accuracy is shown as correlation between simulated genetic value and predicted phenotype of individuals. Genotypes from European individuals in the GERA cohort were used for simulation. Boxplots show results across six replicates. In the left panels, the LD structure was removed by permuting dosage values for each SNP across all individuals. In the right panels, the original genotypes were used for simulation. Expected prediction accuracies were derived for the case of unlinked genotypes and are shown as red horizontal bars. In each section, the prediction accuracy of three predictors is shown: (1) single trait BLUP, (2) multi-trait BLUP (MT-BLUP), and (3) weighted approximate BLUP (summary statistic-based multi-trait predictor: wMT-SBLUP). Simulation in genotypes without LD results in prediction accuracies, which conform to expectations. In the presence of LD, the expected prediction accuracy depends very much on the choice of Meff
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We also provide a theoretical expectation for the loss in prediction accuracy that occurs when using an independent reference sample to compute SBLUP effects compared to a predictor based on BLUP effects (see Methods section), and we detail the loss of prediction accuracy in our simulation study (Fig. 2b, Supplementary Figs. 1 and 4).
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We then applied our approach to the PGC schizophrenia24,25 and bipolar data, two psychiatric disorders known to have a high genetic correlation26. The availability of combined individual-level data for both disorders enabled a direct comparison of the MT-BLUP16 and wMT-SBLUP approaches. We calculated all predictors for the previously used16 PGC wave 1 (PGC1) data sets24 and compared the prediction accuracy (correlation between predicted values and phenotypes adjusted for sex, cohort and the first 20 principal components) across diseases and approaches. We find comparable but slightly lower accuracies in the wMT-SBLUP predictors as compared to the MT-BLUP predictors (0.151 vs 0.156 in bipolar disorder and 0.217 vs 0.219 in schizophrenia) and an increase in prediction accuracy as compared to the single-trait (BLUP) predictors (0.128 in bipolar disorder, 0.198 in schizophrenia) (Fig. 3). Our results demonstrate that creating SBLUP genetic predictors using an independent LD reference sample and combining these in a weighted sum results in prediction accuracy comparable to a full MT-BLUP prediction for common complex disease traits, at a much lower computational burden.Fig. 3Prediction accuracy for schizophrenia and bipolar disorder from several single-trait and multi-trait predictors. Prediction accuracy of seven different types of predictors using PGC1 schizophrenia and bipolar disorder data. Single-trait predictor (lighter colours) are on the left, multi-trait predictors (darker colours) are on the right. Black error bars indicate correlation coefficient standard errors, calculated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{se}}_r = \sqrt {\frac{{1 - r^2}}{{n - 2}}}$$\end{document}ser=1-r2n-2
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Prediction accuracy for schizophrenia and bipolar disorder from several single-trait and multi-trait predictors. Prediction accuracy of seven different types of predictors using PGC1 schizophrenia and bipolar disorder data. Single-trait predictor (lighter colours) are on the left, multi-trait predictors (darker colours) are on the right. Black error bars indicate correlation coefficient standard errors, calculated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{se}}_r = \sqrt {\frac{{1 - r^2}}{{n - 2}}}$$\end{document}ser=1-r2n-2
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We then applied our approach to the larger PGC wave 2 (PGC2) data sets for schizophrenia25 and bipolar disorder (see Methods section), which included the PGC1 data. To test whether the addition of more cohorts improved prediction accuracy, we estimate wMT-SBLUP predictors in the PGC2 data. Having shown the resemblance of wMT-SBLUP and MT-BLUP by theory, simulation and in the PGC1 data, we refrained from running a MT-BLUP model in the PGC2 data to avoid the computational burden of analysing the combined schizophrenia bipolar data set. For schizophrenia, there were 36 cohorts (26,412 cases and 32,440 controls in total) and for bipolar disorder there were 23 cohorts (18,865 cases and 30,460 controls in total). We conducted a cohort-wise leave-one-out cross-validation approach to examine variation in prediction accuracy across cohorts.
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For schizophrenia, we find that prediction accuracy increases in 20 of the 36 cohorts of the PGC2 data when using a wMT-SBLUP predictor as compared to a SBLUP predictor (Supplementary Fig. 5). However, the median correlation (0.300 with an SBLUP predictor, and 0.304 with a wMT-SBLUP predictor) and mean correlation (0.295 with a SBLUP predictor and 0.294 with a wMT-SBLUP predictor) across the 36 PGC2 cohorts did not improve with a wMT-BLUP predictor. For bipolar disorder, we find an improvement of the wMT-SBLUP predictor over the SBLUP predictor in 17 out of the 23 cohorts (Supplementary Fig. 6), with a mean correlation increase from 0.212 to 0.229 and a median correlation increase from 0.210 to 0.225. To evaluate whether this is because the weights we used for schizophrenia and bipolar disorder do not represent the mixing proportions that lead to the highest accuracy in this data set or whether other factors explain the variable results across cohorts, we created multi-trait predictors using not only weights calculated from Eq. (17) but also weights corresponding to any other mixing proportion of the two disorders (Supplementary Figs. 5, 6 and 7). This demonstrates (i) that our calculated weights are very close to the empirically optimal weights when averaged across cohorts (Supplementary Fig. 7), (ii) that there is substantial heterogeneity across cohorts as shown by the variable prediction accuracies of single-trait and cross-trait predictors across cohorts, which is supported by previous studies25, and (iii) that, for some test set cohorts, there is no mixing proportion that will lead to a multi-trait predictor which outperforms a single-trait predictor. The larger gain in accuracy that results from supplementing a bipolar disorder predictor with schizophrenia data compared to supplementing a schizophrenia predictor with bipolar disorder data is consistent with greater power of the schizophrenia discovery sample. We find that for both single-trait and multi-trait predictors the SBLUP predictors outperform the OLS predictors in almost all cohorts (Supplementary Figs. 5 and 6).
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In principle, any number of traits can be combined into a multi-trait predictor at almost no computational cost. We therefore extended our approach to create wMT-SBLUP predictors from 34 phenotypes for which we could access summary statistics. In order to calculate wMT-SBLUP weights, we used LD score regression to estimate SNP heritability and genetic correlations of the 34 summary statistics traits. The results are mostly in line with previous reports23 (Supplementary Fig. 8, Supplementary Data 1). As test set, we used 112,338 individuals in the UK Biobank data. We matched 6 of the 34 discovery traits to traits in the UK Biobank (Supplementary Table 1) and created wMT-SBLUP predictors. For the wMT-SBLUP predictor of each focal trait, we included predictor traits with genetic correlation p-value < 0.05. For all traits, wMT-SBLUP genetic predictors were more accurate than any single-trait (SBLUP) predictor (Fig. 4). wMT-SBLUP predictors generally improved prediction accuracy over single-trait GWAS OLS predictors (Supplementary Fig. 9) and were similar to wMT-LDPred predictors (Supplementary Figs. 10 and 11.) We observe the largest increases in accuracy for Type 2 diabetes (47.8%) and depression (34.8%). Accuracy for height (0.7%) and body mass index (BMI) (1.4%) increase only marginally. As shown in our theory and simulation study, the magnitude of increase in prediction accuracy of a wMT-SBLUP predictor over a single-trait SBLUP predictor depends upon the prediction accuracies of all the traits included in the index and the genetic correlation among phenotypes. As GWAS sample sizes increase and genomic predictors increase in accuracy, a wMT-SBLUP approach will likely become increasingly beneficial.Fig. 4Prediction accuracy for single-trait and multi-trait predictors in UK Biobank traits. Prediction accuracy for six traits in the UK Biobank for multi-trait predictors (light blue bars, wMT-SBLUP) and single-trait predictors (colourful bars on the right, SBLUP). Black bars show the correlation coefficient standard error. The multi-trait predictors for each trait are composed of all traits for which colourful bars are shown (rGp-value < 0.05). Smaller bars on the right show, from top to bottom, sample size, SNP heritability, rG, and weights (given by Eq. (15)) for each trait
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Prediction accuracy for single-trait and multi-trait predictors in UK Biobank traits. Prediction accuracy for six traits in the UK Biobank for multi-trait predictors (light blue bars, wMT-SBLUP) and single-trait predictors (colourful bars on the right, SBLUP). Black bars show the correlation coefficient standard error. The multi-trait predictors for each trait are composed of all traits for which colourful bars are shown (rGp-value < 0.05). Smaller bars on the right show, from top to bottom, sample size, SNP heritability, rG, and weights (given by Eq. (15)) for each trait
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In summary, we demonstrate that multivariate predictors derived from GWAS summary statistics can increase prediction accuracy in a wide range of traits. This approach has particular utility in risk prediction of traits for which it is hard to generate large sample sizes for GWAS, as SNP heritability and sample size are the two factors that determine prediction accuracy of a polygenic trait, when using a single-trait predictor. The increase in prediction accuracy of a multi-trait over a standard single-trait genetic predictor is therefore greatest when the additional traits included in the predictor have higher SNP heritability and sample size than the trait to be predicted, as well as a high genetic correlation with the trait to be predicted. We show how genetic predictors from GWAS OLS effects, LDPred effects or SBLUP effects can be combined, yielding an approach that is general across different phenotypes.
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Special consideration should be given to the risk of sample overlap between the summary statistics data used to create the predictor and the prediction target. Sample overlap will lead to inflated estimates of accuracy, and while here we were able to take steps to avoid individuals being recorded across multiple data sets, further work is required to negate these effects within this framework. In principle, assuming perfect homogeneity between training and test set and perfect estimates of SNP heritability and genetic correlation, there is no limit to the number of traits that can be combined using our approach. In practice, however, there will be little benefit of combining traits with low genetic correlation, as they will not influence the predictor much. Some added traits might even reduce accuracy, if the genetic correlation is not estimated accurately. The focus of our analysis was the prediction of genetic risk and we aimed to provide a fast, computationally efficient, general framework for genomic prediction. This sets it apart from other multi-trait approaches like phenome-wide association studies, which focus on the effects of individual SNPs on multiple phenotypes. We note, however, that a multi-trait testing approach can in principle also be used to increase the power to identify loci associated with specific traits as demonstrated in the recently developed MTAG method27. Another potential caveat of our analysis is that prediction accuracy increases for a focal trait may come from the addition of traits that are standardly measured on patients, and improved frameworks are required to identify marker effects conditionally on known health risk factors. Despite these limitations, current evidence suggests that genetic correlations among phenotypes are pervasive23, sample sizes of GWAS are increasing6 and public availability of genome-wide summary statistics is becoming the norm28, meaning that genomic prediction of complex common disease will continually improve especially when predictors of multiple phenotypes are integrated across studies within this framework.
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We consider a general linear mixed model:4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{y}} = {\bf{Wb}} + {\bf{\epsilon }}$$\end{document}y=Wb+ϵwhere y is the phenotype, W a matrix of SNP genotypes, where values are standardised to give the ijth element as: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_{ij} = \left( {x_{ij} - 2p_j} \right){\mathrm{/}}\sqrt {2p_j\left( {1 - p_j} \right)}$$\end{document}wij=xij-2pj∕2pj1-pj, with xij the number of minor alleles (0, 1 or 2) for the ith individual at the jth SNP and pj the minor allele frequency. b are the genetic effects for each SNP, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{\epsilon }}$$\end{document}ϵ the residual error. The dimensions of y, W, b and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{\epsilon }}$$\end{document}ϵ are dependent upon the number of phenotypes, k, the number of SNP markers, M, and the number of individuals, N, and are described in the sections below. We denote the distributional properties var(b) = B, var(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{\epsilon }}$$\end{document}ϵ) = R and var(y) = WBW′ + R.
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For human complex diseases and quantitative phenotypes, GWASs have typically estimated the solutions for b of Eq. (1) one SNP at a time using OLS regression29 as:5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{b}}_{{\mathrm{OLS}}} = {\mathrm{diag}}\left[ {{{{\bf W}{\prime}{\bf W}}}} \right]^{ - 1}{{{\bf W}{\prime}{\bf y}}}$$\end{document}b^OLS=diagW′W-1W′ywhere diag[W′W] has diagonal elements \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$w_j\prime w_j$$\end{document}wj′wj and off-diagonal elements of zero. However, by analysing one SNP at a time, GWAS effect size estimates do not account for the covariance structure among SNPs and they are not unbiased in the sense that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathit{E}}\left[ {{\bf{b}}|{\hat{\bf b}}} \right] = {\hat{\bf b}}$$\end{document}Eb∣b^=b^12. BLUP of the SNP effects have the property \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\it{E}}\left[ {{\bf{b}}|{\hat{\bf b}}} \right] = {\hat{\bf b}}$$\end{document}Eb∣b^=b^, are used in genomic prediction in animal and plant breeding30 and more recently in human medical genetics, yielding improved prediction accuracy for a number of traits over genetic predictors created from OLS SNP estimates16,17. In a general form, BLUP solutions for b of Eq. (1) can be written using Henderson’s mixed model equations31 as:6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{b}}_{{\mathrm{BLUP}}} = \left[ {{{{\bf W}{\prime}{\bf R}}}^{ - {\mathrm{1}}}{\bf{W}}{{ + }}{\bf{B}}^{ - 1}} \right]^{ - 1}{{{\bf W}{\prime}{\bf R}}}^{ - 1}{\bf{y}}$$\end{document}b^BLUP=W′R-1W+B-1-1W′R-1yand if R is diagonal, then Eq. (6) can be reduced to:7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{b}}_{{\mathrm{BLUP}}} = \left[ {{{{\bf W}{\prime}{\bf W}}} + {\bf{B}}^{ - 1}{\bf{R}}} \right]^{ - 1}{{{\bf W}{\prime}{\bf y}}}$$\end{document}b^BLUP=W′W+B-1R-1W′y
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Below, we describe how Eqs. (6) and (7) can be used to estimate BLUP SNP effects for a single trait and for multiple traits jointly from individual-level phenotype–genotype data. We then show how Eqs. (6) and (7) can be approximated to obtain BLUP SNP effects for single and multiple traits in the absence of individual-level data from publically available GWAS summary statistics and an independent reference sample.
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For a univariate analysis of trait k, y of Eq. (4) is a column vector of length N × 1 and W has dimension N × M. Assuming b is an M × 1 vector of random SNP effects for trait k, with distribution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{b}}\sim N\left( {0,{\bf{I}}_M\sigma _{b_k}^2} \right)$$\end{document}b~N0,IMσbk2, then \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{B}} = {\bf{I}}_M\sigma _{b_k}^2$$\end{document}B=IMσbk2 with IM is an identity matrix of dimension M. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{\epsilon }}$$\end{document}ϵ of Eq. (1) is a column vector of independent residual effects, with distribution \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{\epsilon }}\sim N\left( {0,{\bf{I}}_N\sigma _{{\it{\epsilon }}_k}^2} \right)$$\end{document}ϵ~N0,INσϵk2, giving \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\bf{R}} = {\bf{I}}_N\sigma _{\epsilon _k}^2$$\end{document}R=INσϵk2, with IN an identity matrix of dimension N. Substituting these expressions into Eq. (6) means that Eq. (7) can then be written as:8\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\widehat {\bf{b}}_{{\mathrm{BLUP}}_k} = \left[ {{\bf{W}}_k\prime {\bf{W}}_k + {\bf{I}}_M\lambda _k} \right]^{ - 1}{\bf{W}}_k\prime {\bf{y}}_k$$\end{document}b^BLUPk=Wk′Wk+IMλk-1Wk′ykwith \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _k = \sigma _{\epsilon _k}^2{\mathrm{/}}\sigma _{{\it{b}}_k}^2$$\end{document}λk=σϵk2∕σbk2.
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