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1.  Assessing Risk Prediction Models Using Individual Participant Data From Multiple Studies 
Pennells, Lisa | Kaptoge, Stephen | White, Ian R. | Thompson, Simon G. | Wood, Angela M. | Tipping, Robert W. | Folsom, Aaron R. | Couper, David J. | Ballantyne, Christie M. | Coresh, Josef | Goya Wannamethee, S. | Morris, Richard W. | Kiechl, Stefan | Willeit, Johann | Willeit, Peter | Schett, Georg | Ebrahim, Shah | Lawlor, Debbie A. | Yarnell, John W. | Gallacher, John | Cushman, Mary | Psaty, Bruce M. | Tracy, Russ | Tybjærg-Hansen, Anne | Price, Jackie F. | Lee, Amanda J. | McLachlan, Stela | Khaw, Kay-Tee | Wareham, Nicholas J. | Brenner, Hermann | Schöttker, Ben | Müller, Heiko | Jansson, Jan-Håkan | Wennberg, Patrik | Salomaa, Veikko | Harald, Kennet | Jousilahti, Pekka | Vartiainen, Erkki | Woodward, Mark | D'Agostino, Ralph B. | Bladbjerg, Else-Marie | Jørgensen, Torben | Kiyohara, Yutaka | Arima, Hisatomi | Doi, Yasufumi | Ninomiya, Toshiharu | Dekker, Jacqueline M. | Nijpels, Giel | Stehouwer, Coen D. A. | Kauhanen, Jussi | Salonen, Jukka T. | Meade, Tom W. | Cooper, Jackie A. | Cushman, Mary | Folsom, Aaron R. | Psaty, Bruce M. | Shea, Steven | Döring, Angela | Kuller, Lewis H. | Grandits, Greg | Gillum, Richard F. | Mussolino, Michael | Rimm, Eric B. | Hankinson, Sue E. | Manson, JoAnn E. | Pai, Jennifer K. | Kirkland, Susan | Shaffer, Jonathan A. | Shimbo, Daichi | Bakker, Stephan J. L. | Gansevoort, Ron T. | Hillege, Hans L. | Amouyel, Philippe | Arveiler, Dominique | Evans, Alun | Ferrières, Jean | Sattar, Naveed | Westendorp, Rudi G. | Buckley, Brendan M. | Cantin, Bernard | Lamarche, Benoît | Barrett-Connor, Elizabeth | Wingard, Deborah L. | Bettencourt, Richele | Gudnason, Vilmundur | Aspelund, Thor | Sigurdsson, Gunnar | Thorsson, Bolli | Kavousi, Maryam | Witteman, Jacqueline C. | Hofman, Albert | Franco, Oscar H. | Howard, Barbara V. | Zhang, Ying | Best, Lyle | Umans, Jason G. | Onat, Altan | Sundström, Johan | Michael Gaziano, J. | Stampfer, Meir | Ridker, Paul M. | Michael Gaziano, J. | Ridker, Paul M. | Marmot, Michael | Clarke, Robert | Collins, Rory | Fletcher, Astrid | Brunner, Eric | Shipley, Martin | Kivimäki, Mika | Ridker, Paul M. | Buring, Julie | Cook, Nancy | Ford, Ian | Shepherd, James | Cobbe, Stuart M. | Robertson, Michele | Walker, Matthew | Watson, Sarah | Alexander, Myriam | Butterworth, Adam S. | Angelantonio, Emanuele Di | Gao, Pei | Haycock, Philip | Kaptoge, Stephen | Pennells, Lisa | Thompson, Simon G. | Walker, Matthew | Watson, Sarah | White, Ian R. | Wood, Angela M. | Wormser, David | Danesh, John
American Journal of Epidemiology  2013;179(5):621-632.
Individual participant time-to-event data from multiple prospective epidemiologic studies enable detailed investigation into the predictive ability of risk models. Here we address the challenges in appropriately combining such information across studies. Methods are exemplified by analyses of log C-reactive protein and conventional risk factors for coronary heart disease in the Emerging Risk Factors Collaboration, a collation of individual data from multiple prospective studies with an average follow-up duration of 9.8 years (dates varied). We derive risk prediction models using Cox proportional hazards regression analysis stratified by study and obtain estimates of risk discrimination, Harrell's concordance index, and Royston's discrimination measure within each study; we then combine the estimates across studies using a weighted meta-analysis. Various weighting approaches are compared and lead us to recommend using the number of events in each study. We also discuss the calculation of measures of reclassification for multiple studies. We further show that comparison of differences in predictive ability across subgroups should be based only on within-study information and that combining measures of risk discrimination from case-control studies and prospective studies is problematic. The concordance index and discrimination measure gave qualitatively similar results throughout. While the concordance index was very heterogeneous between studies, principally because of differing age ranges, the increments in the concordance index from adding log C-reactive protein to conventional risk factors were more homogeneous.
doi:10.1093/aje/kwt298
PMCID: PMC3927974  PMID: 24366051
C index; coronary heart disease; D measure; individual participant data; inverse variance; meta-analysis; risk prediction; weighting
2.  Using Multivariable Mendelian Randomization to Disentangle the Causal Effects of Lipid Fractions 
PLoS ONE  2014;9(10):e108891.
Background
Previous Mendelian randomization studies have suggested that, while low-density lipoprotein cholesterol (LDL-c) and triglycerides are causally implicated in coronary artery disease (CAD) risk, high-density lipoprotein cholesterol (HDL-c) may not be, with causal effect estimates compatible with the null.
Principal Findings
The causal effects of these three lipid fractions can be better identified using the extended methods of ‘multivariable Mendelian randomization’. We employ this approach using published data on 185 lipid-related genetic variants and their associations with lipid fractions in 188,578 participants, and with CAD risk in 22,233 cases and 64,762 controls. Our results suggest that HDL-c may be causally protective of CAD risk, independently of the effects of LDL-c and triglycerides. Estimated causal odds ratios per standard deviation increase, based on 162 variants not having pleiotropic associations with either blood pressure or body mass index, are 1.57 (95% credible interval 1.45 to 1.70) for LDL-c, 0.91 (0.83 to 0.99, p-value  = 0.028) for HDL-c, and 1.29 (1.16 to 1.43) for triglycerides.
Significance
Some interventions on HDL-c concentrations may influence risk of CAD, but to a lesser extent than interventions on LDL-c. A causal interpretation of these estimates relies on the assumption that the genetic variants do not have pleiotropic associations with risk factors on other pathways to CAD. If they do, a weaker conclusion is that genetic predictors of LDL-c, HDL-c and triglycerides each have independent associations with CAD risk.
doi:10.1371/journal.pone.0108891
PMCID: PMC4193746  PMID: 25302496
3.  The INTERVAL trial to determine whether intervals between blood donations can be safely and acceptably decreased to optimise blood supply: study protocol for a randomised controlled trial 
Trials  2014;15(1):363.
Background
Ageing populations may demand more blood transfusions, but the blood supply could be limited by difficulties in attracting and retaining a decreasing pool of younger donors. One approach to increase blood supply is to collect blood more frequently from existing donors. If more donations could be safely collected in this manner at marginal cost, then it would be of considerable benefit to blood services. National Health Service (NHS) Blood and Transplant in England currently allows men to donate up to every 12 weeks and women to donate up to every 16 weeks. In contrast, some other European countries allow donations as frequently as every 8 weeks for men and every 10 weeks for women. The primary aim of the INTERVAL trial is to determine whether donation intervals can be safely and acceptably decreased to optimise blood supply whilst maintaining the health of donors.
Methods/Design
INTERVAL is a randomised trial of whole blood donors enrolled from all 25 static centres of NHS Blood and Transplant. Recruitment of about 50,000 male and female donors started in June 2012 and was completed in June 2014. Men have been randomly assigned to standard 12-week versus 10-week versus 8-week inter-donation intervals, while women have been assigned to standard 16-week versus 14-week versus 12-week inter-donation intervals. Sex-specific comparisons will be made by intention-to-treat analysis of outcomes assessed after two years of intervention. The primary outcome is the number of blood donations made. A key secondary outcome is donor quality of life, assessed using the Short Form Health Survey. Additional secondary endpoints include the number of ‘deferrals’ due to low haemoglobin (and other factors), iron status, cognitive function, physical activity, and donor attitudes. A comprehensive health economic analysis will be undertaken.
Discussion
The INTERVAL trial should yield novel information about the effect of inter-donation intervals on blood supply, acceptability, and donors’ physical and mental well-being. The study will generate scientific evidence to help formulate blood collection policies in England and elsewhere.
Trial registration
Current Controlled Trials ISRCTN24760606, 25 January 2012.
doi:10.1186/1745-6215-15-363
PMCID: PMC4177700  PMID: 25230735
whole blood donation; randomised controlled trial; donation frequency; blood supply; donor well-being
4.  Diabetes Mellitus, Fasting Glucose, and Risk of Cause-Specific Death 
The New England journal of medicine  2011;364(9):829-841.
BACKGROUND
The extent to which diabetes mellitus or hyperglycemia is related to risk of death from cancer or other nonvascular conditions is uncertain.
METHODS
We calculated hazard ratios for cause-specific death, according to baseline diabetes status or fasting glucose level, from individual-participant data on 123,205 deaths among 820,900 people in 97 prospective studies.
RESULTS
After adjustment for age, sex, smoking status, and body-mass index, hazard ratios among persons with diabetes as compared with persons without diabetes were as follows: 1.80 (95% confidence interval [CI], 1.71 to 1.90) for death from any cause, 1.25 (95% CI, 1.19 to 1.31) for death from cancer, 2.32 (95% CI, 2.11 to 2.56) for death from vascular causes, and 1.73 (95% CI, 1.62 to 1.85) for death from other causes. Diabetes (vs. no diabetes) was moderately associated with death from cancers of the liver, pancreas, ovary, colorectum, lung, bladder, and breast. Aside from cancer and vascular disease, diabetes (vs. no diabetes) was also associated with death from renal disease, liver disease, pneumonia and other infectious diseases, mental disorders, nonhepatic digestive diseases, external causes, intentional self-harm, nervous-system disorders, and chronic obstructive pulmonary disease. Hazard ratios were appreciably reduced after further adjustment for glycemia measures, but not after adjustment for systolic blood pressure, lipid levels, inflammation or renal markers. Fasting glucose levels exceeding 100 mg per deciliter (5.6 mmol per liter), but not levels of 70 to 100 mg per deciliter (3.9 to 5.6 mmol per liter), were associated with death. A 50-year-old with diabetes died, on average, 6 years earlier than a counterpart without diabetes, with about 40% of the difference in survival attributable to excess nonvascular deaths.
CONCLUSIONS
In addition to vascular disease, diabetes is associated with substantial premature death from several cancers, infectious diseases, external causes, intentional self-harm, and degenerative disorders, independent of several major risk factors. (Funded by the British Heart Foundation and others.)
doi:10.1056/NEJMoa1008862
PMCID: PMC4109980  PMID: 21366474
5.  A Review of Published Analyses of Case-Cohort Studies and Recommendations for Future Reporting 
PLoS ONE  2014;9(6):e101176.
The case-cohort study design combines the advantages of a cohort study with the efficiency of a nested case-control study. However, unlike more standard observational study designs, there are currently no guidelines for reporting results from case-cohort studies. Our aim was to review recent practice in reporting these studies, and develop recommendations for the future. By searching papers published in 24 major medical and epidemiological journals between January 2010 and March 2013 using PubMed, Scopus and Web of Knowledge, we identified 32 papers reporting case-cohort studies. The median subcohort sampling fraction was 4.1% (interquartile range 3.7% to 9.1%). The papers varied in their approaches to describing the numbers of individuals in the original cohort and the subcohort, presenting descriptive data, and in the level of detail provided about the statistical methods used, so it was not always possible to be sure that appropriate analyses had been conducted. Based on the findings of our review, we make recommendations about reporting of the study design, subcohort definition, numbers of participants, descriptive information and statistical methods, which could be used alongside existing STROBE guidelines for reporting observational studies.
doi:10.1371/journal.pone.0101176
PMCID: PMC4074158  PMID: 24972092
6.  Carotid intima-media thickness progression to predict cardiovascular events in the general population (the PROG-IMT collaborative project): a meta-analysis of individual participant data 
Lancet  2012;379(9831):2053-2062.
Summary
Background
Carotid intima-media thickness (cIMT) is related to the risk of cardiovascular events in the general population. An association between changes in cIMT and cardiovascular risk is frequently assumed but has rarely been reported. Our aim was to test this association.
Methods
We identified general population studies that assessed cIMT at least twice and followed up participants for myocardial infarction, stroke, or death. The study teams collaborated in an individual participant data meta-analysis. Excluding individuals with previous myocardial infarction or stroke, we assessed the association between cIMT progression and the risk of cardiovascular events (myocardial infarction, stroke, vascular death, or a combination of these) for each study with Cox regression. The log hazard ratios (HRs) per SD difference were pooled by random effects meta-analysis.
Findings
Of 21 eligible studies, 16 with 36 984 participants were included. During a mean follow-up of 7·0 years, 1519 myocardial infarctions, 1339 strokes, and 2028 combined endpoints (myocardial infarction, stroke, vascular death) occurred. Yearly cIMT progression was derived from two ultrasound visits 2–7 years (median 4 years) apart. For mean common carotid artery intima-media thickness progression, the overall HR of the combined endpoint was 0·97 (95% CI 0·94–1·00) when adjusted for age, sex, and mean common carotid artery intima-media thickness, and 0·98 (0·95–1·01) when also adjusted for vascular risk factors. Although we detected no associations with cIMT progression in sensitivity analyses, the mean cIMT of the two ultrasound scans was positively and robustly associated with cardiovascular risk (HR for the combined endpoint 1·16, 95% CI 1·10–1·22, adjusted for age, sex, mean common carotid artery intima-media thickness progression, and vascular risk factors). In three studies including 3439 participants who had four ultrasound scans, cIMT progression did not correlate between occassions (reproducibility correlations between r=−0·06 and r=−0·02).
Interpretation
The association between cIMT progression assessed from two ultrasound scans and cardiovascular risk in the general population remains unproven. No conclusion can be derived for the use of cIMT progression as a surrogate in clinical trials.
Funding
Deutsche Forschungsgemeinschaft.
doi:10.1016/S0140-6736(12)60441-3
PMCID: PMC3918517  PMID: 22541275
7.  Impact of Length or Relevance of Questionnaires on Attrition in Online Trials: Randomized Controlled Trial 
Background
There has been limited study of factors influencing response rates and attrition in online research. Online experiments were nested within the pilot (study 1, n = 3780) and main trial (study 2, n = 2667) phases of an evaluation of a Web-based intervention for hazardous drinkers: the Down Your Drink randomized controlled trial (DYD-RCT).
Objectives
The objective was to determine whether differences in the length and relevance of questionnaires can impact upon loss to follow-up in online trials.
Methods
A randomized controlled trial design was used. All participants who consented to enter DYD-RCT and completed the primary outcome questionnaires were randomized to complete one of four secondary outcome questionnaires at baseline and at follow-up. These questionnaires varied in length (additional 23 or 34 versus 10 items) and relevance (alcohol problems versus mental health). The outcome measure was the proportion of participants who completed follow-up at each of two follow-up intervals: study 1 after 1 and 3 months and study 2 after 3 and 12 months.
Results
At all four follow-up intervals there were no significant effects of additional questionnaire length on follow-up. Randomization to the less relevant questionnaire resulted in significantly lower rates of follow-up in two of the four assessments made (absolute difference of 4%, 95% confidence interval [CI] 0%-8%, in both study 1 after 1 month and in study 2 after 12 months). A post hoc pooled analysis across all four follow-up intervals found this effect of marginal statistical significance (unadjusted difference, 3%, range 1%-5%, P = .01; difference adjusted for prespecified covariates, 3%, range 0%-5%, P = .05).
Conclusions
Apparently minor differences in study design decisions may have a measurable impact on attrition in trials. Further investigation is warranted of the impact of the relevance of outcome measures on follow-up rates and, more broadly, of the consequences of what we ask participants to do when we invite them to take part in research studies.
Trial registration
ISRCTN Register 31070347; http://www.controlled-trials.com/ISRCTN31070347/31070347 Archived by WebCite at (http://www.webcitation.org/62cpeyYaY)
doi:10.2196/jmir.1733
PMCID: PMC3236666  PMID: 22100793
Attrition; retention; missing data; response rates; alcohol; online
8.  Impact and Costs of Incentives to Reduce Attrition in Online Trials: Two Randomized Controlled Trials 
Background
Attrition from follow-up is a major methodological challenge in randomized trials. Incentives are known to improve response rates in cross-sectional postal and online surveys, yet few studies have investigated whether they can reduce attrition from follow-up in online trials, which are particularly vulnerable to low follow-up rates.
Objectives
Our objective was to determine the impact of incentives on follow-up rates in an online trial.
Methods
Two randomized controlled trials were embedded in a large online trial of a Web-based intervention to reduce alcohol consumption (the Down Your Drink randomized controlled trial, DYD-RCT). Participants were those in the DYD pilot trial eligible for 3-month follow-up (study 1) and those eligible for 12-month follow-up in the DYD main trial (study 2). Participants in both studies were randomly allocated to receive an offer of an incentive or to receive no offer of an incentive. In study 1, participants in the incentive arm were randomly offered a £5 Amazon.co.uk gift voucher, a £5 charity donation to Cancer Research UK, or entry in a prize draw for £250. In study 2, participants in the incentive arm were offered a £10 Amazon.co.uk gift voucher. The primary outcome was the proportion of participants who completed follow-up questionnaires in the incentive arm(s) compared with the no incentive arm.
Results
In study 1 (n = 1226), there was no significant difference in response rates between those participants offered an incentive (175/615, 29%) and those with no offer (162/611, 27%) (difference = 2%, 95% confidence interval [CI] –3% to 7%). There was no significant difference in response rates among the three different incentives offered. In study 2 (n = 2591), response rates were 9% higher in the group offered an incentive (476/1296, 37%) than in the group not offered an incentive (364/1295, 28%) (difference = 9%, 95% CI 5% to 12%, P < .001). The incremental cost per extra successful follow-up in the incentive arm was £110 in study 1 and £52 in study 2.
Conclusion
Whereas an offer of a £10 Amazon.co.uk gift voucher can increase follow-up rates in online trials, an offer of a lower incentive may not. The marginal costs involved require careful consideration.
Trial registration
ISRCTN31070347; http://www.controlled-trials.com/ISRCTN31070347 (Archived by WebCite at http://www.webcitation.org/5wgr5pl3s)
doi:10.2196/jmir.1523
PMCID: PMC3221348  PMID: 21371988
Nonresponse; attrition; Internet; alcohol drinking; randomized controlled trial
9.  Derivation and assessment of risk prediction models using case-cohort data 
Background
Case-cohort studies are increasingly used to quantify the association of novel factors with disease risk. Conventional measures of predictive ability need modification for this design. We show how Harrell’s C-index, Royston’s D, and the category-based and continuous versions of the net reclassification index (NRI) can be adapted.
Methods
We simulated full cohort and case-cohort data, with sampling fractions ranging from 1% to 90%, using covariates from a cohort study of coronary heart disease, and two incidence rates. We then compared the accuracy and precision of the proposed risk prediction metrics.
Results
The C-index and D must be weighted in order to obtain unbiased results. The NRI does not need modification, provided that the relevant non-subcohort cases are excluded from the calculation. The empirical standard errors across simulations were consistent with analytical standard errors for the C-index and D but not for the NRI. Good relative efficiency of the prediction metrics was observed in our examples, provided the sampling fraction was above 40% for the C-index, 60% for D, or 30% for the NRI. Stata code is made available.
Conclusions
Case-cohort designs can be used to provide unbiased estimates of the C-index, D measure and NRI.
doi:10.1186/1471-2288-13-113
PMCID: PMC3848813  PMID: 24034146
Case-cohort; Risk prediction; Discrimination; Reclassification; Cardiovascular disease
10.  Use of allele scores as instrumental variables for Mendelian randomization 
Background An allele score is a single variable summarizing multiple genetic variants associated with a risk factor. It is calculated as the total number of risk factor-increasing alleles for an individual (unweighted score), or the sum of weights for each allele corresponding to estimated genetic effect sizes (weighted score). An allele score can be used in a Mendelian randomization analysis to estimate the causal effect of the risk factor on an outcome.
Methods Data were simulated to investigate the use of allele scores in Mendelian randomization where conventional instrumental variable techniques using multiple genetic variants demonstrate ‘weak instrument’ bias. The robustness of estimates using the allele score to misspecification (for example non-linearity, effect modification) and to violations of the instrumental variable assumptions was assessed.
Results Causal estimates using a correctly specified allele score were unbiased with appropriate coverage levels. The estimates were generally robust to misspecification of the allele score, but not to instrumental variable violations, even if the majority of variants in the allele score were valid instruments. Using a weighted rather than an unweighted allele score increased power, but the increase was small when genetic variants had similar effect sizes. Naive use of the data under analysis to choose which variants to include in an allele score, or for deriving weights, resulted in substantial biases.
Conclusions Allele scores enable valid causal estimates with large numbers of genetic variants. The stringency of criteria for genetic variants in Mendelian randomization should be maintained for all variants in an allele score.
doi:10.1093/ije/dyt093
PMCID: PMC3780999  PMID: 24062299
Mendelian randomization; allele scores; genetic risk scores; instrumental variables; weak instruments
11.  Within-person variability in calculated risk factors: Comparing the aetiological association of adiposity ratios with risk of coronary heart disease 
Background Within-person variability in measured values of a risk factor can bias its association with disease. We investigated the extent of regression dilution bias in calculated variables and its implications for comparing the aetiological associations of risk factors.
Methods Using a numerical illustration and repeats from 42 300 individuals (12 cohorts), we estimated regression dilution ratios (RDRs) in calculated risk factors [body-mass index (BMI), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR)] and in their components (height, weight, waist circumference, and hip circumference), assuming the long-term average exposure to be of interest. Error-corrected hazard ratios (HRs) for risk of coronary heart disease (CHD) were compared across adiposity measures per standard-deviation (SD) change in: (i) baseline and (ii) error-corrected levels.
Results RDRs in calculated risk factors depend strongly on the RDRs, correlation, and comparative distributions of the components of these risk factors. For measures of adiposity, the RDR was lower for WHR [RDR: 0.72 (95% confidence interval 0.65–0.80)] than for either of its components [waist circumference: 0.87 (0.85–0.90); hip circumference: 0.90 (0.86–0.93) or for BMI: 0.96 (0.93–0.98) and WHtR: 0.87 (0.85–0.90)], predominantly because of the stronger correlation and more similar distributions observed between waist circumference and hip circumference than between height and weight or between waist circumference and height. Error-corrected HRs for BMI, waist circumference, WHR, and WHtR, were respectively 1.24, 1.30, 1.44, and 1.32 per SD change in baseline levels of these variables, and 1.24, 1.27, 1.35, and 1.30 per SD change in error-corrected levels.
Conclusions The extent of within-person variability relative to between-person variability in calculated risk factors can be considerably larger (or smaller) than in its components. Aetiological associations of risk factors should be compared through the use of error-corrected HRs per SD change in error-corrected levels of these risk factors.
doi:10.1093/ije/dyt077
PMCID: PMC3733701  PMID: 23918853
Regression dilution bias; measurement error; within-person variation; adiposity measures
12.  Methodological Challenges in Online Trials 
Health care and health care services are increasingly being delivered over the Internet. There is a strong argument that interventions delivered online should also be evaluated online to maximize the trial’s external validity. Conducting a trial online can help reduce research costs and improve some aspects of internal validity. To date, there are relatively few trials of health interventions that have been conducted entirely online. In this paper we describe the major methodological issues that arise in trials (recruitment, randomization, fidelity of the intervention, retention, and data quality), consider how the online context affects these issues, and use our experience of one online trial evaluating an intervention to help hazardous drinkers drink less (DownYourDrink) to illustrate potential solutions. Further work is needed to develop online trial methodology.
doi:10.2196/jmir.1052
PMCID: PMC2762798  PMID: 19403465
Internet; randomized controlled trial; research design; alcohol drinking
13.  Bayesian methods for meta-analysis of causal relationships estimated using genetic instrumental variables 
Statistics in medicine  2010;29(12):1298-1311.
Genetic markers can be used as instrumental variables, in an analogous way to randomization in a clinical trial, to estimate the causal relationship between a phenotype and an outcome variable. Our purpose is to extend the existing methods for such Mendelian randomization studies to the context of multiple genetic markers measured in multiple studies, based on the analysis of individual participant data. First, for a single genetic marker in one study, we show that the usual ratio of coefficients approach can be reformulated as a regression with heterogeneous error in the explanatory variable. This can be implemented using a Bayesian approach, which is next extended to include multiple genetic markers. We then propose a hierarchical model for undertaking a meta-analysis of multiple studies, in which it is not necessary that the same genetic markers are measured in each study. This provides an overall estimate of the causal relationship between the phenotype and the outcome, and an assessment of its heterogeneity across studies. As an example, we estimate the causal relationship of blood concentrations of C-reactive protein on fibrinogen levels using data from 11 studies. These methods provide a flexible framework for efficient estimation of causal relationships derived from multiple studies. Issues discussed include weak instrument bias, analysis of binary outcome data such as disease risk, missing genetic data, and the use of haplotypes.
doi:10.1002/sim.3843
PMCID: PMC3648673  PMID: 20209660
Mendelian randomization; instrumental variables; causal association; meta-analysis; Bayesian methods
14.  Individual progression of carotid intima media thickness as a surrogate for vascular risk (PROG-IMT): Rationale and design of a meta-analysis project 
American heart journal  2010;159(5):730-736.e2.
Carotid intima media thickness (IMT) progression is increasingly used as a surrogate for vascular risk. This use is supported by data from a few clinical trials investigating statins, but established criteria of surrogacy are only partially fulfilled. To provide a valid basis for the use of IMT progression as a study end point, we are performing a 3-step meta-analysis project based on individual participant data.
Objectives of the 3 successive stages are to investigate (1) whether IMT progression prospectively predicts myocardial infarction, stroke, or death in population-based samples; (2) whether it does so in prevalent disease cohorts; and (3) whether interventions affecting IMT progression predict a therapeutic effect on clinical end points.
Recruitment strategies, inclusion criteria, and estimates of the expected numbers of eligible studies are presented along with a detailed analysis plan.
doi:10.1016/j.ahj.2010.02.008
PMCID: PMC3600980  PMID: 20435179
17.  Predicting the extent of heterogeneity in meta-analysis, using empirical data from the Cochrane Database of Systematic Reviews 
Background Many meta-analyses contain only a small number of studies, which makes it difficult to estimate the extent of between-study heterogeneity. Bayesian meta-analysis allows incorporation of external evidence on heterogeneity, and offers advantages over conventional random-effects meta-analysis. To assist in this, we provide empirical evidence on the likely extent of heterogeneity in particular areas of health care.
Methods Our analyses included 14 886 meta-analyses from the Cochrane Database of Systematic Reviews. We classified each meta-analysis according to the type of outcome, type of intervention comparison and medical specialty. By modelling the study data from all meta-analyses simultaneously, using the log odds ratio scale, we investigated the impact of meta-analysis characteristics on the underlying between-study heterogeneity variance. Predictive distributions were obtained for the heterogeneity expected in future meta-analyses.
Results Between-study heterogeneity variances for meta-analyses in which the outcome was all-cause mortality were found to be on average 17% (95% CI 10–26) of variances for other outcomes. In meta-analyses comparing two active pharmacological interventions, heterogeneity was on average 75% (95% CI 58–95) of variances for non-pharmacological interventions. Meta-analysis size was found to have only a small effect on heterogeneity. Predictive distributions are presented for nine different settings, defined by type of outcome and type of intervention comparison. For example, for a planned meta-analysis comparing a pharmacological intervention against placebo or control with a subjectively measured outcome, the predictive distribution for heterogeneity is a log-normal (−2.13, 1.582) distribution, which has a median value of 0.12. In an example of meta-analysis of six studies, incorporating external evidence led to a smaller heterogeneity estimate and a narrower confidence interval for the combined intervention effect.
Conclusions Meta-analysis characteristics were strongly associated with the degree of between-study heterogeneity, and predictive distributions for heterogeneity differed substantially across settings. The informative priors provided will be very beneficial in future meta-analyses including few studies.
doi:10.1093/ije/dys041
PMCID: PMC3396310  PMID: 22461129
Meta-analysis; heterogeneity; intervention studies; Bayesian analysis
18.  Modelling bias in combining small area prevalence estimates from multiple surveys 
Summary
Combining information from multiple surveys can improve the quality of small area estimates. Customary approaches, such as the multiple-frame and statistical matching methods, require individual level data, whereas in practice often only multiple aggregate estimates are available. Commercial surveys usually produce such estimates without clear description of the methodology that is used. In this context, bias modelling is crucial, and we propose a series of Bayesian hierarchical models which allow for additive biases. Some of these models can also be fitted in a classical context, by using a mixed effects framework. We apply these methods to obtain estimates of smoking prevalence in local authorities across the east of England from seven surveys. All the surveys provide smoking prevalence estimates and confidence intervals at the local authority level, but they vary by time, sample size and transparency of methodology. Our models adjust for the biases in commercial surveys but incorporate information from all the sources to provide more accurate and precise estimates.
doi:10.1111/j.1467-985X.2010.00648.x
PMCID: PMC3041928  PMID: 21379388
Bias modelling; Hierarchical models; Meta-analysis; Mixed effects models; Multiple survey data; Small area estimation; Smoking prevalence
19.  Routine Antenatal Anti-D Prophylaxis in Women Who Are Rh(D) Negative: Meta-Analyses Adjusted for Differences in Study Design and Quality 
PLoS ONE  2012;7(2):e30711.
Background
To estimate the effectiveness of routine antenatal anti-D prophylaxis for preventing sensitisation in pregnant Rhesus negative women, and to explore whether this depends on the treatment regimen adopted.
Methods
Ten studies identified in a previous systematic literature search were included. Potential sources of bias were systematically identified using bias checklists, and their impact and uncertainty were quantified using expert opinion. Study results were adjusted for biases and combined, first in a random-effects meta-analysis and then in a random-effects meta-regression analysis.
Results
In a conventional meta-analysis, the pooled odds ratio for sensitisation was estimated as 0.25 (95% CI 0.18, 0.36), comparing routine antenatal anti-D prophylaxis to control, with some heterogeneity (I2 = 19%). However, this naïve analysis ignores substantial differences in study quality and design. After adjusting for these, the pooled odds ratio for sensitisation was estimated as 0.31 (95% CI 0.17, 0.56), with no evidence of heterogeneity (I2 = 0%). A meta-regression analysis was performed, which used the data available from the ten anti-D prophylaxis studies to inform us about the relative effectiveness of three licensed treatments. This gave an 83% probability that a dose of 1250 IU at 28 and 34 weeks is most effective and a 76% probability that a single dose of 1500 IU at 28–30 weeks is least effective.
Conclusion
There is strong evidence for the effectiveness of routine antenatal anti-D prophylaxis for prevention of sensitisation, in support of the policy of offering routine prophylaxis to all non-sensitised pregnant Rhesus negative women. All three licensed dose regimens are expected to be effective.
doi:10.1371/journal.pone.0030711
PMCID: PMC3272015  PMID: 22319580
20.  Prospective study of insulin-like growth factor-I, insulin-like growth factor-binding protein 3, genetic variants in the IGF1 and IGFBP3 genes and risk of coronary artery disease 
Although experimental studies have suggested that insulin-like growth factor I (IGF-I) and its binding protein IGFBP-3 might have a role in the aetiology of coronary artery disease (CAD), the relevance of circulating IGFs and their binding proteins in the development of CAD in human populations is unclear. We conducted a nested case-control study, with a mean follow-up of six years, within the EPIC-Norfolk cohort to assess the association between circulating levels of IGF-I and IGFBP-3 and risk of CAD in up to 1,013 cases and 2,055 controls matched for age, sex and study enrolment date. After adjustment for cardiovascular risk factors, we found no association between circulating levels of IGF-I or IGFBP-3 and risk of CAD (odds ratio: 0.98 (95% Cl 0.90-1.06) per 1 SD increase in circulating IGF-I; odds ratio: 1.02 (95% Cl 0.94-1.12) for IGFBP-3). We examined associations between tagging single nucleotide polymorphisms (tSNPs) at the IGF1 and IGFBP3 loci and circulating IGF-I and IGFBP-3 levels in up to 1,133 cases and 2,223 controls and identified three tSNPs (rs1520220, rs3730204, rs2132571) that showed independent association with either circulating IGF-I or IGFBP-3 levels. In an assessment of 31 SNPs spanning the IGF1 or IGFBP3 loci, none were associated with risk of CAD in a meta-analysis that included EPIC-Norfolk and eight additional studies comprising up to 9,319 cases and 19,964 controls. Our results indicate that IGF-I and IGFBP-3 are unlikely to be importantly involved in the aetiology of CAD in human populations.
PMCID: PMC3166154  PMID: 21915365
Epidemiology; Genetics of cardiovascular disease; Risk factors; IGF1; IGFBP3
21.  On-line Randomized Controlled Trial of an Internet Based Psychologically Enhanced Intervention for People with Hazardous Alcohol Consumption 
PLoS ONE  2011;6(3):e14740.
Background
Interventions delivered via the Internet have the potential to address the problem of hazardous alcohol consumption at minimal incremental cost, with potentially major public health implications. It was hypothesised that providing access to a psychologically enhanced website would result in greater reductions in drinking and related problems than giving access to a typical alcohol website simply providing information on potential harms of alcohol. DYD-RCT Trial registration: ISRCTN 31070347.
Methodology/Principal Findings
A two-arm randomised controlled trial was conducted entirely on-line through the Down Your Drink (DYD) website. A total of 7935 individuals who screened positive for hazardous alcohol consumption were recruited and randomized. At entry to the trial, the geometric mean reported past week alcohol consumption was 46.0 (SD 31.2) units. Consumption levels reduced substantially in both groups at the principal 3 month assessment point to an average of 26.0 (SD 22.3) units. Similar changes were reported at 1 month and 12 months. There were no significant differences between the groups for either alcohol consumption at 3 months (intervention: control ratio of geometric means 1.03, 95% CI 0.97 to 1.10) or for this outcome and the main secondary outcomes at any of the assessments. The results were not materially changed following imputation of missing values, nor was there any evidence that the impact of the intervention varied with baseline measures or level of exposure to the intervention.
Conclusions/Significance
Findings did not provide support for the hypothesis that access to a psychologically enhanced website confers additional benefit over standard practice and indicate the need for further research to optimise the effectiveness of Internet-based behavioural interventions. The trial demonstrates a widespread and potentially sustainable demand for Internet based interventions for people with hazardous alcohol consumption, which could be delivered internationally.
Trial Registration
Controlled-Trials.com ISRCTN31070347
doi:10.1371/journal.pone.0014740
PMCID: PMC3052303  PMID: 21408060
22.  Objectively Measured Physical Activity and Fat Mass in Children: A Bias-Adjusted Meta-Analysis of Prospective Studies 
PLoS ONE  2011;6(2):e17205.
Background
Studies investigating the prevention of weight gain differ considerably in design and quality, which impedes pooling them in conventional meta-analyses, the basis for evidence-based policy making. This study is aimed at quantifying the prospective association between measured physical activity and fat mass in children, using a meta-analysis method that allows inclusion of heterogeneous studies by adjusting for differences through eliciting and incorporating expert opinion.
Methods
Studies on prevention of weight gain using objectively measured exposure and outcome were eligible; they were adopted from a recently published systematic review. Differences in study quality and design were considered as internal and external biases and captured in checklists. Study results were converted to correlation coefficients and biases were considered either additive or proportional on this scale. The extent and uncertainty of biases in each study were elicited in a formal process by six quantitatively-trained assessors and five subject-matter specialists. Biases for each study were combined across assessors using median pooling. Results were combined across studies by random-effects meta-analysis.
Results
The combined correlation of the unadjusted results from the six studies was −0.04 (95%CI: −0.22, 0.14) with considerable heterogeneity (I2 = 78%), which makes it difficult to interpret the result. After bias-adjustment the pooled correlation was −0.01 (95%CI: −0.18, 0.16) with apparent study compatibility (I2 = 0%).
Conclusion
By using this method the prospective association between physical activity and fat mass could be quantitatively synthesized; the result suggests no association. Objectively measured physical activity may not be the key determinant of unhealthy weight gain in children.
doi:10.1371/journal.pone.0017205
PMCID: PMC3044163  PMID: 21383837
23.  Dietary energy density and adiposity: Employing bias adjustments in a meta-analysis of prospective studies 
BMC Public Health  2011;11:48.
Background
Dietary studies differ in design and quality making it difficult to compare results. This study quantifies the prospective association between dietary energy density (DED) and adiposity in children using a meta-analysis method that adjusts for differences in design and quality through eliciting and incorporating expert opinion on the biases and their uncertainty.
Method
Six prospective studies identified by a previous systematic literature search were included. Differences in study quality and design were considered respectively as internal and external biases and captured in bias checklists. Study results were converted to correlation coefficients; biases were considered either additive or proportional on this scale. The extent and uncertainty of the internal and external biases in each study were elicited in a formal process by five quantitatively-trained assessors and five subject-matter specialists. Biases for each study were combined across assessors using median pooling and results combined across studies by random-effects meta-analysis.
Results
The unadjusted combined correlation between DED and adiposity change was 0.06 (95%CI 0.01, 0.11; p = 0.013), but with considerable heterogeneity (I2 = 52%). After bias-adjustment the pooled correlation was 0.17 (95%CI - 0.11, 0.45; p = 0.24), and the studies were apparently compatible (I2 = 0%).
Conclusions
This method allowed quantitative synthesis of the prospective association between DED and adiposity change in children, which is important for the development of evidence-informed policy. Bias adjustment increased the magnitude of the positive association but the widening confidence interval reflects the uncertainty of the assessed biases and implies that higher quality studies are required.
doi:10.1186/1471-2458-11-48
PMCID: PMC3038903  PMID: 21255448
24.  A re-evaluation of random-effects meta-analysis 
Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of ‘set shifting’ ability in people with eating disorders.
doi:10.1111/j.1467-985X.2008.00552.x
PMCID: PMC2667312  PMID: 19381330
Meta-analysis; Prediction; Random-effects models; Systematic reviews
25.  Accounting for uncertainty in health economic decision models by using model averaging 
Health economic decision models are subject to considerable uncertainty, much of which arises from choices between several plausible model structures, e.g. choices of covariates in a regression model. Such structural uncertainty is rarely accounted for formally in decision models but can be addressed by model averaging. We discuss the most common methods of averaging models and the principles underlying them. We apply them to a comparison of two surgical techniques for repairing abdominal aortic aneurysms. In model averaging, competing models are usually either weighted by using an asymptotically consistent model assessment criterion, such as the Bayesian information criterion, or a measure of predictive ability, such as Akaike's information criterion. We argue that the predictive approach is more suitable when modelling the complex underlying processes of interest in health economics, such as individual disease progression and response to treatment.
doi:10.1111/j.1467-985X.2008.00573.x
PMCID: PMC2667305  PMID: 19381329
Akaike's information criterion; Bayesian information criterion; Health economics; Model averaging; Model uncertainty

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