Statistical methods for the time-to-event analysis of individual participant data from multiple epidemiological studies

Abstract

Background: Meta-analysis of individual participant time-to-event data from multiple prospective epidemiological studies enables detailed investigation of exposure-risk relationships, but involves a number of analytical challenges.

Methods: This article describes statistical approaches adopted in the Emerging Risk Factors Collaboration, in which primary data from more than 1 million participants in more than 100 prospective studies have been collated to enable detailed analyses of various risk markers in relation to incident cardiovascular disease outcomes.

Results: Analyses have been principally based on Cox proportional hazards regression models stratified by sex, undertaken in each study separately. Estimates of exposure-risk relationships, initially unadjusted and then adjusted for several confounders, have been combined over studies using meta-analysis. Methods for assessing the shape of exposure-risk associations and the proportional hazards assumption have been developed. Estimates of interactions have also been combined using meta-analysis, keeping separate within- and between-study information. Regression dilution bias caused by measurement error and within-person variation in exposures and confounders has been addressed through the analysis of repeat measurements to estimate corrected regression coefficients. These methods are exemplified by analysis of plasma fibrinogen and risk of coronary heart disease, and Stata code is made available.

Conclusion: Increasing numbers of meta-analyses of individual participant data from observational data are being conducted to enhance the statistical power and detail of epidemiological studies. The statistical methods developed here can be used to address the needs of such analyses.

Figure 1

Study-specific HRs and 95% CIs (log scale) for the relationship of baseline fibrinogen with CHD in 31 studies, and meta-analysis. A 95% prediction interval for the true HR in a new study is also shown. Results are adjusted for age at baseline as a linear term. For acronyms to studies, see Ref. 10. RE, random effects; FE, fixed effects; NA, not applicable.

Figure 2

Combined log HRs with 95% CIs based on floating absolute risks for the relationship between baseline fibrinogen (g/l) and CHD risk, plotted against mean baseline fibrinogen in fifths. From multivariate random-effects meta-analysis, adjusted for a linear effect of age at baseline in each study separately.

Figure 3

Interaction of baseline fibrinogen and age, derived from a proportional hazards model with time-dependent effect of age in each study and combined using multivariate random-effects meta-analysis. Log HRs with 95% CIs based on floating absolute risks, plotted against mean baseline fibrinogen in fifths.