Meta-analysis for individual participant data with a continuous exposure: A case study

Abstract

Objective: Methods for meta-analysis of studies with individual participant data and continuous exposure variables are well described in the statistical literature but are not widely used in clinical and epidemiological research. The purpose of this case study is to make the methods more accessible.

Study design and setting: A two-stage process is demonstrated. Response curves are estimated separately for each study using fractional polynomials. The study-specific curves are then averaged pointwise over all studies at each value of the exposure. The averaging can be implemented using fixed effects or random effects methods.

Results: The methodology is illustrated using samples of real data with continuous outcome and exposure data and several covariates. The sample data set, segments of Stata and R code, and outputs are provided to enable replication of the results.

Conclusion: These methods and tools can be adapted to other situations, including for time-to-event or categorical outcomes, different ways of modelling exposure-outcome curves, and different strategies for covariate adjustment.

Keywords: Continuous variables; Fractional polynomials; Individual participant data; Meta-analysis.

Figure 1.

Scatter plots and lowess fits for age at natural menopause and baseline body mass index for the sample data set.

Figure 2.

Lowess plots of predicted values (and 95% confidence intervals) for age at natural menopause by body mass index for each study separately.

Figure 3.

Lowess plots of the weights for each study that are used in the fixed effects and random effects meta-analyses.

Figure 4.

Results of meta-analysis of the association between age at natural menopause and body mass index: lowess plots for estimates and 95% confidence intervals.