Individual participant data meta-analysis to examine interactions between treatment effect and participant-level covariates: Statistical recommendations for conduct and planning

Abstract

Precision medicine research often searches for treatment-covariate interactions, which refers to when a treatment effect (eg, measured as a mean difference, odds ratio, hazard ratio) changes across values of a participant-level covariate (eg, age, gender, biomarker). Single trials do not usually have sufficient power to detect genuine treatment-covariate interactions, which motivate the sharing of individual participant data (IPD) from multiple trials for meta-analysis. Here, we provide statistical recommendations for conducting and planning an IPD meta-analysis of randomized trials to examine treatment-covariate interactions. For conduct, two-stage and one-stage statistical models are described, and we recommend: (i) interactions should be estimated directly, and not by calculating differences in meta-analysis results for subgroups; (ii) interaction estimates should be based solely on within-study information; (iii) continuous covariates and outcomes should be analyzed on their continuous scale; (iv) nonlinear relationships should be examined for continuous covariates, using a multivariate meta-analysis of the trend (eg, using restricted cubic spline functions); and (v) translation of interactions into clinical practice is nontrivial, requiring individualized treatment effect prediction. For planning, we describe first why the decision to initiate an IPD meta-analysis project should not be based on between-study heterogeneity in the overall treatment effect; and second, how to calculate the power of a potential IPD meta-analysis project in advance of IPD collection, conditional on characteristics (eg, number of participants, standard deviation of covariates) of the trials (potentially) promising their IPD. Real IPD meta-analysis projects are used for illustration throughout.

Keywords: effect modifier; individual participant data (IPD); meta-analysis; subgroup effect; treatment-covariate interaction.

Figure 1

A two‐stage IPD meta‐analysis of treatment‐sex interactions, summarizing the difference in the effect of antihypertensive treatment for males compared to females. Note: The interactions refer to the difference between males and females in the treatment effect (ie, their difference in the mean difference in final systolic blood pressure for treatment vs control, after adjusting for baseline), with negative values indicating that the treatment effect is better in females than males [Colour figure can be viewed at wileyonlinelibrary.com]

Figure 2

Does age interact with the effect of antihypertensive treatment on systolic blood pressure? Findings from an IPD meta‐analysis of 10 trials, showing difference in results based on across‐study (solid line) and within‐study (dashed lines) information. Across‐study relationship (from meta‐regression of trial's treatment effect estimates vs mean age) denoted by gradient of solid line. Participant‐level relationship using within‐study information (ie, treatment‐sex interaction within each trial) denoted by gradient of dashed lines and the summary gradient (${\widehat{\mathrm{\gamma }}}_{\mathrm{W}})$ is −0.036 (95% CI: −0.19 to 0.12). Each block represents one trial, and the block size is proportional to the size of the trial.

Figure 3

Summary of the nonlinear interaction between age and effect of hypertension treatment on final SBP value. Figure created by fitting an analysis of covariance model in each study separately, with the interaction between age and treatment modeled via a restricted cubic spline function (with knot positions of 39, 60, and 75), and then the study‐specific parameter estimates (relating to the interaction) pooled in a multivariate random‐effects meta‐analysis

Figure 4

Introduction to modeling nonlinear relationships in a single study using restricted cubic splines; for further details we recommend the reader refer to Harrell45

Figure 5

(A): Overview of the first stage of a two‐stage multivariate IPD meta‐analysis to summarize a nonlinear treatment‐covariate interaction using a restricted cubic spline. The steps are described in relation to the hypertension example of Figure 3 which examined a treatment‐age interaction.

Figure 5

(B): Overview of the second stage of a two‐stage multivariate IPD meta‐analysis to summarize a nonlinear treatment‐covariate interaction using a restricted cubic spline. The steps are described in relation to the hypertension example of Figure 3 which examined a treatment‐age interaction

Figure 6

The predicted effect of antihypertensive treatment on SBP conditional on an individual's age, based on a multivariate meta‐analysis either with or without aggregation bias in the summary treatment‐age interactions

Figure 7

Evidence of a potential nonlinear interaction between baseline SBP and the effect of hypertension treatment on the rate of CVD, even though there was no between‐study heterogeneity in the overall treatment effect