Individual participant data meta-analysis with mixed-effects transformation models

Abstract

One-stage meta-analysis of individual participant data (IPD) poses several statistical and computational challenges. For time-to-event outcomes, the approach requires the estimation of complicated nonlinear mixed-effects models that are flexible enough to realistically capture the most important characteristics of the IPD. We present a model class that incorporates general normally distributed random effects into linear transformation models. We discuss extensions to model between-study heterogeneity in baseline risks and covariate effects and also relax the assumption of proportional hazards. Within the proposed framework, data with arbitrary random censoring patterns can be handled. The accompanying $\textsf{R}$ package tramME utilizes the Laplace approximation and automatic differentiation to perform efficient maximum likelihood estimation and inference in mixed-effects transformation models. We compare several variants of our model to predict the survival of patients with chronic obstructive pulmonary disease using a large data set of prognostic studies. Finally, a simulation study is presented that verifies the correctness of the implementation and highlights its efficiency compared to an alternative approach.

Keywords: Individual participant data; Meta-analysis; Mixed-effects model; Prognostic modeling; Regression; Time-to-event outcomes; Transformation model.

Fig. 1.

Conditional mean effects of the prognostic factors and their 95% pointwise confidence intervals.

Fig. 2.

Model 4: 95% pointwise confidence intervals and predictive intervals of the prognostic factor effects on the log-cumulative hazard scale.

Fig. 3.

Comparison of the distribution of the time-varying fixed-effects estimates from the simulation study (500 iterations). (A) The log-cumulative baseline hazard is presented, while (B–D) depict the time-dependent conditional mean effects of the three covariates.