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

Biostatistics, vol. 23, pp. 1083–1098

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.

Authors 5

1. Bálint Tamási

   University of Zurich

   Affiliation as printed

   Institut für Epidemiologie, Biostatistik und Prävention, Departement Biostatistik, Universität Zürich , Hirschengraben 84, CH-8001 Zürich, Switzerland

2. Michael J. Crowther

   Karolinska Institutet

   Affiliation as printed

   Department of Medical Epidemiology and Biostatistics , Karolinska Institutet, 171 77 Stockholm, Sweden

3. Milo Alan Puhan

   University of Zurich

   Affiliation as printed

   Institut für Epidemiologie, Biostatistik und Prävention, Departement Epidemiologie, Universität Zürich , Hirschengraben 84, CH-8001 Zürich, Switzerland

4. Ewout Willem Steyerberg Aachen Department of Biomedical Data Sciences

   Leiden University Medical Center

   Affiliation as printed

   Department of Biomedical Data Sciences, Leiden University Medical Center , Albinusdreef 2, 2333 ZA Leiden, the Netherlands

5. Torsten Hothorn corresponding

   University of Zurich

   Affiliation as printed

   Institut für Epidemiologie, Biostatistik und Prävention, Departement Biostatistik, Universität Zürich , Hirschengraben 84, CH-8001 Zürich, Switzerland