Multilevel mixed effects parametric survival models using adaptive Gauss-Hermite quadrature with application to recurrent events and IPD meta-analysis

Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multi-centre clinical trials, and Individual Participant Data (IPD) meta-analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper we extend parametric frailty models including the exponential, Weibull, and Gompertz proportional hazards models, and the log logistic, log normal and generalised gamma accelerated failure time models, to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modelled on the log cumulative hazard scale using restricted cubic splines, to include random effects, whilst also allowing for non-proportional hazards (timedependent effects). Maximum likelihood is used to estimate the models utilising adaptive or non-adaptive Gauss-Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multi-centre trial and IPD meta-analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection, and an IPD metaanalysis of prognostic factor studies in patients with breast cancer. User-friendly Stata software is provided to implement the methods. Copyright c © 0000 John Wiley & Sons, Ltd.