Computational issues in fitting joint frailty models for recurrent events with an associated terminal event

Joint frailty regression models are intended for the analysis of recurrent event times in the presence of informative drop-outs. They have been proposed for clinical trials to estimate the effect of some treatment on the rate of recurrent heart failure hospitalisations in the presence of drop-outs due to cardiovascular death. Whereas a R-software-package for fitting joint frailty models is available, some technical issues have to be solved in order to use SAS^Ⓡ1 software, which is required in the regulatory environment of clinical trials.

First, we demonstrate how to solve these issues by deriving proper likelihood-decompositions, in particular for the case of non-normally distributed random terms. Second, we perform a simulation study to evaluate the accuracy of different software-implementations (in SAS and R) in terms of convergence behavior, bias of model parameter estimates and coverage probabilities of confidence intervals. Therefore we developed SAS macros that facilitate the analysis and simulation of joint frailty data. These are provided as supplementary material along with comprehensive manuals.

Whereas estimates for regression coefficients are unbiased irrespective of the software, the bias of the remaining (nuisance) parameter estimates strongly depends on the software: SAS is shown to be much more efficient in avoiding bias compared to R. However, even in SAS a careful choice of the implementation is required to get reliable results, in particular for the joint gamma frailty model. By far the best performance is reached with a SAS-implementation that makes use of the probability integral transformation method.

We have shown, that getting reliable results from joint frailty models is not straightforward and users should be aware about the computational options between and within software packages. Based on our simulation study, we elaborate recommendations on these options. In addition, our provided SAS macros may encourage statistical practitioners to apply these models in clinical trials with recurrent event data and potentially informative drop-outs.