Non-PH multivariate survival models based on the GTDL

Correlated survival times may be modelled by introducing a random effect, or frailty, component into the hazard function. For multivariate survival data we extend a non-PH model, the generalized time-dependent logistic (GTDL) survival model (MacKenzie, 1996, 1997), to include random effects. The extension leads to two different, but related, non-PH models according to the method of incorporating the random effects. The h-likelihood procedures of Ha, Lee and Song (2001) and Ha and Lee (2003), which obviate the need for marginalization (over the random effect distribution), are derived for these extended models and their properties discussed. The new models are used to analyze two practical examples in the survival literature and the results are compared with those obtained from fitting the PH and PH frailty models.