The random-effects proportional hazards model with grouped survival data: a comparison between the grouped continuous and continuation ratio versions

When analysing grouped time survival data having a hierarchical structure it is often appropriate to assume a random-effects proportional hazards model for the latent continuous time and then to derive the corresponding grouped time model. There are two formally equivalent grouped time versions of the proportional hazards model obtained from different perspectives, known as the continuation ratio and the grouped continuous models. However, the two models require distinct estimation procedures and, more importantly, they differ substantially when extended to time-dependent covariates and/or non-proportional effects. The paper discusses these issues in the context of random-effects models, illustrating the main points with an application to a complex data set on job opportunities for a cohort of graduates.