Sometimes, survival data come in clusters, and multivariate, or frailty, models are appropriate to use.
Ever since the paper by Vaupel, Manton & Stallard (1979), the concept of frailty has spread in even wider circles of the research community. Although their primary purpose was to show various consequences of admitting individual frailties (“individuals age faster than cohorts,” due to the selection effect), the effect was that people started to implement their frailty model in Cox regression models.
Let us assume that in a follow-up study, the cohort is not homogeneous but instead consists of two equally sized groups with differing hazard rates. Assume further ...