A Frailty Model for Crossing-Hazard Data

The crossing hazards are often observed in clinical trials on time-to-event. This indicates a strong non-proportional hazards (non-PH) structure and may occur due to a heterogeneity between survival data. Frailty, a random-effect term in hazard models, usually accounts such heterogeneity and the resulting marginal model, which is obtained by integrating out the frailty, leads to a non-PH model. Accordingly, in this paper we propose how to model the crossing hazards via a frailty and to fit the proposed model using SAS PROC NLMIXED. The proposed method is illustrated with a well-known data set from a randomized clinical trial on gastric cancer patients, where the aim of trial is to investigate the effect of chemotherapy (group 1) and combined chemotherapy and radiotherapy (group 2) on survival times of gastric cancer patients.