Non-proportional hazards model with a PVF frailty term: application with a melanoma dataset

Abstract

Survival data analysis often uses the Cox proportional hazards (PH) model. This model is widely applied due to its straightforward interpretation of the hazard ratio under the assumption that the hazard rates for two subjects remain constant over time. However, in several randomized clinical trials with long-term survival data comparing two new treatments, it is frequently observed that Kaplan-Meier plots exhibit crossing survival curves. This violation of the PH assumption of the Cox PH model can not be applied to evaluate the treatment's effect on survival. This paper introduces a novel long-term survival model with non-PH that incorporates a frailty term into the hazard function. This model allows us to examine the effect of prognostic factors on survival and quantify the degree of unobservable heterogeneity. The model parameters are estimated using the maximum likelihood estimation procedure, and we evaluate the performance of the proposed models through simulation studies. Additionally, we demonstrate the applicability of our approach by fitting the models to a real skin cancer dataset.

Keywords:

• Cure rate models
• generalized time-dependent log-log model
• maximum likelihood estimation
• random effects
• skin cancer

Mathematical subject classifications:

• 62N02
• 62N03

Acknowledgments

The authors thank the Oncology Foundation of São Paulo for providing the melanoma dataset.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research of Francisco Louzada is supported by the Brazilian Organizations, CNPq (Grant number: 308849/2021-3) and FAPESP (Grant number: 2013/07375-0). The research of Vinicius F. Calsavara is supported in part by the NIH National Center for Advancing Translational Sciences UCLA CTSI UL1 TR001881.