Estimating Unknown Heterogeneity in Head and Neck Cancer Survival: A Parametric Shared Frailty Approach

Abstract

The term frailty was introduced by Vaupel et al., 1979, to indicate that different individuals are at risks even though on the surface they may appear to be quite similar with respect to the measurable attributes such as age, sex, habits etc. The term frailty can be utilized to represent an unobservable random effect shared by subjects with similar risks in the analysis of time to event data and/or mortality rates. In this article, we make use of the parametric shared frailty models to a real life data for identifying the distributional form of baseline hazard function. The gamma shared frailty, with disease stages as clusters, with log-logistic baseline hazard model came out to be the best choice for modeling survival data of Head and Neck cancer patients treated with radiotherapy. The suitability of the best-chosen model is justified considering two significant covariates, namely, age of the patients and habit of their alcohol consumption. We obtain the estimates of frailty (or unknown heterogeneity) for five stages of disease taken as clusters for Gamma- log-logistic shared frailty model.