Amoud Class for Hazard-Based and Odds-Based Regression Models: Application to Oncology Studies

Abstract

The purpose of this study is to propose a novel, general, tractable, fully parametric class for hazard-based and odds-based models of survival regression for the analysis of censored lifetime data, named as the “Amoud class (AM)” of models. This generality was attained using a structure resembling the general class of hazard-based regression models, with the addition that the baseline odds function is multiplied by a link function. The class is broad enough to cover a number of widely used models, including the proportional hazard model, the general hazard model, the proportional odds model, the general odds model, the accelerated hazards model, the accelerated odds model, and the accelerated failure time model, as well as combinations of these. The proposed class incorporates the analysis of crossing survival curves. Based on a versatile parametric distribution (generalized log-logistic) for the baseline hazard, we introduced a technique for applying these various hazard-based and odds-based regression models. This distribution allows us to cover the most common hazard rate shapes in practice (decreasing, constant, increasing, unimodal, and reversible unimodal), and various common survival distributions (Weibull, Burr-XII, log-logistic, exponential) are its special cases. The proposed model has good inferential features, and it performs well when different information criteria and likelihood ratio tests are used to select hazard-based and odds-based regression models. The proposed model’s utility is demonstrated by an application to a right-censored lifetime dataset with crossing survival curves.