A hybrid hazard-based model using two-piece distributions

Cox proportional hazards model is widely used to study the relationship between the survival time of an event and covariates. Its primary objective is parameter estimation assuming a constant relative hazard throughout the entire follow-up time. The baseline hazard is thus treated as a nuisance parameter. However, if the interest is to predict possible outcomes like specific quantiles of the distribution (e.g. median survival time), survival and hazard functions, it may be more convenient to use a parametric baseline distribution. Such a parametric model should however be flexible enough to allow for various shapes of e.g. the hazard function. In this paper we propose flexible hazard-based models for right censored data using a large class of two-piece asymmetric baseline distributions. The effect of covariates is characterized through time-scale changes on hazard progression and on the relative hazard ratio; and can take three possible functional forms: parametric, semi-parametric (partly linear) and non-parametric. In the first case, the usual full likelihood estimation method is applied. In the semi-parametric and non-parametric settings a general profile (local) likelihood estimation approach is proposed. An extensive simulation study investigates the finite-sample performances of the proposed method. Its use in data analysis is illustrated in real data examples.