On the Generalised Piecewise Constant Hazard Model with Application to Breast Cancer

Abstract

In survival analysis, a baseline hazard function is combined with hazard multipliers which depend on covariate values through a logarithmic link function and a linear predictor. Hence, the form of dependence of the hazard multipliers on covariates is usually specified. This research is focused on a way of relaxing the specification of the form of dependence of the hazard on the covariates in survival analysis using the generalised piecewise constant hazard (GPCH) model where the covariates are made ordinal. The Bayesian approach to inference is used with priors based on the parametric model which allowed for main and interaction effects using R functions. A secondary data set of breast cancer consisting of 300 patients with four complete covariates which include age, gender, mode of diagnosis and location of breast cancer from the University of Ilorin teaching hospital, Ilorin, Nigeria for a period of five years was used for illustration. The choice of prior will allow a compromise which relaxes the form of dependence of the hazard function while imposing enough structure to exploit the information in the finite data set by specifying correlations in the prior distribution between log-hazards for neighbouring covariate profiles.