On Piece-Wise Modelling of Survival Data With Time Changing Covariate Function

Abstract

Survival analysis involve the set of statistical techniques or procedures used to study time until an event occurs, these techniques are not without some conditions. One of the basic assumptions is that, to enable a straight forward interpretation of hazard rates of subject’s covariate(s) on some reference categories or in situations where variables are continuous in nature, the hazard rates must be constant through time “also known as the proportional hazard assumption” for cox regression. This assumption is often violated in medical practice where subject’s vital statistics or measures are often time varying, as their medical situations changes with time. This paper under study a modification of Piece wise survival model, where three levels of Weibull distribution were assumed for baseline hazards, the sensitivity of the baselines were assessed under four (4) censoring percentages (0%, 25%, 50%, & 75%) and sample sizes (n=100, n=500 & n=1000), for when models were Single parametric (SPM) and when partitioned – Piece wise Parametric Model (PPM). A Piece-wise Bayesian hazard model with structured additive predictors in which the functional form of time varying covariate was incorporated in a non-proportional hazards framework was developed, capable of incorporating complex situations in a more flexible framework. Analysis was done utilizing MCMC simulation technique. Results revealed on comparison that the PPM outperformed the SPM with smaller DIC values and larger predictive powers with the LPML criterion and consistently so throughout all simulations.