Non-proportional hazard model without frailty and with frailty distribution under mixtures of baseline distribution

Abstract

Proportional hazards (PH) model is one of the most commonly used methods in the analysis of time-to-event data. The assumption of (PH) model which states that the ratio of the hazards for any two individuals is constant over time may not hold if the hazard ratio varies with time. It is therefore necessary to use methods that do not assume proportionality to investigate the effects of covariates on survival time which leads us to non-proportional hazard (NPH) model. The PH model under frailty setting is a natural extension of the standard PH model to address the erroneous assumption that the baseline survival times are independently and identically distributed.This study compared non-proportional hazard (NPH) model without frailty and with frailty using Integrated Nested Laplace Approximation (INLA) method under the mixture of Weibull-Weibull, Lognormal-Lognormal and Weibull-Lognormal baseline distributions. Data were simulated from mixture of Weibull-Weibull, Lognormal-Lognormal and Weibull-Lognormal baseline hazard distributions for different sample sizes and censoring percentages. The NPH model without frailty and with frailty were then fitted to the data using Deviance Information Criterion (DIC) as the comparing metric.It was observed that the NPH model with frailty performed better than the NPH model without frailty in the three mixture of baseline distribution considered and also for all sample sizes and censoring percentages considered.