Parametric Frailty Model with Time-Dependent Covariates

Abstract

The parametric frailty model has been used in this study where, the term frailty is used to represent an unobservable random effect shared by subjects with similar (unmeasured) risks in the analysis of mortality rate. In real-life environment, the application of frailty models have been widely used by biostatistician, economists and epidemiologist to donate proneness to disease, accidents and other events because there are persistent differences in susceptibility among individuals. When heterogeneity is ignored in a study of survival analysis the result will produce an incorrect estimation of parameters and standard errors. This study used gamma and Weibull distribution for the frailty model. The first objective of this study is to investigate parametric model with time dependent covariates on frailty model. The derivation is using either classical maximum likelihood or Monte Carlo integration. The second objective is to measure the effectiveness of Gamma and Weibull frailty model with and without time-dependent covariates. This is done by calculating the root mean square error (RMSE). The last objective is to assess the goodness of fit of Gamma and Weibull frailty model with and without time-dependent covariates using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Simulation is used in order to obtain the RMSE, AIC ad BIC value if time-dependent covariate does not exists. Between both models with time-dependent covariate, Weibull frailty distribution has lower AIC and BIC compared to Gamma frailty distribution. Therefore, Weibull frailty distribution with time-dependent covariate is preferable when a time-dependent covariate exists in a data.