Parametric Frailty Model with Time-Dependent Covariates
Mohd Asrul Affendi Abdullah1, Emir Mukhriz Zaimi2, Siti Afiqah Muhamad Jamil3
1Mohd Asrul Affendi Abdullah*, Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, Johor, Malaysia.
2Emir Mukhriz Zaimi, Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, Johor, Malaysia.
3Siti Afiqah Muhamad Jamil, Department of Mathematics and Statistics, Universiti Tun Hussein Onn Malaysia, Pagoh Campus, Johor, Malaysia.
Manuscript received on January 02, 2020. | Revised Manuscript received on January 15, 2020. | Manuscript published on January 30, 2020. | PP: 952-956 | Volume-8 Issue-5, January 2020. | Retrieval Number: D7625118419/2020©BEIESP | DOI: 10.35940/ijrte.D7625.018520
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
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.
Keywords: Weibull Frailty, Gamma Frailty, AIC, BIC, RMSE.
Scope of the Article: Mobility and Location-dependent services.