Analysis of Diabetes Data using Extended Cox Model with Frailty under Partial and Penalized partial likelihood estimation methods
Abstract
Data on Diabetes were analyzed using partial likelihood (Pl) and penalized partial likelihood (Ppl) estimation methods in non-proportional hazards model with dichotomous time-varying covariates. Gamma and Inverse Gaussian frailty distributions were used to account for patient- specific unobserved heterogeneity. Four likelihood configurations were formed from the combinations of the two estimation methods and frailty distributions. These are Partial likelihood with Gamma frailty, Partial likelihood with Inverse Gaussian frailty, Penalized partial likelihood with Gamma frailty and Penalized partial likelihood with Gamma frailty. The results revealed that age and body mass index of the patients significantly increased the risk of death from diabetes, while regular exercise had significant decreased risk of death. Penalized partial likelihood estimation method generally outperformed models with Partial likelihood under all scenarios for the data and Gamma frailty provided a better fit in accounting for unobserved heterogeneity among the diabetic patients.
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