Parameter Estimation for the Exponentiated Rayleigh Model with Covariates under Right Censored

Abstract

In this study, the exponentiated Rayleigh (ER) model is extended to include covariates in the presence of right censored data. The maximum likelihood estimation (MLE) for the parameter estimates were assessed using the bias, standard error (SE) and root mean square error (RMSE) of the parameter estimates at various sample sizes and censoring proportion (cp) via simulation study. Additionally, the coverage probability study is conducted to compare three methods of constructing confidence intervals: Wald, jackknife and bootstrap-t method. The coverage probability study showed that the best confidence interval estimation technique for parameters β₀ and β₁ is the bootstrap-t method. However, for the parameter γ, at α = 0.05 (α = 0.1) the bootstrap-t (Wald) method is preferred. The model is then applied to preclinical data on refractory F98 glioma and compared to the Kaplan-Meier estimate. The Akaike information criterion (AIC) is used to evaluate the performances of the exponential, Weibull and log-logistic regression models against the extended ER model. Based on the AIC value, the extended ER model is the best fitting model for the data. The analysis shows that treating treatment groups in the data as a covariate in the extended ER model is significant. Hence, it is concluded that different treatments affect the survival times of rats in the data.