Bathtub hazard model with covariate and right censored data

Abstract

Lifetime distributions that present bathtub-shaped failure rates are becoming increasingly important especially when dealing with medical data. In this research, a two-parameter bathtub hazard model was extended to incorporate covariates in the presence of right censored data. The parameter estimates were computed based on maximum likelihood estimation (MLE) method. A simulation study was then executed to assess the performance of parameter estimates based on their bias, standard error (SE) and root mean square error (RMSE) at various censoring proportions and sample sizes. The results suggested that the performance of the estimator is better at larger sample size as it lower the standard error and root mean square error (RMSE). A decrease in censoring proportions yield smaller SE and RMSE values, whereas the values of bias decrease as the sample sizes and censoring proportions increase. Finally, the extended model was applied to a real medical data. Also, three confidence interval estimation (Wald, bootstrap-p, bootstrap-t) were obtained for each of the parameters of the model. The results suggested that the real data fitted the bathtub hazard model well.