Interval Estimation for Parameters of a Bathtub Hazard Model

Abstract

In this study, a two-parameter lifetime model has been extended to incorporate covariate in the presence of right-censored data. The model has bathtub-shaped or increasing failure rate function which enables it to fit real lifetime data set. The method of maximum likelihood was used to estimate the parameters in the model and a simulation study was then conducted to evaluate the performance of parameter estimates at various sample sizes and censoring proportion levels. The results from simulation study show that larger sample sizes and smaller censoring proportion give better estimates. Further, two interval estimation methods: Wald and likelihood ratio were constructed, and the performance of these methods was evaluated based on a coverage probability study. Both Wald and likelihood ratio techniques appear to have better performance when the sample size is larger. Also, a real right-censored lifetime data on patients with multiple myeloma was employed to illustrate the practical application of the extended model.