Sensitivity analysis of predictive modeling for responses from the three-parameter Weibull model with a follow-up doubly censored sample of cancer patients

The purpose of this paper is to derive the predictive densities for future responses from the three-parameter Weibull model given a doubly censored sample. The predictive density for a single future response, bivariate future response, and a set of future responses has been derived when the shape parameter [alpha] is unknown. A real data example representing 44 patients who were diagnosed with laryngeal cancer (2000-2007) at a local hospital is used to illustrate the predictive results for the four stages of cancer. The survival days of eight out of the 44 patients could not be calculated as the patients were lost to follow-up. They were the first four and the last four patients' survival days in order. Thus, the recorded data for the survival days of 36 patients composed of 18 male and 18 female patients with cancer of the larynx are used for the predictive analysis. Furthermore, a subgroup level of the male and female patients follow-up data are considered to obtain the future survival days. A sensitivity study of the mean, standard deviation, and 95% highest predictive density (HPD) interval of the future survival days with respect to stages and doses are performed when the shape parameter [alpha] is unknown.