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 αα 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 αα is unknown.

► We developed the predictive densities for future responses given a follow-up doubly censored sample of larynx cancer patients.
► We obtained 95% highest predictive density intervals for the mean survival days of all patients as well as for males and females separately.
► It was noted from the findings that dose plays a critical role in reducing the predictive survival days.
► We found females’ survival days are higher than that of males, although the average age of males is lower than that of females.
► Knowing that smoking is a risk factor of larynx cancer, one would agree with the results because males tend to smoke more than females.