Goodness-of-fit tests based on Kullback-Leibler divergence for bladder cancer survival analysis: Applications to exponentiated exponential distribution

Bladder cancer is among the ten most common types of cancer worldwide, with approximately 550,000 new cases occurring each year. It accounts for comprehensively compared to 3% of all newly diagnosed cancer cases and contributes to 2.1% of cancer-related deaths globally. This article introduces goodness-of-fit tests that aim to fit the exponentialized exponential distribution. These tests are based on the Kullback-Leibler difference and have been applied to censored and complete samples of Bladder Cancer Patients. We calculated critical values and statistical power measurements, considering the best and worst bandwidth scenarios. We then comprehensively compared essential values and power across various parameters, accounting for optimal and suboptimal bandwidth choices derived from the Kullback–Leibler difference. In the final phase of our study, we used a dataset of individuals diagnosed with bladder cancer to demonstrate the practical applicability of our proposed research. Finally, this modeling type can benefit researchers and healthcare professionals through time-to-event analysis (survival analysis), investigation of events, medical decision-making, and risk prediction.