A new statistical model for advanced modeling of cancer disease data

Classical probability models often struggle to capture the variability and complex patterns inherent in biomedical data, particularly lifetime data. To address these limitations, the generalized odd beta prime Generalized (GOBP-G) class of distributions is introduced, along with an extension called the generalized odd beta prime-Weibull (GOBPW) distribution. This new model offers enhanced flexibility and can represent a variety of data characteristics, from symmetric to skewed distributions, as well as diverse hazard rate patterns, such as increasing, bathtub, and decreasing trends. These features make the GOBPW model suitable for statistical analysis in biomedical and engineering applications. This study derives key properties of the GOBPW distribution, including its moments, moment-generating function, entropy measures, stress-strength function, quantile function, and order statistics. The cumulative and probability density functions are also developed, providing a foundational structure for the model. Multiple estimation methods are employed to assess the accuracy and reliability of parameter estimates. Monte Carlo simulations further validate the model's robustness across various conditions. The practical utility of the GOBPW model is demonstrated through applications to three datasets: remission times of 132 bladder cancer patients (CD1), survival times of 73 acute bone cancer patients (CD2), and blood cancer data (CD3). Various evaluation metrics, including Akaike information criterion (AIC), Bayesian information criterion (BIC), Hannan–Quinn information criterion (HQIC), and consistent Akaike's information criterion (CAIC) were used to assess the performance of the competing models. For CD1, the GOBPW model achieves the lowest AIC (381.0622) and BIC (772.1244) among competing models. For CD2, GOBPW again demonstrates superior performance with the lowest AIC (140.2969) and BIC (290.5938), by capturing the extreme value behavior of acute bone cancer survival times more effectively. For CD3, the GOBPW model provides the best fit with an AIC of 65.7700 and BIC of 141.5400, outperforming all other competing models. This research offers a valuable tool for enhanced decision-making in medical data analysis, positioning the GOBPW distribution as a powerful alternative to traditional statistical models.