On Stacy’s Generalized Gamma Competing Risks Model: Estimation Procedure with Applications to Blood Cancer Data

Competing risks modeling plays a pivotal role in both reliability analysis for scientific and engineering fields and survival analysis within medical research. In real-world scenarios, failure or death (from a biological perspective) often arises from multiple risk factors that compete with one another. To adequately capture these complexities, it is essential to employ a flexible probabilistic framework, such as the competing risks model, which ensures suitability for intricate risk scenarios (e.g., analyzing data from aggressive diseases where treatment response and disease progression are closely interwoven). This study introduces Stacy’s competing risks model, built upon Stacy’s generalized gamma distribution, offering enhanced robustness and flexibility over existing models. The paper first develops the mathematical properties of the proposed model, followed by a detailed exploration of parameter estimation through various estimation methods. A key focus is accurately estimating shape parameters to gain deeper insights into the survival and failure mechanisms associated with the underlying phenomenon. The performance of different estimation approaches is assessed using Monte Carlo simulations, with results indicating that the least square, Cramér–von Mises, Anderson–Darling, right Anderson–Darling, and weighted least square had better performance and stable estimation accuracy compared with maximum likelihood maximum product of spacings methods. The model is applied to two real-world blood cancer datasets to demonstrate practical applicability, showing the superior performance and outstanding fit of the Anderson–Darling method among the other methods. The findings highlight the superior performance of Stacy’s competing risks model, supported by low Kolmogorov–Smirnov statistics and high p-values, affirming its suitability and robustness in modeling blood cancer data compared to other standard models.