A new competing risks model with applications to blood cancer data

Competing risks models are invaluable probabilistic models in survival analysis, a particular part of medical research. Such models deal with research problems that involve multiple potential risk factors that compete with each other to cause death (i.e., failure from a statistical perspective). Competing risks models' flexibility must be thoroughly explored to guarantee suitability for multifaceted risk scenarios (e.g., modeling data of malicious diseases where factors such as treatment response and progression are intertwined). This article considers a new competing risks model called the additive generalized linear-exponential (AGLE) competing risks model. The proposed model is expected to be more robust and superior to other well-known models when modeling real-life data. A mathematical treatment for the properties of the new model is first considered. Afterward, model parameters estimation via various estimation methods is discussed. The critical role of estimating shape parameters in understanding blood cancer's survival and failure mechanisms is highlighted. Furthermore, the bias and root mean square error of different estimation methods are examined numerically through Monte Carlo simulations. The simulation study indicated that the maximum product of spacings estimation method for the model parameters has the optimal balance of bias and variance as the sample sizes increase. Two real-life blood cancer data sets are analyzed to illustrate the application of the proposed model. The analysis outcomes support the AGLE model's robustness, with low Kolmogorov-Smirnov statistics and high p-value, affirming its superior fit for blood cancer data compared to other well-known models.