A hybrid Log-Logistic-Weibull Regression Model for survival analysis in leukemia patients and radiation data
Mohamed A. Abd Elgawad, Abubakar Usman, Sani Ibrahim Doguwa, Ibrahim Abubakar Sadiq, Yahaya Zakari, Aliyu Ismail Ishaq, Ahmad Abubakar Suleiman, Atef F. Hashem
Abstract
Recently, researchers developed survival regression models and applied them to a wide range of survival data. To model these diverse forms of survival datasets, a new model, termed the Log-Logistic-Weibull Regression Model for Modeling the Survival Time of Leukemia Cancer Patients, is proposed. The proposed approach comprises two baseline values, an intercept that is independent of the covariates, and two covariates that characterize how changes in the covariates affect the patients' outcomes (survival times). An extensive simulation study is carried out to investigate the consistency of the estimators. The findings and trends show that increasing the sample size improves parameter estimate accuracy and precision across all methods. The maximum product of spacings regularly outperforms the other techniques. For the real-world application, Leukemia Cancer Survival Data is used with two important covariates (observed variables from the patients): white blood cell count (WBC) at diagnosis and a binary variate AG that indicates a positive (AG = 1) or negative (AG = 2) test related to white blood cell characteristics, with 1 = death and 0 = life. The coefficient of WBC (white blood cell count) was found to be 6.9601 (an increase of WBC), indicating that as WBC increases will result in a shorter survival. Similarly, the Coefficient for AG = 1 (positive test) is 1.5001, indicating a higher hazard. This indicates a positive test result in a higher hazard or shorter survival time than an AG = 0 (negative test). The hypothesis is presented and tested based on the effect of covariates on the outcome; otherwise, the results revealed that WBC and AG = 1 have an effect on the Leukemia Cancer Patients' Survival time based on the p-value. Both in training and test datasets, including subgroups like choice, non-choice, packet, and non-packet scenarios, the LL-Weibull model once again outperformed other models in the analysis of the radiation dataset across a number of evaluation measures (AIC, BIC, HQIC, and CAIC). The model captured the susceptibility dynamics influenced by radiation exposure and offered a better fit and predictive power. This demonstrates how the LL-Weibull model can be used to model a variety of survival data outside of oncology, such as toxicological or environmental studies.