A Weibull-fréchet Proportional Hazard Model with Applications to Tuberculosis Data
Abdulfatai Lawal *
Department of Mathematics and Statistics, Kaduna Polytechnic, Nigeria.
Tasi'u Musa
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.
Yakubu Aliyu
Department of Statistics, Ahmadu Bello University, Zaria, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper extends the application of survival analysis by adopting a Weibull-Fréchet distribution within the framework of the Cox Proportional Hazard (PH) model. The study focuses on 319 Tuberculosis (TB) patients from National TB and Leprosy Center Hospital, Kaduna, Nigeria (NTLCHKN). It extends the Weibull-Fréchet distribution via it hazard function to a proportional Hazard model framework and estimated the parameters using maximum likelihood estimation with Newton Raphson optimization in R-software. In the analysis of NTLCHKN data, the Weibull-Fréchet Proportional Hazard (WFr) Model demonstrates superior fitting compared to the Weibull Proportional Hazard Model. Consequently, result from the model identifies age, gender, type of TB, smoking history, and comorbidities (hepatitis and HIV-AIDS) as significant predictors of TB mortality. This research contributes to the ongoing advancements in survival analysis, highlighting the efficacy of the distribution in modeling TB mortality and providing valuable insights for tailored interventions and improved patient outcomes in TB management. Thus, the model can be employed as preferred alternative choice for researchers and practitioners engaged in tuberculosis survival data or other phenomenon data on survival analysis.
Keywords: Tuberculosis, proportional hazards, Cox’s model, Weibull-Fréchet distribution