Accelerated Failure Time (AFT) and Weighted Least Square Estimation (WLSE) With Five Different Underlying Distributions: A Model Comparison to the Application of Cancer Survival Data Analysis

Survival data have been extensively analyzed using the parametric model. As cited in the literature in the statistical area of survival analysis, an alternative to the widely used cox proportional hazard (PH) model is the accelerated failure time (AFT) model, which is parametric model. If the model imposed distribution and homoscedasticity assumption are met, the AFT model is more effective and comprehensible than the cox PH model. However, most of the real datasets are heteroscedastic which violate the fundamental assumption. The weighted least square estimation (WLSE), a method that is just developed recently, is a semi-parametric methodology that can handle homoscedastic and heteroscedastic data. Furthermore, a valid inference can be obtained from the WLSE. In this paper, we used AFT with the application of WLSE method to a real dataset specifically on cancer data. The findings show that among the different distributions that were generated, the Weibull having the lowest AIC and BIC values, made the best fit of the model which further determine the factor associated on cancer data. With the use of homoscedasticity test, the data was found to be homoscedastic. The finding also show that, in case of homoscedastic data, the Weibull AFT outperformed in terms of generating more significant effects and more precise estimations of covariates effect than the WLSE method. Thus, it is recommended to use AFT model rather than the WLSE when the homoscedasticity assumption is met.