Exploring time-to-event analysis models: A study of accelerated failure time and weighted least square estimation

Background: This study explores time-to-event analysis models, focusing on the comparison between accelerated failure time (AFT) and weighted least square estimation (WLSE) methods in analyzing survival data, emphasizing the challenge of heteroscedasticity in real-world datasets. Methods: Using the North Central Cancer Treatment Group (NCCTG) Lung Cancer dataset, five parametric AFT distributions (exponential, Weibull, log-logistic, log-normal, and generalized gamma) were evaluated. The log-likelihood method was utilized to calculate the AIC and BIC values for each distribution to determine the best fit model. Results: Among the different distributions tested, the Weibull distribution was identified as the best fit model based with the lowest AIC and BIC values of 2311.70 and 2318.56, respectively. This distribution played a crucial role in determining factors associated with the cancer data. Specifically, the variablecalories consumed at a meal (meal.cal) was associated with cancer patient recovery, with an estimate of 0.00004 and a standard error of 0.0002. Results indicated homoscedastic data through the Breusch-Pagan test. Moreover, the results demonstrated that when dealing with homoscedastic data, the Weibull AFT model outperformed WLSE in producing statistically significant effects and precise estimates. Conclusion: For data exhibiting homoscedasticity, the AFT method yielded superior results compared to WLSE in terms of statistical significance and precision. Therefore, it is advisable to employ AFT for homoscedastic data and WLSE for heteroscedastic data to enhance the accuracy of covariate effect estimates in survival analysis.