The Comparison of Survival Right Censored Log-Logistic Models for Breast Cancer Bootstrap Data

Breast cancer is a significant global health concern, with increasing incidence and mortality rates particularly affecting women worldwide. In Malaysia, limited data exists on how survival rates vary across different age groups, despite evidence that breast cancer behavior differs by age. Due to time constraints, this study only included data from 32 patients and five variables. This study addresses the gap by examining survival rates in two age groups of breast cancer patients from Johor, Malaysia, using right-censored data from 32 women treated at Hospital Sultan Ismail. The cutoff point of $\mathbf{5 2}$ years is based on the mean age of the dataset, which helps simplify the analysis while ensuring meaningful comparison within the available data. Due to limited data, bootstrapping methods were employed to address small sample sizes, while survival analysis, specifically the Kaplan-Meier method, was used to assess survival patterns. Contrary to previous findings, older patients showed a higher probability of survival. The accuracy of bootstrapping method was validated through coverage probability, which exceeded $70 \%$ for all datasets. The log-logistic model with 100 replications was the best fit based on statistical measures like AIC, BIC, and p-values. Despite no significant interactions between variables, this study highlights the need for further research with additional variables and parametric models to improve breast cancer survival analysis in Malaysia