Bootstrap Resampling Method for Assessing Model Adequacy of the Gompertz Model with Right-Censored Data - Azid @ Maarof, Nur Niswah Naslina; Arasan, Jayanthi; Zulkafli , Hani Syahida (Journal of Quality Measurement and Analysis, 2026)
Traditional Cox-Snell residuals are widely used for assessing goodness-of-fit in survival models, but they often perform inadequately in the presence of high censoring or small sample sizes, leading to poor model diagnostics. To address this limitation, this study extends the Gompertz parametric survival model by incorporating a single fixed covariate under right-censored data and proposes new modifications to the Cox-Snell residuals aimed at improving diagnostic accuracy. A comprehensive simulation study was conducted across varying levels of censoring and sample sizes, using maximum likelihood estimation to fit the model. Four novel residuals were developed by applying harmonic mean, geometric mean, bootstrap harmonic mean, and bootstrap geometric mean transformations to the standard Cox-Snell residuals. These modified residuals were evaluated using regression diagnostics consisting of intercept, slope, and R-squared values obtained from plots of the residuals against the cumulative hazard function. The findings show that the bootstrap-based residuals, particularly the bootstrap harmonic mean and bootstrap geometric mean, consistently provide better goodness-of-fit assessments than both the traditional Cox-Snell residuals and their non-bootstrap counterparts. These results highlight the potential of the proposed residuals to enhance model evaluation, especially in settings with substantial censoring or limited data.