Assessing the adequacy of the gompertz regression model in the presence of right censored data

Abstract

The Gompertz distribution is often used to model human mortality and establish actuarial tables. Cox-Snell residual is the most general practice to evaluate the model adequacy. However, standard statistical procedures are not amenable to handle the censored observations. Therefore, this research investigates the adequacy of the two parameter Gompertz parametric survival model that was extended to incorporate with fixed covariate in the presence of right censored data. Performance of the model is assessed and compared at various combinations of sample sizes and censoring proportions via simulation study. The newly proposed modifications to the Cox-Snell residuals based on the geometric mean and harmonic mean as well as the jackknife means were compared with Cox-Snell and Modified Cox-Snell residuals via simulation studies at different settings. The log-cumulative hazard plot of residuals is obtained by plotting the proposed residuals against the cumulative hazard function to assess the model’s fit. Based on the model adequacy study, we found out that jackknife geometric mean and jackknife harmonic mean outperform CS, MCS, GMCS and HMCS residuals.