Performance of Hypothesis Tests for Gompertz Distribution with Right and Interval Censored Data

Abstract

This study compared the performance of two hypothesis tests for the parameters of the Gompertz distribution in the presence of a covariate, right and interval censored data. Firstly, the performance of maximum likelihood estimation (with and without midpoint imputation) was assessed for this model at various censoring proportion (cp), sample sizes (n) and study periods (k) by computing the values of bias, standard error (SE) and root mean square error (RMSE) via simulation study. Following that, the power analysis was conducted to evaluate the performance of the Wald and Likelihood ratio (LR) test for the parameters of this model at various cp, n, k and effect sizes. The results indicated that the maximum likelihood estimates obtained via midpoint imputation performed better than the ones obtained without imputation. The results of the power analysis showed that the LR test performed better for parameter β₁ whereas the Wald test performed better for parameter γ. Finally, the model was fit to the real survival data of 94 patients with breast cancer, whose lifetimes were  either right or interval-censored. The covariate this study was the treatment type which were radiation therapy alone or the combination of radiation with chemotherapy.