Robustness of the quartiles of survival time and survival probability

A simulation study was undertaken to investigate the robustness of the quartiles of survival times, survival probability (when survival time was equal to the quartile), and regression coefficients in the presence of covariates [by comparing the estimated values under the correct model (Weibull) with those obtained under the assumed models, such as Weibull, exponential, loglogistic, Cox proportional hazards, and product-limit estimator] when the assumptions related to the underlying model were violated. Two simulation experiments were conducted: the first for when the underlying model was Weibull with no covariate, and the second for when the underlying model was Weibull with one continuous covariate. An evaluation of the objectives of this study was done utilizing a real data set from the Lung Cancer Study Group 771. The results for both simulation experiments were quite comparable and consistent. In general, the exponential model performed poorly in estimating the quartiles (except the median) and the survival probabilities. The loglogistic model and product-limit estimator performed reasonably well for lower quartile and median. For the upper quartile when the shape parameter was less than 1.5 the performance was poor. For the regression coefficients, the estimates for beta1 and beta2 were biased under exponential model and the estimate for mu was quite biased under the loglogistic model. The performance of the Cox model was quite reasonable and only when the shape parameter was 0.7, the amount of bias for beta2 was slightly more than 10%. The results for the real data and the simulated data were comparable, which demonstrates the real application of this study.