Effects of Model Misspecification in Estimating Covariate Effects in Survival Analysis for Small Sample Sizes

The results of a Monte Carlo study of the size and power of parametric and semiparametric approaches to inference on covariate effects in survival (time-to-events) models in the presence of model misspecification and an independent censoring mechanism are reported. Basic models employed are a parametric model, where both a baseline distribution and the dependence structure of covariates on the failure times are fully specified (exponential, Weibull, log logistic, log normal, and normal regression models are studied), and a semi-parametric approach (due to Cox) in which the baseline distribution is unspecified. The Cox model performs very well compared to the parametric models for distributions with proportional hazard rates and appears to be robust with regard to the proportional hazard assumption. Appropriate parametric models have the potential of improving the size and power of the tests, although overall they are not appreciably better than the Cox model. In comparing the small sample performance of three statistical tests, the likelihood ratio and Wald tests closely agree with each other (likelihood ratio having a slight advantage), while the score test tends to perform much poorer since it inflates the size and power more than the other two.