Effect of covariate omission in Weibull accelerated failure time model: a caution

The accelerated failure time model is presented as an alternative to the proportional hazard model in the analysis of survival data. We investigate the effect of covariates omission in the case of applying a Weibull accelerated failure time model. In an uncensored setting, the asymptotic bias of the treatment effect is theoretically zero when important covariates are omitted; however, the asymptotic variance estimator of the treatment effect could be biased and then the size of the Wald test for the treatment effect is likely to exceed the nominal level. In some cases, the test size could be more than twice the nominal level. In a simulation study, in both censored and uncensored settings, Type I error for the test of the treatment effect was likely inflated when the prognostic covariates are omitted. This work remarks the careless use of the accelerated failure time model. We recommend the use of the robust sandwich variance estimator in order to avoid the inflation of the Type I error in the accelerated failure time model, although the robust variance is not commonly used in the survival data analyses.