A note on Using regression models to analyze randomized trials: asymptotically valid hypothesis tests despite incorrectly specified models.

In the context of randomized trials, Rosenblum and van der Laan (2009, Biometrics 63, 937-945) considered the null hypothesis of no treatment effect on the mean outcome within strata of baseline variables. They showed that hypothesis tests based on linear regression models and generalized linear regression models are guaranteed to have asymptotically correct Type I error regardless of the actual data generating distribution, assuming the treatment assignment is independent of covariates. We consider another important outcome in randomized trials, the time from randomization until failure, and the null hypothesis of no treatment effect on the survivor function conditional on a set of baseline variables. By a direct application of arguments in Rosenblum and van der Laan (2009), we show that hypothesis tests based on multiplicative hazards models with an exponential link, i.e., proportional hazards models, and multiplicative hazards models with linear link functions where the baseline hazard is parameterized, are asymptotically valid under model misspecification provided that the censoring distribution is independent of the treatment assignment given the covariates. In the case of the Cox model and linear link model with unspecified baseline hazard function, the arguments in Rosenblum and van der Laan (2009) cannot be applied to show the robustness of a misspecified model. Instead, we adopt an approach used in previous literature (Struthers and Kalbfleisch, 1986, Biometrika 73, 363-369) to show that hypothesis tests based on these models, including models with interaction terms, have correct type I error.