Tests for no treatment effect in randomized clinical trials

Abstract

We propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals. These residuals result from regressing the response on covariates, but not treatment. In contrast to model-based score tests, this procedure maintains nominal size when the model is misspecified, and, in particular, when relevant covariates are omitted from the regression. The efficiency of the procedure is evaluated for regressions with some, but not all, required covariates. For many generalized linear models and survival models, conventional model-based score tests are shown to have supranominal size when relevant covariates are omitted, but logistic regression and the proportional hazards model are robust.