  Hypothesis tests based on linear models are widely accepted by organizations
that regulate clinical trials. These tests are derived using strong assumptions
about the data-generating process so that the resulting inference can be based
on parametric distributions. Because these methods are well understood and
robust, they are sometimes applied to data that depart from assumptions, such
as ordinal integer scores. Permutation tests are a nonparametric alternative
that require minimal assumptions which are often guaranteed by the
randomization that was conducted. We compare analysis of covariance (ANCOVA), a
special case of linear regression that incorporates stratification, to several
permutation tests based on linear models that control for pretreatment
covariates. In simulations of randomized experiments using models which violate
some of the parametric regression assumptions, the permutation tests maintain
power comparable to ANCOVA. We illustrate the use of these permutation tests
alongside ANCOVA using data from a clinical trial comparing the effectiveness
of two treatments for gastroesophageal reflux disease. Given the considerable
costs and scientific importance of clinical trials, an additional nonparametric
method, such as a linear model permutation test, may serve as a robustness
check on the statistical inference for the main study endpoints.
