Test for Trend with a Multinomial Outcome

There is no established procedure for testing for trend with nominal outcomes that would provide both a global hypothesis test and outcome-specific inference. We derive a simple formula for such a test using a weighted sum of Cochran-Armitage test statistics evaluating the trend in each outcome separately. The test is shown to be equivalent to the score test for multinomial logistic regression, however the new formulation enables the derivation of a sample size formula and multiplicity-adjusted inference for individual outcomes. The proposed methods are implemented in the R package multiCA.