Test equality in binary data for a 4 × 4 crossover trial under a Latin-square design

When there are four or more treatments under comparison, the use of a crossover design with a complete set of treatment-receipt sequences in binary data is of limited use because of too many treatment-receipt sequences. Thus, we may consider use of a 4 × 4 Latin square to reduce the number of treatment-receipt sequences when comparing three experimental treatments with a control treatment. Under a distribution-free random effects logistic regression model, we develop simple procedures for testing non-equality between any of the three experimental treatments and the control treatment in a crossover trial with dichotomous responses. We further derive interval estimators in closed forms for the relative effect between treatments. To evaluate the performance of these test procedures and interval estimators, we employ Monte Carlo simulation. We use the data taken from a crossover trial using a 4 × 4 Latin-square design for studying four-treatments to illustrate the use of test procedures and interval estimators developed here. Copyright © 2016 John Wiley & Sons, Ltd.