Conditional Monte Carlo randomization tests for regression models

We discuss the computation of randomization tests for clinical trials of two treatments when the primary outcome is based on a regression model. We begin by revisiting the seminal paper of Gail, Tan, and Piantadosi (1988), and then describe a method based on Monte Carlo generation of randomization sequences. The tests based on this Monte Carlo procedure are design based, in that they incorporate the particular randomization procedure used. We discuss permuted block designs, complete randomization, and biased coin designs. We also use a new technique by Plamadeala and Rosenberger (2012) for simple computation of conditional randomization tests. Like Gail, Tan, and Piantadosi, we focus on residuals from generalized linear models and martingale residuals from survival models. Such techniques do not apply to longitudinal data analysis, and we introduce a method for computation of randomization tests based on the predicted rate of change from a generalized linear mixed model when outcomes are longitudinal. We show, by simulation, that these randomization tests preserve the size and power well under model misspecification.