Likelihood based inferences for trials incorporating participant's treatment choice

Randomized clinical trials are the gold standard for clinical trials as they reduce bias and minimize variability between different arms of a study. One of the drawbacks of these designs is their lack of flexibility to incorporate participant's treatment choice, which may reduce recruitment rates and/or reduce participant's tolerance if they receive a non-preferred treatment. Designs incorporating choice allow a subset of participants to choose their preferred treatment. Most of the current methods to analyze these types of designs are based on an ANOVA approach that do not allow for inclusion of covariates in the model. In this paper, we propose an alternative approach based on likelihood methods that can be used with a broad class of distributions and allow for inclusion of covariates and multiple study arms in the model. Using simulations, we evaluate these methods for a variety of continuous and categorical outcomes. Finally, we illustrate these methods by analyzing change in six minute walking distance from a behavioral intervention study for women with heart disease.