Causal Inference in Hybrid Intervention Trials Involving Treatment Choice
Randomized allocation of treatments is a cornerstone of experimental design but has drawbacks when a limited set of individuals are willing to be randomized, or the act of randomization undermines the success of the treatment. Choice-based experimental designs allow a subset of the participants to choose their treatments. We discuss here causal inferences for hybrid experimental designs in which some participants are randomly allocated to treatments and others receive their treatment preference. This work was motivated by the Women Take Pride (WTP) study, a doubly randomized preference trial (DRPT) that assessed behavioral interventions for women with heart disease. We propose a model for estimating the causal effects in the subpopulations defined by treatment preferences, and thus preference effects. We describe an EM algorithm for computing maximum likelihood estimates of the model parameters. We illustrate the method by analyzing sickness impact profile (SIP) scores and treatment adherence in the WTP data. Our results show some evidence that SIP scores were improved when women received their preferred treatment and strong preference effects on program adherence; that is, women assigned to their preferred treatment were more likely to adhere to the program. We also provide a framework for assessing the DRPT and other hybrid trial designs and discuss some alternative designs from the perspective of the strength of assumptions required to make causal inferences. Please see the supplemental material for a correction to this article.