Randomization inference in a group-randomized trial of treatments for depression: Covariate adjustment, noncompliance, and quantile effects

In the Prospect Study, in 10 pairs of two primary-care practices, one practice was picked at random to receive a depression care manager to treat its depressed patients. Randomization inference, properly performed, reflects the assignment of practices, not patients, to treatment or control. Yet, pertinent data describe individual patients: depression outcomes, baseline covariates, compliance with treatment. The methods discussed use only (i) the random assignment of clusters to treatment or control and (ii) the hypothesis about effects being tested or inverted for confidence intervals, so they are randomization inferences in Fisher's strict sense. There is no assumption that the covariance model generated the data, that compliers resemble noncompliers, that dependence is from additive random cluster effects, that individuals in a same cluster do not interfere with one another, or that units are sampled from a population. We contrast methods of covariance adjustment, never assuming the models are true, obtaining exact randomization inferences. We consider exact inference about effects proportional to doses with noncompliance and effects whose magnitude varies with the degree of improvement that would occur without treatment. A simulation examines power.