Beyond intent to treat (ITT): A complier average causal effect (CACE) estimation primer.

Randomized control trials (RCTs) have long been the gold standard for allowing causal inferences to be made regarding the efficacy of a treatment under investigation, but traditional RCT data analysis perspectives do not take into account a common reality: imperfect participant compliance to treatment. Recent advances in both maximum likelihood parameter estimation and mixture modeling methodology have enabled treatment effects to be estimated, in the presence of less than ideal levels of participant compliance, via a Complier Average Causal Effect (CACE) structural equation mixture model. CACE is described in contrast to "intent to treat" (ITT), "per protocol", and "as treated" RCT data analysis perspectives. CACE model assumptions, specification, estimation, and interpretation will all be demonstrated with simulated data generated from a randomized controlled trial of cognitive-behavioral therapy for Juvenile Fibromyalgia. CACE analysis model figures, linear model equations, and Mplus estimation syntax examples are all provided. Data needed to reproduce analyses in this article are available as supplemental materials (online only) in the Appendix of this article.