We consider a Markov structure for partially unobserved time-varying compliance classes in the Imbens-Rubin (1997) compliance model framework. The context is a longitudinal randomized intervention study where subjects are randomized once at baseline, outcomes and patient adherence are measured at multiple follow-ups, and patient adherence to their randomized treatment could vary over time. We propose a nested latent compliance class model where we use time-invariant subject-specific compliance principal strata to summarize longtudinal trends of subject-specific time-varying compliance patterns. The principal strata are formed using Markov models that related current compliance behavior to compliance history. Treatment effects are estimated as intent-to -treat effects within the compliance principal strata.
Lin, Julia Y.; TenHave, Thomas R.; and Elliott, Michael R., "Nested Markov Compliance Class Model in the Presence of Time-Varying Noncompliance" (August 2006). UPenn Biostatistics Working Papers. Working Paper 11.