Longitudinal nested compliance class model in the presence of time -varying noncompliance

We propose nested latent compliance class models for analyzing longitudinal randomized trials when subjects do not always adhere to the treatment to which they are randomized, and treatment adherence may vary over time. Traditional intention-to-treat and as-treated analyses may produce biased causal effect estimates in the presence of subject noncompliance. Utilizing nested latent compliance class models that use subject-specific and time-invariant superclasses allow us to summarize longitudinal trends of compliance patterns, and estimate the effect of the intervention using intent-to-treat contrasts within principal strata (PS) corresponding to longitudinal compliance behavior patterns. First we propose a conditional independence model where the time-varying compliance classes within a subject are assumed to be independent given compliance superclass and covariates. Then we propose a Markov model where time-varying compliance classes are assumed to relate to history of compliance, compliance superclass, and covariates. Finally, we search for good predictors of longitudinal compliance and examine the relationship between longitudinal compliance and mortality. We illustrate these models with analyses of a randomized intervention study of elderly patients in primary care clinics with depression. Our analyses show that those who are highly compliant with treatment assignment are more likely to benefit from the intervention and show improvement in their depression severity. Those with history of compliance are more likely to comply with their treatment assignment than those with history of noncompliance. In this intervention study, subjects with higher physical functioning are more likely to be highly compliant than subjects with lower physical functioning. Additionally, highly compliant subjects have lower 4-year all-cause mortality than noncompliant subjects