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Summary: We consider a Markov structure for partially unobserved time-varying compliance classes in the Imbens-Rubin (1997, The Annals of Statistics 25, 305-327) 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 longitudinal trends of subject-specific time-varying compliance patterns. The principal strata are formed using Markov models that relate current compliance behavior to compliance history. Treatment effects are estimated as intent-to-treat effects within the compliance principal strata.

Motivated by the need to meaningfully implement the Institute of Medicine's (IOM's) definition of health care disparity, this paper proposes statistical frameworks that lay out explicitly the needed causal assumptions for defining disparity measures. Our key emphasis is that a scientifically defensible disparity measure must take into account the direction of the causal relationship between allowable covariates that are not considered to be contributors to disparity and non-allowable covariates that are considered to be contributors to disparity, to avoid flawed disparity measures based on implausible populations that are not relevant for clinical or policy decisions. However, these causal relationships are usually unknown and undetectable from observed data. Consequently, we must make strong causal assumptions in order to proceed. Two frameworks are proposed in this paper, one is the conditional disparity framework under the assumption that allowable covariates impact non-allowable covariates but not vice versa. The other is the marginal disparity framework under the assumption that non-allowable covariates impact allowable ones but not vice versa. We establish theoretical conditions under which the two disparity measures are the same and present a theoretical example showing that the difference between the two disparity measures can be arbitrarily large. Using data from the Collaborative Psychiatric Epidemiology Survey, we also provide an example where the conditional disparity is misled by Simpson's paradox, whereas the marginal disparity approach handles it correctly.

Lin et al. (http://www.biostatsresearch.com/upennbiostat/papers/, 2006) proposed a nested Markov compliance class model in the Imbens and Rubin compliance class model framework to account for time-varying subject noncompliance in longitudinal randomized intervention studies. We use superclasses, or latent compliance class principal strata, to describe longitudinal compliance patterns, and time-varying compliance classes are assumed to depend on the history of compliance. In this paper, we search for good subject-level baseline predictors of these superclasses and also examine the relationship between these superclasses and all-cause mortality. Since the superclasses are completely latent in all subjects, we utilize multiple imputation techniques to draw inferences. We apply this approach to a randomized intervention study for elderly primary care patients with depression., (Copyright 2007 John Wiley & Sons, Ltd.)

Purpose: We review and compare two causal modeling approaches that correspond to two major and distinct classes of inference - efficacy and intervention-based inference - in the context of randomized trials with subject noncompliance., Methods: We review the definitions of efficacy and intervention-based effects in the clinical trials literature and relate these to two separate and distinct causal modeling approaches: the structural mean modeling (SMM) approach and the principal stratification, instrumental variable approach., Results: The SMM-based efficacy approach focuses on the effect of actually receiving treatment. In contrast, the principal stratification method addresses the effect of treatment assignment within partially unobserved latent subgroups defined by compliance behavior. While these approaches differ in terms of philosophy, model definitions, and estimation, they estimate the same causal effect under certain assumptions, but estimate very different causal effects when those assumptions are relaxed. We illustrate these results using a randomized psychiatry trial where the focus is physician compliance to the designated protocol and the other examines patient compliance to the designated protocol, both from the same trial., Limitations: The validity of the models under the instrumental variable, SMM and principal stratification approaches depends on modeling assumptions, some of which may not be verifiable from the observed data and potentially less realistic than the no-confounding assumption made by non-causal approaches., Conclusions: This comparison in terms of efficacy versus intervention-based effects in causal modeling parallels the explanatory versus pragmatic approaches in clinical trials research; therefore researchers should weigh carefully when choosing causal modeling methodology based on whether efficacy or intervention-based effects are of interest.