The cross-section conditional compliance model (Imbens and Rubin 1997) posits the exists of up to four types of experimental subjects in a randomized trial setting with two arms (e.g., treatment and control): "compliers," who comply with the treatment arm to which they are assigned; "always-takers," who always take the treatment; "never-takers," who always take the control; and "defiers," who take the control if assigned to treatment and the treatment if assigned to control. (In setting where those assigned to the control cannot access the treatment, only compliers and never-takers can exist.) These types are "principal strata" that are assumed to exist before treatment assignment: meaningful causal estimators exist only among compliers and defiers (if the latter are assumed to exist) since they are the only subjects whose treatment will be affect by assignment. These principal strata are at least partially latent (e.g., those on control who take the control could be either compliers or never-takers).

We extend the conditional compliance model (Imbens and Rubin 1997) to the longitudinal setting by the use of latent classes or "superclasses": time-invariant principal strata that summarize compliance class behavior across time.

• "Longitudinal Nested Compliance Class Model in the Presence of Time-Varying Noncompliance," Lin JY, Ten Have TR, and Elliott MR (2008), Journal of the American Statistical Association, 103, 462-473.
This manuscript defines superclass principal strata using a latent class conditional independence model (Clogg 1995).
• "Nested Markov Compliance Class Model in the Presence of Time-Varying Noncompliance," Lin JY, Ten Have TR, and Elliott MR (2009), Biometrics, 65, 505-513.
This manuscript extends the latent class conditional independence model for modeling the superclasses to accommodate autoregressive structure in compliance behavior using latent transition models (Collins and Wugalter 1992, Reboussin et al. 2002).
• "Baseline Patient Characteristics and Mortality Associated with Longitudinal Intervention Compliance," Lin JY, Ten Have TR, and Elliott MR (2007), Statistics in Medicine, 26, 5100-5115.
This manuscript utilizes the model of "Nested Markov Compliance Class Model in the Presence of Time-Varying Noncompliance" to conduct exploratory analyses of compliance class predictors, and the examine the relationship between baseline compliance class membership and all-cause mortality.