Mixed Effects Models--Discrete Data with Non-Compliance

University Of Pennsylvania, Philadelphia PA

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Abstract

DESCRIPTION (provided by applicant): We propose extending current statistical methodologies for estimating causal treatment effects under non-ignorable treatment non-compliance in psychiatric randomized trials to modeling clustered discrete responses with mixed effects logistic models. By non-ignorable non-compliance, we mean non-adherence to randomized treatment assignments that is associated with unmeasured factors related to outcome. This work is motivated by the bias that results with intent-to-treat and treatment-received analyses in these contexts, the absence of mixed effects discrete response methodology for non-compliance, the compatibility between the presence of random effects and the interpretation of causal effects, and the psychiatric-based justification of underlying time-varying latent variables and time-invariant random effect structures that account for confounding relationships between outcomes and compliance. In addition to developing models and estimation approaches, the methodological focus will be on sensitivity analyses using data analyses and simulations by varying the nature and degree of these assumptions. Specifically, we intend to extend several current methods for noncompliance (Robins' semi-parametric causal models, instrumental variable models, compliance score and latent class models, and non-counterfactual models) to the mixed effects discrete response context and to nested levels of compliance (e.g., patient and provider compliance). Several estimation methods will be investigated: 1) a numerical integration approach that allows asymmetric random effects distributions in multiple random effects frameworks including nested random effects; 2) generalized estimating-equations for mixed effects models; and 3) penalized quasi-likelihood (PQL) for data with few but large clusters (e.g., primary care practices) and large variance components, where it has been shown to yield consistent estimators (Ten Have and Localio 1999). These methods will be assessed with simulations and applications to motivating datasets from four randomized studies including two primary care practice-based trials for depression, a trial of treating depression in a nursing home, and a randomized behavioral intervention for cardiovascular disease.