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Adjustment for Variable Adherence Under Hierarchical Structure: Instrumental Variable Modeling Through Compound Residual Inclusion

Holmes, Tyson H. PhD*; Zulman, Donna M. MD, MS†,‡; Kushida, Clete A. MD, PhD§

doi: 10.1097/MLR.0000000000000464
Online Articles: Applied Methods

Background: Variable adherence to assigned conditions is common in randomized clinical trials.

Objectives: A generalized modeling framework under longitudinal data structures is proposed for regression estimation of the causal effect of variable adherence on outcome, with emphasis upon adjustment for unobserved confounders.

Research Design: A nonlinear, nonparametric random-coefficients modeling approach is described. Estimates of local average treatment effects among compliers can be obtained simultaneously for all assigned conditions to which participants are randomly assigned within the trial. Two techniques are combined to address time-varying and time-invariant unobserved confounding—residual inclusion and nonparametric random-coefficients modeling. Together these yield a compound, 2-stage residual inclusion, instrumental variables model.

Subjects: The proposed method is illustrated through a set of simulation studies to examine small-sample bias and in application to neurocognitive outcome data from a large, multicenter, randomized clinical trial in sleep medicine for continuous positive airway pressure treatment of obstructive sleep apnea.

Results: Results of simulation studies indicate that, relative to a standard comparator, the proposed estimator reduces bias in estimates of the causal effect of variable adherence. Bias reductions were greatest at higher levels of residual variance and when confounders were time varying.

Conclusions: The proposed modeling framework is flexible in the distributions of outcomes that can be modeled, applicable to repeated measures longitudinal structures, and provides effective reduction of bias due to unobserved confounders.

*Stanford University Human Immune Monitoring Center, Institute for Immunity Transplantation and Infection, Stanford University School of Medicine, Stanford

Center for Innovation to Implementation, VA Palo Alto Health Care System, Menlo Park

Department of Medicine, Division of General Medical Disciplines

§Stanford Sleep Medicine Center and Department of Psychiatry and Behavioral Sciences, Stanford University School of Medicine, Stanford, CA

T.H.H. was supported in part by the Department of Veterans Affairs Office of Specialty Care Transformation. D.M.Z. was supported by a Department of Veterans Affairs HSR&D Career Development Award (CDA 12-173). APPLES was funded by contract 5UO1-HL-068060 from the National Heart, Lung and Blood Institute. The APPLES pilot studies were supported by grants from the American Academy of Sleep Medicine and the Sleep Medicine Education and Research Foundation to Stanford University and by the National Institute of Neurological Disorders and Stroke (N44-NS-002394) to SAM Technology.

C.A.K. has received research support from Cephalon, Jawbone, ResMed, Pacific Medico, and Apnex; and is a consultant for Seven Dreamers, Zephyr Sleep Technologies, Morphy, and Nokia. The other authors have no conflict of interest to declare.

Reprints: Tyson H. Holmes, PhD, Stanford University Human Immune Monitoring Center, Institute for Immunity Transplantation and Infection, 299 Campus Drive, Fairchild Science Building, Stanford, CA 94305. E-mail:

Copyright © 2017 Wolters Kluwer Health, Inc. All rights reserved.