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Med Care. 2017 Dec;55(12):e120-e130. doi: 10.1097/MLR.0000000000000464. Epub 2016 Jan 13.

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

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*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.



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


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.


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.


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 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.


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.

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