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Title: Structural nested models for cluster-randomized trials with cluster-level non-adherence Authors:  Babette Brumback - University of Florida (United States) [presenting]
Abstract: Much attention has been paid to estimating the causal effect of adherence to a randomized protocol using instrumental variables to adjust for unmeasured confounding. The interest stems from a wish to estimate the effect of cluster-level adherence on individual-level binary outcomes with a three-armed cluster-randomized trial and polytomous adherence. We developed two structural-nested modeling approaches for estimation; the approaches differ in the handling of measured individual-level confounders of the effect of randomization on the outcome. The first approach uses a weighted generalized structural nested mean model, which adjusts for the confounders using weights, and the second approach uses an ordinary generalized structural nested mean model, which stratifies on the confounders. The two approaches target different estimands. The methodology accommodates cluster-randomized trials with unequal probability of selecting individuals. Furthermore, we developed a method to implement the approaches with relatively simple programming. The approaches work reasonably well, but when the structural-nested model does not fit the data, there may be no solution to the estimating equation. We investigate the performance of the approaches using simulated data, and we also use them to estimate the effect on pupil absence of school-level adherence to a randomized water, sanitation, and hygiene intervention in western Kenya.