A1619
Title: Nonparametric treatment model smoothing under sparsity for causal inference with longitudinal treatments
Authors: Mireille Schnitzer - Universite de Montreal (Canada) [presenting]
David Berger - Universite de Montreal (Canada)
Yan Liu - Universite de Montreal (Canada)
David Benkeser - Emory University (United States)
Abstract: Marginal structural models (MSM) for longitudinal treatments are often fit using estimates of the probability of treatment at each time point, conditional on covariate history. Such approaches are limited by data sparsity in the treatment model, i.e. practical positivity violations, which can greatly increase estimation variance. However, it is possible to smooth model features, including removing covariates that have no relationship with the outcome, in order to retain adjustment for confounding while sometimes greatly decreasing variance. A longitudinal outcome adaptive LASSO is previously proposed to perform covariate reduction in working parametric treatment models, which was successful in theory and practice at reducing estimation variance under structural and modeling assumptions. However, in addition to relying on parametric models, this approach does not allow for uniform convergence of the estimation of the treatment model functions, precluding inference for the MSM parameters. Therefore, the proposal is to extend the nonparametric outcome-highly-adaptive LASSO to longitudinal treatments, obtaining a regular asymptotically linear estimator under data-adaptive learning of the outcome model, under purposeful misspecification of the treatment model.
