Data‐adaptive longitudinal model selection in causal inference with collaborative targeted minimum loss‐based estimation

Abstract

Causal inference methods have been developed for longitudinal observational study designs where confounding is thought to occur over time. In particular, one may estimate and contrast the population mean counterfactual outcome under specific exposure patterns. In such contexts, confounders of the longitudinal treatment‐outcome association are generally identified using domain‐specific knowledge. However, this may leave an analyst with a large set of potential confounders that may hinder estimation. Previous approaches to data‐adaptive model selection for this type of causal parameter were limited to the single time‐point setting. We develop a longitudinal extension of a collaborative targeted minimum loss‐based estimation (C‐TMLE) algorithm that can be applied to perform variable selection in the models for the probability of treatment with the goal of improving the estimation of the population mean counterfactual outcome under a fixed exposure pattern. We investigate the properties of this method through a simulation study, comparing it to G‐Computation and inverse probability of treatment weighting. We then apply the method in a real‐data example to evaluate the safety of trimester‐specific exposure to inhaled corticosteroids during pregnancy in women with mild asthma. The data for this study were obtained from the linkage of electronic health databases in the province of Quebec, Canada. The C‐TMLE covariate selection approach allowed for a reduction of the set of potential confounders, which included baseline and longitudinal variables.

Causal Inference using Multivariate Generalized Linear Mixed-Effects Models with Longitudinal Data

“…The work has several advantages. First, existing ways of incorporating propensity score (PS) in Bayesian causal inference (D. Li, Iddi, Thompson, Donohue, & Initiative, 2019) include specifying outcome distribution conditional on PS (Zhou et al, 2019), having shared priors between propensity and outcome models, or using an inverse probability weighting or doubly robust estimator (Schnitzer, Sango, Ferreira Guerra, & Van der Laan, 2020); our method provides a new way to connect the propensity with the outcomes and time-varying confounders via the dependence structure on the subject-specific unobserved heterogeneity of the model components. Second, our method naturally incorporates unmeasured time-invariant factors via the random effects in MGLMM, for which the estimated covariances partially inform possible existence of unmeasured confounders.…”