Modern Innovations in Longitudinal Causal Inference for Health Applications

Numerous methods have been proposed in the last two decades for performing variable selection when the goal is to estimate the average treatment effect of a point exposure on an outcome. Much less work has focused on developing methods for performing variable selection when the goal is instead to estimate the causal effect of a longitudinal exposure on an outcome. We introduce a Bayesian model averaging approach to estimate the parameters of longitudinal marginal structural models. The Bayesian model averaging framework provides us with a principled way to produce valid post-selection inferences. We further devise an informative prior distribution that favors the selection of adjustment sets that produces estimators with reduced variance as compared with adjustment sets that include all potential confounders. We show through simulation results that our proposed method outperforms fully adjusted estimators and even performs similarly to an oracle estimator in several scenarios.  

Mediation analysis is crucial for understanding how a treatment exerts effects on an outcome via an intermediate variable, known as the mediator. Zero-inflated count outcomes and time-varying mediators are prevalent in fields such as biomedicine and biostatistics. To address the complex structure of the data, we extend existing mediation analysis methodologies by integrating a functional mediator in the context of zero-inflated count outcomes. The potential outcomes framework is employed to define the mediation effects of interest in this context and to provide the theoretical underpinning for our approach, including conditions for effect identification. Estimation and inference on the direct and indirect effects are performed by a quasi-Bayesian Monte Carlo approximation method using the well-known mediation formula. The methods are applied to study gender disparity in the number of re-admission to ICU for patients in MIMIC-IV, an electronic health record database.
 

Effect modification occurs when the impact of the treatment on an outcome varies based on the levels of other covariates known as effect modifiers. Modeling these effect differences is important for etiological goals and for purposes of optimizing treatment. Structural nested mean models (SNMMs) are useful causal models for estimating the potentially heterogeneous effect of a time-varying exposure on the mean of an outcome in the presence of time-varying confounding. A data-adaptive selection approach is necessary if the effect modifiers are unknown a priori and need to be identified. Although variable selection techniques are available for estimating the conditional average treatment effects using marginal structural models or for developing optimal dynamic treatment regimens, all of these methods consider a single end-of-follow-up outcome. In the context of an SNMM for repeated outcomes, we propose a doubly robust penalized G-estimator for the causal effect of a time-varying exposure with a simultaneous selection of effect modifiers and prove the oracle property of our estimator. We conduct a simulation study for the evaluation of its performance in finite samples and verification of its double-robustness property. Our work is motivated by the study of hemodiafiltration for treating patients with end-stage renal disease at the Centre Hospitalier de l'Université de Montréal. We apply the proposed method to investigate the effect heterogeneity of dialysis facility on the repeated session-specific hemodiafiltration outcomes. 

Longitudinal causal inference methods for non-stochastic interventions are sometimes severely limited by data sparsity due to the natural high-dimensionality of the longitudinal problem. Ad hoc statistical model smoothing is typically recommended in order to make the identifiability and estimation problem tractable. While nuisance functions with reduced dimensionality may be sufficient to identify the parameter of interest, the robust learning of these smoothed functions, and inference for the parameter of interest, have not yet been well-addressed in the literature. In this work, we propose a longitudinal version of the outcome-highly-adaptive LASSO that performs model smoothing in the time-point-specific propensity scores. We investigate the regular asymptotic linearity of the estimator both theoretically and empirically, and present results of the estimation variance reduction due to the smoothing procedure. 

Methods to develop optimal dynamic treatment regimes, such as q-learning and g-estimation, are typically used to find the optimal treatment drug to prescribe according to patient characteristics. However, these approaches could also be used to derive optimal decision rules for visit timing. In this work, we propose an extended doubly-robust approach to dynamic weighted ordinary least squares that can be used to derive optimal decision rules for visit and add-on drug treatment each month. The approach is demonstrated theoretically and in large simulation studies. It is compared with other dynamic treatment regimes approaches, such as Q-learning. Challenges in the estimation, such as longitudinal missing data, are discussed. The approach is further applied to data from the SPRINT trial in the United States to assess whether we can detect effect modification by patient characteristics, for the effect of visits and add-on treatment on a final blood pressure outcome. This is joint work with Tianze Jiao from the University of Florida.