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Register a new userAssignment-Control Plots: A Visual Companion for Causal Inference Study Design
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Added by
Rachael C Aikens
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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An important step for any causal inference study design is understanding the distribution of the treated and control subjects in terms of measured baseline covariates. However, not all baseline variation is equally important. In the observational context, balancing on baseline variation summarized in a propensity score can help reduce bias due to self-selection. In both observational and experimental studies, controlling baseline variation associated with the expected outcomes can help increase the precision of causal effect estimates. We propose a set of visualizations which decompose the space of measured covariates into the different types of baseline variation important to the study design. These ``assignment-control plots and variations thereof visually illustrate core concepts of causal inference and suggest new directions for methodological research on study design. As a practical demonstration, we illustrate one application of assignment-control plots to a study of cardiothoracic surgery. While the family of visualization tools for studies of causality is relatively sparse, simple visual tools can be an asset to education, application, and methods development.
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Marginal structural models (MSM) with inverse probability weighting (IPW) are used to estimate causal effects of time-varying treatments, but can result in erratic finite-sample performance when there is low overlap in covariate distributions across different treatment patterns. Modifications to IPW which target the average treatment effect (ATE) estimand either introduce bias or rely on unverifiable parametric assumptions and extrapolation. This paper extends an alternate estimand, the average treatment effect on the overlap population (ATO) which is estimated on a sub-population with a reasonable probability of receiving alternate treatment patterns in time-varying treatment settings. To estimate the ATO within a MSM framework, this paper extends a stochastic pruning method based on the posterior predictive treatment assignment (PPTA) as well as a weighting analogue to the time-varying treatment setting. Simulations demonstrate the performance of these extensions compared against IPW and stabilized weighting with regard to bias, efficiency and coverage. Finally, an analysis using these methods is performed on Medicare beneficiaries residing across 18,480 zip codes in the U.S. to evaluate the effect of coal-fired power plant emissions exposure on ischemic heart disease hospitalization, accounting for seasonal patterns that lead to change in treatment over time.
Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.
In a comprehensive cohort study of two competing treatments (say, A and B), clinically eligible individuals are first asked to enroll in a randomized trial and, if they refuse, are then asked to enroll in a parallel observational study in which they can choose treatment according to their own preference. We consider estimation of two estimands: (1) comprehensive cohort causal effect -- the difference in mean potential outcomes had all patients in the comprehensive cohort received treatment A vs. treatment B and (2) randomized trial causal effect -- the difference in mean potential outcomes had all patients enrolled in the randomized trial received treatment A vs. treatment B. For each estimand, we consider inference under various sets of unconfoundedness assumptions and construct semiparametric efficient and robust estimators. These estimators depend on nuisance functions, which we estimate, for illustrative purposes, using generalized additive models. Using the theory of sample splitting, we establish the asymptotic properties of our proposed estimators. We also illustrate our methodology using data from the Bypass Angioplasty Revascularization Investigation (BARI) randomized trial and observational registry to evaluate the effect of percutaneous transluminal coronary balloon angioplasty versus coronary artery bypass grafting on 5-year mortality. To evaluate the finite sample performance of our estimators, we use the BARI dataset as the basis of a realistic simulation study.
The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and testing those assumptions is important to assess the validity of causal inference. We develop model criticism for Bayesian causal inference, building on the idea of posterior predictive checks to assess model fit. Our approach involves decomposing the problem, separately criticizing the model of treatment assignments and the model of outcomes. Conditioned on the assumption of unconfoundedness---that the treatments are assigned independently of the potential outcomes---we show how to check any additional modeling assumption. Our approach provides a foundation for diagnosing model-based causal inferences.
Weighting methods are a common tool to de-bias estimates of causal effects. And though there are an increasing number of seemingly disparate methods, many of them can be folded into one unifying regime: causal optimal transport. This new method directly targets distributional balance by minimizing optimal transport distances between treatment and control groups or, more generally, between a source and target population. Our approach is model-free but can also incorporate moments or any other important functions of covariates that the researcher desires to balance. We find that the causal optimal transport outperforms competitor methods when both the propensity score and outcome models are misspecified, indicating it is a robust alternative to common weighting methods. Finally, we demonstrate the utility of our method in an external control study examining the effect of misoprostol versus oxytocin for treatment of post-partum hemorrhage.
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