Causal Inference with Complex Treatments: A Survey

Observational studies are often used to understand relationships between exposures and outcomes. They do not, however, allow conclusions about causal relationships to be drawn unless statistical techniques are used to account for the imbalance of confounders across exposure groups. Propensity score and balance weighting (PSBW) are useful techniques that aim to reduce the imbalances between exposure groups by weighting the groups to look alike on the observed confounders. Despite the plethora of available methods to estimate PSBW, there is little guidance on what one defines as adequate balance, and unbiased and robust estimation of the causal treatment effect is not guaranteed unless several conditions hold. Accurate inference requires that 1. the treatment allocation mechanism is known, 2. the relationship between the baseline covariates and the outcome is known, 3. adequate balance of baseline covariates is achieved post-weighting, 4. a proper set of covariates to control for confoun …

Estimating the individual treatment effect (ITE) from observational data is essential in medicine. A central challenge in estimating the ITE is handling confounders, which are factors that affect both an intervention and its outcome. Most previous work relies on the unconfoundedness assumption, which posits that all the confounders are measured in the observational data. However, if there are unmeasurable (latent) confounders, then confounding bias is introduced. Fortunately, noisy proxies for the latent confounders are often available and can be used to make an unbiased estimate of the ITE. In this paper, we develop a novel adversarial learning framework to make unbiased estimates of the ITE using noisy proxies.

Much research has been devoted to the problem of estimating treatment effects from observational data; however, most methods assume that the observed variables only contain confounders, i.e., variables that affect both the treatment and the outcome. Unfortunately, this assumption is frequently violated in real-world applications, since some variables only affect the treatment but not the outcome, and vice versa. Moreover, in many cases only the proxy variables of the underlying confounding factors can be observed. In this work, we first show the importance of differentiating confounding factors from instrumental and risk factors for both average and conditional average treatment effect estimation, and then we propose a variational inference approach to simultaneously infer latent factors from the observed variables, disentangle the factors into three disjoint sets corresponding to the instrumental, confounding, and risk factors, and use the disentangled factors for treatment effect est …

The defining challenge for causal inference from observational data is the presence of `confounders', covariates that affect both treatment assignment and the outcome. To address this challenge, practitioners collect and adjust for the covariates, hoping that they adequately correct for confounding. However, including every observed covariate in the adjustment runs the risk of including `bad controls', variables that induce bias when they are conditioned on. The problem is that we do not always know which variables in the covariate set are safe to adjust for and which are not. To address this problem, we develop Nearly Invariant Causal Estimation (NICE). NICE uses invariant risk minimization (IRM) [Arj19] to learn a representation of the covariates that, under some assumptions, strips out bad controls but preserves sufficient information to adjust for confounding. Adjusting for the learned representation, rather than the covariates themselves, avoids the induced bias and provides valid …

State-of-the-art methods for conditional average treatment effect (CATE) estimation make widespread use of representation learning. Here, the idea is to reduce the variance of the low-sample CATE estimation by a (potentially constrained) low-dimensional representation. However, low-dimensional representations can lose information about the observed confounders and thus lead to bias, because of which the validity of representation learning for CATE estimation is typically violated. In this paper, we propose a new, representation-agnostic framework for estimating bounds on the representation-induced confounding bias that comes from dimensionality reduction (or other constraints on the representations) in CATE estimation.