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1. Overlap in observational studies with high-dimensional covariates

   D’Amour, A; Ding, P; Feller, A; Lei, L; Sekhon, J (January 2020, Journal of econometrics)

   Estimating causal effects under exogeneity hinges on two key assumptions: unconfoundedness and overlap. Researchers often argue that unconfoundedness is more plausible when more covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in observational studies with high-dimensional covariates and formalize curse-of-dimensionality argument, suggesting that these assumptions are stronger than investigators likely realize. Our key innovation is to explore how strict overlap restricts global discrepancies between the covariate distributions in the treated and control populations. Exploiting results from information theory, we derive explicit bounds on the average imbalance in covariate means under strict overlap and show that these bounds become more restrictive as the dimension grows large. We discuss how these implications interact with assumptions and procedures commonly deployed in observational causal inference, including sparsity and trimming. 

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2. Asymptotic theory of rerandomization in treatment–control experiments

   https://doi.org/10.1073/pnas.1808191115  

   Li, Xinran; Ding, Peng; Rubin, Donald B. (September 2018, Proceedings of the National Academy of Sciences)

   Although complete randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect. 

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3. Constructing multiple, independent analyses in the regression discontinuity design with multiple cutoffs

   https://doi.org/10.1353/obs.2024.a946585  

   Lee, Youjin; Tan, Chichun; Karmakar, Bikram (January 2024, Observational Studies)

   Abstract: The regression discontinuity (RD) design is a commonly used non-experimental approach for evaluating policy or program effects. However, this approach heavily relies on the untestable assumption that distribution of confounders or average potential outcomes near or at the cutoff are comparable. When there are multiple cutoffs that create several discontinuities in the treatment assignments, factors that can lead this assumption to the failure at one cutoff may overlap with those at other cutoffs, invalidating the causal effects from each cutoff. In this study, we propose a novel approach for testing the causal hypothesis of no RD treatment effect that can remain valid even when the assumption commonly considered in the RD design does not hold. We propose leveraging variations in multiple available cutoffs and constructing a set of instrumental variables (IVs). We then combine the evidence from multiple IVs with a direct comparison under the local randomization framework. This reinforced design that combines multiple factors from a single data can produce several, nearly independent inferential results that depend on very different assumptions with each other. Our proposed approach can be extended to a fuzzy RD design. We apply our method to evaluate the effect of having access to higher achievement schools on students' academic performances in Romania. 

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4. Causal Matching using Random Hyperplane Tessellations

   Dalvi, Abhishek; Ashtekar, Neil; Honavar, Vasant G (April 2024, Proceedings of Machine Learning Research: Proceedings of the Third Conference on Causal Learning and Reasoning)

   Matching is one of the simplest approaches for estimating causal effects from observational data. Matching techniques compare the observed outcomes across pairs of individuals with similar covariate values but different treatment statuses in order to estimate causal effects. However, traditional matching techniques are unreliable given high-dimensional covariates due to the infamous curse of dimensionality. To overcome this challenge, we propose a simple, fast, yet highly effective approach to matching using Random Hyperplane Tessellations (RHPT). First, we prove that the RHPT representation is an approximate balancing score – thus maintaining the strong ignorability assumption – and provide empirical evidence for this claim. Second, we report results of extensive experiments showing that matching using RHPT outperforms traditional matching techniques and is competitive with state-of-the-art deep learning methods for causal effect estimation. In addition, RHPT avoids the need for computationally expensive training of deep neural networks. 

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5. Double Machine Learning Density Estimation for Local Treatment Effects with Instruments

   Jung, Y.; Tian, J.; Bareinboim, E. (January 2021, Advances in neural information processing systems)

   It is common to quantify causal effects with mean values, which, however, may fail to capture significant distribution differences of the outcome under different treatments. We study the problem of estimating the density of the causal effect of a binary treatment on a continuous outcome given a binary instrumental variable in the presence of covariates. Specifically, we consider the local treatment effect, which measures the effect of treatment among those who comply with the assignment under the assumption of monotonicity (only the ones who were offered the treatment take it). We develop two families of methods for this task, kernel-smoothing and model-based approximations -- the former smoothes the density by convoluting with a smooth kernel function; the latter projects the density onto a finite-dimensional density class. For both approaches, we derive double/debiased machine learning (DML) based estimators. We study the asymptotic convergence rates of the estimators and show that they are robust to the biases in nuisance function estimation. We illustrate the proposed methods on synthetic data and a real dataset called 401(k). 

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