Estimation of heterogeneous treatment effects is an active area of research in causal inference. Most of the existing methods, however, focus on estimating the conditional average treatment effects of a single, binary treatment given a set of pre-treatment covariates. In this paper, we propose a method to estimate the heterogeneous causal effects of high-dimensional treatments, which poses unique challenges in terms of estimation and interpretation. The proposed approach is based on a Bayesian mixture of regularized logistic regressions to identify groups of units who exhibit similar patterns of treatment effects. By directly modeling cluster membership with covariates, the proposed methodology allows one to explore the unit characteristics that are associated with different patterns of treatment effects. Our motivating application is conjoint analysis, which is a popular survey experiment in social science and marketing research and is based on a high-dimensional factorial design. We apply the proposed methodology to the conjoint data, where survey respondents are asked to select one of two immigrant profiles with randomly selected attributes. We find that a group of respondents with a relatively high degree of prejudice appears to discriminate against immigrants from non-European countries like Iraq. An open-source software package is available for implementing the proposed methodology.
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The One-versus-One (OvO) strategy is an approach of multi-classification models which focuses on training binary classifiers between each pair of classes. While the OvO strategy takes advantage of balanced training data, the classification accuracy is usually hindered by the voting mechanism to combine all binary classifiers. In this paper, a novel OvO multi-classification model incorporating a joint probability measure is proposed under the deep learning framework. In the proposed model, a two-stage algorithm is developed to estimate the class probability from the pairwise binary classifiers. Given the binary classifiers, the pairwise probability estimate is calibrated by a distance measure on the separating feature hyperplane. From that, the class probability of the subject is estimated by solving a joint probability-based distance minimization problem. Numerical experiments in different applications show that the proposed model achieves generally higher classification accuracy than other state-of-the-art models.
Estimating heterogeneous treatment effects is crucial for informing personalized treatment strategies and policies. While multiple studies can improve the accuracy and generalizability of results, leveraging them for estimation is statistically challenging. Existing approaches often assume identical heterogeneous treatment effects across studies, but this may be violated due to various sources of between-study heterogeneity, including differences in study design, confounders, and sample characteristics. To this end, we propose a unifying framework for multi-study heterogeneous treatment effect estimation that is robust to between-study heterogeneity in the nuisance functions and treatment effects. Our approach, the multi-study R-learner, extends the R-learner to obtain principled statistical estimation with modern machine learning (ML) in the multi-study setting. The multi-study R-learner is easy to implement and flexible in its ability to incorporate ML for estimating heterogeneous treatment effects, nuisance functions, and membership probabilities, which borrow strength across heterogeneous studies. It achieves robustness in confounding adjustment through its loss function and can leverage both randomized controlled trials and observational studies. We provide asymptotic guarantees for the proposed method in the case of series estimation and illustrate using real cancer data that it has the lowest estimation error compared to existing approaches in the presence of between-study heterogeneity.
Estimating dynamic treatment effects is essential across various disciplines, offering nuanced insights into the time-dependent causal impact of interventions. However, this estimation presents challenges due to the "curse of dimensionality" and time-varying confounding, which can lead to biased estimates. Additionally, correctly specifying the growing number of treatment assignments and outcome models with multiple exposures seems overly complex. Given these challenges, the concept of double robustness, where model misspecification is permitted, is extremely valuable, yet unachieved in practical applications. This paper introduces a new approach by proposing novel, robust estimators for both treatment assignments and outcome models. We present a "sequential model double robust" solution, demonstrating that double robustness over multiple time points can be achieved when each time exposure is doubly robust. This approach improves the robustness and reliability of dynamic treatment effects estimation, addressing a significant gap in this field.
We develop a methodology for conducting inference on extreme quantiles of unobserved individual heterogeneity (heterogeneous coefficients, heterogeneous treatment effects, etc.) in a panel data or meta-analysis setting. Inference in such settings is challenging: only noisy estimates of unobserved heterogeneity are available, and approximations based on the central limit theorem work poorly for extreme quantiles. For this situation, under weak assumptions we derive an extreme value theorem and an intermediate order theorem for noisy estimates and appropriate rate and moment conditions. Both theorems are then used to construct confidence intervals for extremal quantiles. The intervals are simple to construct and require no optimization. Inference based on the intermediate order theorem involves a novel self-normalized intermediate order theorem. In simulations, our extremal confidence intervals have favorable coverage properties in the tail. Our methodology is illustrated with an application to firm productivity in denser and less dense areas.
The problem of generalization and transportation of treatment effect estimates from a study sample to a target population is central to empirical research and statistical methodology. In both randomized experiments and observational studies, weighting methods are often used with this objective. Traditional methods construct the weights by separately modeling the treatment assignment and study selection probabilities and then multiplying functions (e.g., inverses) of their estimates. In this work, we provide a justification and an implementation for weighting in a single step. We show a formal connection between this one-step method and inverse probability and inverse odds weighting. We demonstrate that the resulting estimator for the target average treatment effect is consistent, asymptotically Normal, multiply robust, and semiparametrically efficient. We evaluate the performance of the one-step estimator in a simulation study. We illustrate its use in a case study on the effects of physician racial diversity on preventive healthcare utilization among Black men in California. We provide R code implementing the methodology.
A treatment policy defines when and what treatments are applied to affect some outcome of interest. Data-driven decision-making requires the ability to predict what happens if a policy is changed. Existing methods that predict how the outcome evolves under different scenarios assume that the tentative sequences of future treatments are fixed in advance, while in practice the treatments are determined stochastically by a policy and may depend, for example, on the efficiency of previous treatments. Therefore, the current methods are not applicable if the treatment policy is unknown or a counterfactual analysis is needed. To handle these limitations, we model the treatments and outcomes jointly in continuous time, by combining Gaussian processes and point processes. Our model enables the estimation of a treatment policy from observational sequences of treatments and outcomes, and it can predict the interventional and counterfactual progression of the outcome after an intervention on the treatment policy (in contrast with the causal effect of a single treatment). We show with real-world and semi-synthetic data on blood glucose progression that our method can answer causal queries more accurately than existing alternatives.
There are well-established methods for identifying the causal effect of a time-varying treatment applied at discrete time points. However, in the real world, many treatments are continuous or have a finer time scale than the one used for measurement or analysis. While researchers have investigated the discrepancies between estimates under varying discretization scales using simulations and empirical data, it is still unclear how the choice of discretization scale affects causal inference. To address this gap, we present a framework to understand how discretization scales impact the properties of causal inferences about the effect of a time-varying treatment. We introduce the concept of "identification bias", which is the difference between the causal estimand for a continuous-time treatment and the purported estimand of a discretized version of the treatment. We show that this bias can persist even with an infinite number of longitudinal treatment-outcome trajectories. We specifically examine the identification problem in a class of linear stochastic continuous-time data-generating processes and demonstrate the identification bias of the g-formula in this context. Our findings indicate that discretization bias can significantly impact empirical analysis, especially when there are limited repeated measurements. Therefore, we recommend that researchers carefully consider the choice of discretization scale and perform sensitivity analysis to address this bias. We also propose a simple and heuristic quantitative measure for sensitivity concerning discretization and suggest that researchers report this measure along with point and interval estimates in their work. By doing so, researchers can better understand and address the potential impact of discretization bias on causal inference.
This paper develops an approximation to the (effective) $p$-resistance and applies it to multi-class clustering. Spectral methods based on the graph Laplacian and its generalization to the graph $p$-Laplacian have been a backbone of non-euclidean clustering techniques. The advantage of the $p$-Laplacian is that the parameter $p$ induces a controllable bias on cluster structure. The drawback of $p$-Laplacian eigenvector based methods is that the third and higher eigenvectors are difficult to compute. Thus, instead, we are motivated to use the $p$-resistance induced by the $p$-Laplacian for clustering. For $p$-resistance, small $p$ biases towards clusters with high internal connectivity while large $p$ biases towards clusters of small ``extent,'' that is a preference for smaller shortest-path distances between vertices in the cluster. However, the $p$-resistance is expensive to compute. We overcome this by developing an approximation to the $p$-resistance. We prove upper and lower bounds on this approximation and observe that it is exact when the graph is a tree. We also provide theoretical justification for the use of $p$-resistance for clustering. Finally, we provide experiments comparing our approximated $p$-resistance clustering to other $p$-Laplacian based methods.
Estimating heterogeneous treatment effects from observational data is a crucial task across many fields, helping policy and decision-makers take better actions. There has been recent progress on robust and efficient methods for estimating the conditional average treatment effect (CATE) function, but these methods often do not take into account the risk of hidden confounding, which could arbitrarily and unknowingly bias any causal estimate based on observational data. We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on the level of hidden confounding. We derive the B-Learner by adapting recent results for sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into the framework given by Kallus & Oprescu (2023) for robust and model-agnostic learning of conditional distributional treatment effects. The B-Learner can use any function estimator such as random forests and deep neural networks, and we prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods. Semi-synthetic experimental comparisons validate the theoretical findings, and we use real-world data to demonstrate how the method might be used in practice.
Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.
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