Nonparametric estimation in causal inference: optimality in traditional models and newer ones

This project provides new methods for estimating causal effects from non-randomized studies. Quantifying the causal effect of a variable on another one is of fundamental importance in science because it allows for the understanding of what happens if a certain action is taken, e.g., if a drug is prescribed to a patient. When randomized experiments are not feasible, e.g., because of costs or ethical concerns, quantifying the effect of a treatment on an outcome can be very challenging. Roughly, this is because the analysis must ensure that the treated and untreated units are “comparable,” a condition implied by proper randomization. In these settings, the analyst typically proceeds in two steps: 1) they introduce the key assumptions needed to identify the causal effect, and 2) they specify a model for the distribution of the data, often nonparametric, to accommodate modern, complex datasets, as well as the appropriate estimation strategy. One key difficulty in non-randomized studies is that estimating causal effects typically requires estimating nuisance components of the data distribution that are not of direct interest and that can be potentially quite hard to estimate. Focused on the second part of the analysis, this project aims to design optimal methods for estimating causal effects in different settings. Informally, an optimal estimator converges to the true causal effect “as quickly as possible” as a function of the sample size and thus leads to the most precise inferences. Establishing optimality has thus two fundamental benefits: 1) it leads to procedures that make the most efficient use of the available data, and 2) it serves as a benchmark against which future methods can be evaluated. In this respect, the theoretical and methodological contributions of this project are expected to lead to substantial improvements in the analysis of data from many domains, such as medicine and the social sciences. The project also aims to offer opportunities for training and mentoring graduate and undergraduate students. For certain estimands and data structures, the principles of semiparametric efficiency theory can be used to derive optimal estimators. However, they are not directly applicable to causal parameters that are “non-smooth” or for which the nuisance parts of the data distribution can only be estimated at such slow rates that root-n convergence of the causal effect estimator is not attainable. As part of this project, the Principal Investigator aims to study the optimal estimation of prominent examples of non-smooth parameters, such as causal effects defined by continuous treatments. Furthermore, this project will consider optimal estimation of “smooth” parameters, such as certain average causal effects, in newer nonparametric models for which relatively fast rates of convergence are possible, even if certain components of the data distribution can only be estimated at very slow rates. In doing so, the project aims to propose new techniques for reducing the detrimental effect of the nuisance estimators’ bias on the quality of the causal effect estimator. It also aims to design and implement inferential procedures for the challenging settings considered, thereby enhancing the adoption of the methods proposed in practice. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.