Estimating the treatment effect in high-dimensions under interference
Abstract
ABSTRACT (APPROVED FOR PUBLIC RELEASE)Does a specific treatment (e.g., a new hypertension drug, an academic scholarship, a public health mandate) affect the outcome of interest (blood pressure, student performance, health outcome respectively)? Answering this question poses serious challenges if the treated and control groups are incomparable. For example, if a new drug is often prescribed topatients in a critical condition, one cannot (in general) learn the effects of the drug on the healthy population from the observeddata. To circumvent this difficulty, one traditionally assumes that the difference between the two populations can be summarized interms of a few features, and one has access to these features on the study units. In this case, scientists have devised innovative statistical methodology to adjust for these differences post hoc and estimate the relevant causal relationship. Another common assumption is that of no interference i.e., all the study units respond independently to being assigned to the treatment or control group. In sharp contrast, in this age of big data, one has access to a large number of features for each study unit. These features can differ between the treatment and control groups in intricate, and subtle ways. In addition, in settings such as social networks, there is additional interference---an individual#s response is potentially affected by the treatment status of their neighbors. This project will develop new statistical methodology to estimate causal relationships in these modern settings with many features and interference among observational units.Formally, this project will develop novel statistical theory for causal effect estimation in settings with interference and high dimensional covariates. The interference structure will be encoded in terms of an underlying graphon.The project will investigate causal effect estimation under (i) independent treatment assignments, (ii) dependent treatment assignments (specified by Markov Random Fields), (iii) temporal dependence. In each case, we will focus on IPW type estimators for causal estimands of interest and characterize their limiting sampling distribution. We will develop consistent estimates for the sampling variance, thus facilitating uncertainty quantification for the causal effect. The results will be agnostic to sparsity structures in the underlying model. To achieve these goals, this project will crucially employ ideas from graph limit theory, graphical models, variational inference and approximate message passing.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- May 15, 2023
- Source ID
- N000142312489
Entities
People
- Subhabrata Sen
Organizations
- Office of Naval Research
- President and Fellows of Harvard College
- United States Navy