Frontiers in Causal and Missing Data Settings: Robustness, Adaptation, and Inference

A key challenge in causal inference is determining causal effects in the presence of unmeasured variables. Proxy variable methods have become a notable framework for tackling this issue. One influential line of work formulates identification as an eigendecomposition task, recovering intermediate distributions that comprise the target functional. Existing literature in causal inference has demonstrated how eigendecomposition approaches can be used to account for hidden confounding and hidden treatments. Our contribution extends this framework to hidden outcomes, identifying counterfactual distributions and deriving an influence function–based estimation strategy for causal effects. Although methods for handling missing and mismeasured outcomes exist, this work provides what we believe to be the first proximal inference results for hidden outcomes. We illustrate our estimation approach through simulation studies and anticipate results from a real-world data application soon. 

Conformal Prediction (CP) has recently received a tremendous amount of interest, leading to
a wide range of new theoretical and methodological results for predictive inference with formal
theoretical guarantees. However, the vast majority of CP methods assume that all units in the
training data have fully observed data on both the outcome and covariates of primary interest, an
assumption that rarely holds in practice. In reality, training data are often missing the outcome,
a subset of covariates, or both on some units. In addition, time-to-event outcomes in the training
set may be censored due to dropout or administrative end-of-follow-up. Accurately accounting
for such coarsened data in the training sample while fulfilling the primary objective of well-calibrated conformal predictive inference, requires robustness and efficiency considerations. In
this paper, we consider the general problem of obtaining distribution-free valid prediction regions
for an outcome given coarsened training data. Leveraging modern semiparametric theory, we
achieve our goal by deriving the efficient influence function of the quantile of the outcome we aim
to predict, under a given semiparametric model for the coarsened data, carefully combined with
a novel conformal risk control procedure. Our principled use of semiparametric theory has the
key advantage of facilitating flexible machine learning methods such as random forests to learn
the underlying nuisance functions of the semiparametric model. A straightforward application of
the proposed general framework produces prediction intervals with stronger coverage properties
under covariate shift, as well as the construction of multiply robust prediction sets in monotone
missingness scenarios. We further illustrate the performance of our methods through various
simulation studies. (Joint work with Manit Paul and Eric Tchetgen Tchetgen. Available at https://arxiv.org/pdf/2508.15489.) 

The bootstrap is a popular method of constructing confidence intervals due to its ease of use and broad applicability. Theoretical properties of bootstrap procedures have been established in a variety of settings. However, there is limited theoretical research on the use of the bootstrap in the context of estimation of a differentiable functional in a nonparametric or semiparametric model in the presence of nuisance functions. We provide general conditions for consistency of the bootstrap in such scenarios. Our results cover a range of estimator constructions, nuisance estimation methods, bootstrap sampling distributions, and bootstrap confidence interval types. We provide refined results for the empirical bootstrap and smoothed bootstraps, and for one-step estimators, plug-in estimators, empirical mean plug-in estimators, and estimating equations-based estimators. We illustrate the use of our general results by demonstrating the asymptotic validity of bootstrap confidence intervals for the average density value and G-computed conditional mean parameters, and compare their performance in finite samples using numerical studies. Throughout, we emphasize whether and how the bootstrap can produce asymptotically valid confidence intervals when standard methods fail to do so. This is joint work with Zhou Tang. A preprint of the paper is available here: https://arxiv.org/abs/2404.03064. 

In causal inference with observational data when treatment is continuous rather than discrete, new inferential targets arise. Here we form (simultaneous) confidence bands over the continuous treatment effect curve. We form confidence bands based on assuming the curve satisfies shape constraints such as monotonicity, under the assumption of no unmeasured confounding. The assumption of monotonicity (or unimodality) is often a natural one for the treatment effect curve, at least over a reasonable domain of treatment. As is commonly the case, two nuisance functions arise, and our bands are ``doubly robust'' in the sense that they are asymptotically valid if the product of the error rates of the two nuisance functions is small enough. Furthermore, our bands are adaptive to a range of function smoothness values in that when the true smoothness level is unknown the bands still achieve the same (optimal) rate of convergence (in sup-norm) as when the true smoothness level is known. If time permits we will also develop analogous confidence bands under the constraint of concavity.