arXiv subjects

Alec McClean

Publications and source records attributed to Alec McClean.

10 recordsLinked to original sources

arXiv2025

Non-overlap Average Treatment Effect Bounds

The average treatment effect (ATE), the mean difference in potential outcomes under treatment and control, is a canonical causal effect. Overlap, which says that all subjects have non-zero probability of either treatment status, is necessary to identify and estimate the ATE. When overlap fails, the standard solution is to change the estimand, and target a trimmed effect in a subpopulation satisfying overlap. When the outcome is bounded, we demonstrate that this compromise is unnecessary. We derive non-overlap bounds: partial identification bounds on the ATE that do not require overlap. The bounds have width proportional to the size of the non-overlap subpopulation, making them informative in common scenarios when overlap violations are limited. Since the bounds are non-smooth functionals, we derive smooth approximations amenable to semiparametric efficiency theory and propose a Targeted Minimum Loss-Based estimator that is $\sqrt{n}$-consistent and asymptotically normal under nonparametric conditions. A multiplier bootstrap procedure yields uniformly valid confidence sets across all non-overlap subpopulation sizes and smoothing parameters, allowing researchers to report the tightest valid interval. Formally, we compare non-overlap confidence intervals to confidence intervals based on point estimation across multiple overlap regimes. We illustrate the method via simulation studies and real-world data applications.

stat.ME↗

arXiv2025

Propensity score weighting across counterfactual worlds: longitudinal effects under positivity violations

When examining a contrast between two interventions, longitudinal causal inference studies frequently encounter positivity violations when one or both regimes are impossible to observe for some subjects. Existing weighting methods either assume positivity holds or produce effects that conflate interventions' impacts on ultimate outcomes with their effects on intermediate treatments and covariates. We propose a novel class of estimands -- cumulative cross-world weighted effects -- that weights potential outcome differences using propensity scores adapting to positivity violations cumulatively across timepoints and simultaneously across both counterfactual treatment histories. This new estimand isolates mechanistic differences between treatment regimes, is identifiable without positivity assumptions, and circumvents the limitations of existing longitudinal methods. Further, our analysis reveals two fundamental insights about longitudinal causal inference under positivity violations. First, while mechanistically meaningful, these effects correspond to non-implementable interventions, exposing a core interpretability-implementability tradeoff. Second, the identified effects faithfully capture mechanistic differences only under a partial common support assumption; violations cause the identified functional to collapse to zero, even when the causal effect is non-zero. We develop doubly robust-style estimators that achieve asymptotic normality and parametric convergence under nonparametric assumptions on the nuisance estimators. To this end, we reformulate challenging density ratio estimation as regression function estimation, which is achievable with standard machine learning methods. We illustrate our methods through analysis of union membership's effect on earnings.

stat.ME↗

arXiv2025

Longitudinal weighted and trimmed treatment effects with flip interventions

Weighting and trimming are popular methods for addressing positivity violations in causal inference. While well-studied with single-timepoint data, standard methods do not easily generalize to address non-baseline positivity violations in longitudinal data, and remain vulnerable to such violations. In this paper, we extend weighting and trimming to longitudinal data via stochastic ``flip'' interventions, which maintain the treatment status of subjects who would have received the target treatment, and flip others' treatment to the target with probability equal to their weight (e.g., overlap weight, trimming indicator). We first show, in single-timepoint data, that flip interventions yield a large class of weighted average treatment effects, ascribing a novel policy interpretation to these popular weighted estimands. With longitudinal data, we then show that flip interventions provide interpretable weighting or trimming on non-baseline covariates and, crucially, yield effects that are identifiable under arbitrary positivity violations. Moreover, we demonstrate that flip interventions are policy-relevant since they could be implemented in practice. By contrast, we show that alternative approaches for weighting on non-baseline covariates fail to achieve this property. We derive flexible and efficient estimators based on efficient influence functions when the weight is a smooth function of the propensity score. Namely, we construct multiply robust-style and sequentially doubly robust-style estimators that achieve root-n consistency and asymptotic normality under nonparametric conditions. Finally, we demonstrate our methods through an analysis of the effect of union membership on earnings.

stat.ME↗

arXiv2024

Stochastic interventions, sensitivity analysis, and optimal transport

Recent methodological research in causal inference has focused on effects of stochastic interventions, which assign treatment randomly, often according to subject-specific covariates. In this work, we demonstrate that the usual notion of stochastic interventions have a surprising property: when there is unmeasured confounding, bounds on their effects do not collapse when the policy approaches the observational regime. As an alternative, we propose to study generalized policies, treatment rules that can depend on covariates, the natural value of treatment, and auxiliary randomness. We show that certain generalized policy formulations can resolve the "non-collapsing" bound issue: bounds narrow to a point when the target treatment distribution approaches that in the observed data. Moreover, drawing connections to the theory of optimal transport, we characterize generalized policies that minimize worst-case bound width in various sensitivity analysis models, as well as corresponding sharp bounds on their causal effects. These optimal policies are new, and can have a more parsimonious interpretation compared to their usual stochastic policy analogues. Finally, we develop flexible, efficient, and robust estimators for the sharp nonparametric bounds that emerge from the framework.

stat.ME↗

arXiv2024

Comparing causal parameters with many treatments and positivity violations

Comparing outcomes across treatments is essential in medicine and public policy. To do so, researchers typically estimate a set of parameters, possibly counterfactual, with each targeting a different treatment. Treatment-specific means are commonly used, but their identification requires a positivity assumption, that every subject has a non-zero probability of receiving each treatment. This is often implausible, especially when treatment can take many values. Causal parameters based on dynamic stochastic interventions offer robustness to positivity violations. However, comparing these parameters may fail to reflect the effects of the underlying target treatments because the parameters can depend on outcomes under non-target treatments. To clarify when two parameters targeting different treatments yield a useful comparison of treatment efficacy, we propose a comparability criterion: if the conditional treatment-specific mean for one treatment is greater than that for another, then the corresponding causal parameter should also be greater. Many standard parameters fail to satisfy this criterion, but we show that only a mild positivity assumption is needed to identify parameters that yield useful comparisons. We then provide two simple examples that satisfy this criterion and are identifiable under the milder positivity assumption: trimmed and smooth trimmed treatment-specific means with multi-valued treatments. For smooth trimmed treatment-specific means, we develop doubly robust-style estimators that attain parametric convergence rates under nonparametric conditions. We illustrate our methods with an analysis of dialysis providers in New York State.

stat.ME↗

arXiv2024

Calibrated sensitivity models

In causal inference, sensitivity models assess how unmeasured confounders could alter causal analyses, but the sensitivity parameter -- which quantifies the degree of unmeasured confounding -- is often difficult to interpret. For this reason, researchers sometimes compare the sensitivity parameter to an estimate of measured confounding. This is known as calibration, or benchmarking. However, calibrated estimates are not always interpreted correctly, and uncertainty in the estimate of measured confounding is rarely accounted for. To address these limitations, we propose calibrated sensitivity models, which directly bound the degree of unmeasured confounding by a multiple of measured confounding. We develop a clear framework for interpreting calibrated sensitivity models and derive statistical methods for accounting for uncertainty due to estimating measured confounding. Incorporating this uncertainty shows causal analyses may be either less or more robust to unmeasured confounding than suggested by standard approaches. We develop efficient estimators and inferential methods for bounds on the average treatment effect with three calibrated sensitivity models, establishing parametric efficiency and asymptotic normality under doubly robust style nonparametric conditions. We illustrate our methods with an analysis of the effect of mothers' smoking on infant birthweight.

stat.ME↗

arXiv2024

Double Cross-fit Doubly Robust Estimators: Beyond Series Regression

Doubly robust estimators with cross-fitting have gained popularity in causal inference due to their favorable structure-agnostic error guarantees. However, when additional structure, such as H\"{o}lder smoothness, is available then more accurate "double cross-fit doubly robust" (DCDR) estimators can be constructed by splitting the training data and undersmoothing nuisance function estimators on independent samples. We study a DCDR estimator of the Expected Conditional Covariance, a functional of interest in causal inference and conditional independence testing. We first provide a structure-agnostic error analysis for the DCDR estimator with no assumptions on the nuisance functions or their estimators. Then, assuming the nuisance functions are H\"{o}lder smooth, but without assuming knowledge of the true smoothness level or the covariate density, we establish that DCDR estimators with several linear smoothers are $\sqrt{n}$-consistent and asymptotically normal under minimal conditions and achieve fast convergence rates in the non-$\sqrt{n}$ regime. When the covariate density and smoothnesses are known, we propose a minimax rate-optimal DCDR estimator based on undersmoothed kernel regression. Moreover, we show an undersmoothed DCDR estimator satisfies a slower-than-$\sqrt{n}$ central limit theorem, and that inference is possible even in the non-$\sqrt{n}$ regime. Finally, we support our theoretical results with simulations, providing intuition for double cross-fitting and undersmoothing, demonstrating where our estimator achieves $\sqrt{n}$-consistency while the usual "single cross-fit" estimator fails, and illustrating asymptotic normality for the undersmoothed DCDR estimator.

math.ST↗

arXiv2023

Incremental Propensity Score Effects for Criminology: An Application Assessing the Relationship Between Homelessness, Behavioral Health Problems, and Recidivism

This study examines the relationship between homelessness and recidivism among people on probation with and without behavioral health problems. The study also illustrates a new way to summarize the effect of an exposure on an outcome, the Incremental Propensity Score (IPS) effect, which avoids pitfalls of other approaches commonly used in criminology. We assessed the impact of homelessness at probation start on rearrest within one year among a cohort of people on probation (n = 2,453). We estimated IPS effects, considering general and crime-specific recidivism if subjects were more or less likely to be unhoused, and assessed effect variation by behavioral health problem status. We used a doubly robust machine learning estimator to flexibly but efficiently estimate effects. A substantial intervention -- reducing homelessness by roughly 65% -- corresponded to a 9% reduction in the estimated average rate of recidivism (p < .05). Milder interventions showed smaller, non-significant effect sizes. Stratifying by behavioral health problem and rearrest type led to similar results without statistical significance. Minding limitations related to observational data and generalizability, this study suggests large reductions in homelessness lead to significant reductions in rearrest rates. Efforts to reduce recidivism should include interventions that make homelessness less likely, but notable differences in recidivism will require these interventions be sizable. Meanwhile, efforts to establish recidivism risk factors should consider alternative effects, like IPS effects, to maximize validity and reduce bias.

stat.AP↗

arXiv2022

Nonparametric Estimation of Conditional Incremental Effects

Conditional effect estimation has great scientific and policy importance because interventions may impact subjects differently depending on their characteristics. Most research has focused on estimating the conditional average treatment effect (CATE). However, identification of the CATE requires all subjects have a non-zero probability of receiving treatment, or positivity, which may be unrealistic in practice. Instead, we propose conditional effects based on incremental propensity score interventions, which are stochastic interventions where the odds of treatment are multiplied by some factor. These effects do not require positivity for identification and can be better suited for modeling scenarios in which people cannot be forced into treatment. We develop a projection estimator and a flexible nonparametric estimator that can each estimate all the conditional effects we propose and derive model-agnostic error guarantees showing both estimators satisfy a form of double robustness. Further, we propose a summary of treatment effect heterogeneity and a test for any effect heterogeneity based on the variance of a conditional derivative effect and derive a nonparametric estimator that also satisfies a form of double robustness. Finally, we demonstrate our estimators by analyzing the effect of intensive care unit admission on mortality using a dataset from the (SPOT)light study.

stat.ME↗

arXiv2021

Incremental causal effects: an introduction and review

In this chapter, we review the class of causal effects based on incremental propensity scores interventions proposed by Kennedy [2019]. The aim of incremental propensity score interventions is to estimate the effect of increasing or decreasing subjects' odds of receiving treatment; this differs from the average treatment effect, where the aim is to estimate the effect of everyone deterministically receiving versus not receiving treatment. We first present incremental causal effects for the case when there is a single binary treatment, such that it can be compared to average treatment effects and thus shed light on key concepts. In particular, a benefit of incremental effects is that positivity - a common assumption in causal inference - is not needed to identify causal effects. Then we discuss the more general case where treatment is measured at multiple time points, where positivity is more likely to be violated and thus incremental effects can be especially useful. Throughout, we motivate incremental effects with real-world applications, present nonparametric estimators for these effects, and discuss their efficiency properties, while also briefly reviewing the role of influence functions in functional estimation. Finally, we show how to interpret and analyze results using these estimators in practice, and discuss extensions and future directions.

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