arXiv subjects

Caleb H. Miles

Publications and source records attributed to Caleb H. Miles.

14 recordsLinked to original sources

arXiv2026

Causal Effects of Modified Treatment Policies under Positivity Violations: A Partial Identification Approach

Modified treatment policies (MTPs) are interventions based on each individual's natural treatment value. We study mean outcomes under MTPs for continuous treatments, including exposure mixtures. Positivity is the standard sufficient condition for identifying these mean outcomes without extrapolation: policy-generated values remain supported given covariates. With multivariate treatments or continuous covariates, treatment--covariate combinations can be sparse or unsupported. Retaining the policy, our partial-identification framework decomposes its mean outcome into a point-identified contribution inside a positivity region and one outside. We bound the latter by imposing Lipschitz continuity on conditional mean potential outcomes rather than a parametric extrapolation model. The restriction compares each outside mean with the mean at an anchor inside the region. Metric projection minimizes width among one-anchor intervals but concentrates anchors on a lower-dimensional boundary, making the endpoints not pathwise differentiable. Our novel interior-displaced projection moves anchors inward, restoring pathwise differentiability. With a known region, we derive influence functions, characterize when they are efficient, and obtain asymptotically normal estimators and confidence intervals. In simulations, our intervals attain at least nominal coverage where those assuming positivity undercover. In a pesticide-mixture application, protective associations suggested by methods assuming positivity are not robust to modest outcome variation beyond the estimated region.

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arXiv2026

Exploiting independence constraints for efficient estimation of bounds on causal effects in the presence of unmeasured confounding

Causal graphs may inform covariate adjustment for estimating causal effects and improve estimation efficiency by exploiting the graphical structure. In many applications, however, the target causal parameter may not be point-identified due to the presence of unmeasured confounding. Sensitivity analysis methods address this challenge by characterizing bounds on the causal parameter under varying assumptions about the magnitude or form of unmeasured confounding. We focus on semiparametric efficient estimation of causal effects in non-identifiable settings, assuming a known (or hypothesized) causal graph. We propose an influence function projection approach that exploits the conditional independence constraints implied by the graph to improve the efficiency of semiparametric estimators of upper and lower bounds on the average causal effect under a given sensitivity analysis model. Our approach applies across multiple sensitivity analysis frameworks and causal estimands, thereby connecting knowledge of graphical structure with the sensitivity analysis literature. We illustrate our approach through simulations and real data examples thought to be affected by unmeasured confounding, including the effect of labor training program on post-intervention earnings, and the effect of low ejection fraction on heart failure death.

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arXiv2025

Learning density ratios in causal inference using Bregman-Riesz regression

The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detection, independence testing, importance sampling, and diffusion modeling. Naively estimating the numerator and denominator densities separately using, e.g., kernel density estimators, can lead to unstable performance and suffer from the curse of dimensionality as the number of covariates increases. For this reason, several methods have been developed for estimating the density ratio directly based on (a) Bregman divergences or (b) recasting the density ratio as the odds in a probabilistic classification model that predicts whether an observation is sampled from the numerator or denominator distribution. Additionally, the density ratio can be viewed as the Riesz representer of a continuous linear map, making it amenable to estimation via (c) minimization of the so-called Riesz loss, which was developed to learn the Riesz representer in the Riesz regression procedure in causal inference. In this paper we show that all three of these methods can be unified in a common framework, which we call Bregman--Riesz regression. We further show how data augmentation techniques can be used to apply density ratio learning methods to causal problems, where the numerator distribution typically represents an unobserved intervention. We show through simulations how the choice of Bregman divergence and data augmentation strategy can affect the performance of the resulting density ratio learner. A Python package is provided for researchers to apply Bregman--Riesz regression in practice using gradient boosting, neural networks, and kernel methods.

stat.ML↗

arXiv2025

A Cautionary Tale on Integrating Studies with Disparate Outcome Measures for Causal Inference

Data integration approaches are increasingly used to enhance the efficiency and generalizability of studies. However, a key limitation of these methods is the assumption that outcome measures are identical across datasets -- an assumption that often does not hold in practice. Consider the following opioid use disorder (OUD) studies: the XBOT trial and the POAT study, both evaluating the effect of medications for OUD on withdrawal symptom severity (not the primary outcome of either trial). While XBOT measures withdrawal severity using the subjective opiate withdrawal scale, POAT uses the clinical opiate withdrawal scale. We analyze this realistic yet challenging setting where outcome measures differ across studies and where neither study records both types of outcomes. Our paper studies whether and when integrating studies with disparate outcome measures leads to efficiency gains. We introduce three sets of assumptions -- with varying degrees of strength -- linking both outcome measures. Our theoretical and empirical results highlight a cautionary tale: integration can improve asymptotic efficiency only under the strongest assumption linking the outcomes. However, misspecification of this assumption leads to bias. In contrast, a milder assumption may yield finite-sample efficiency gains, yet these benefits diminish as sample size increases. We illustrate these trade-offs via a case study integrating the XBOT and POAT datasets to estimate the comparative effect of two medications for opioid use disorder on withdrawal symptoms. By systematically varying the assumptions linking the SOW and COW scales, we show potential efficiency gains and the risks of bias. Our findings emphasize the need for careful assumption selection when fusing datasets with differing outcome measures, offering guidance for researchers navigating this common challenge in modern data integration.

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arXiv2025

Addressing an extreme positivity violation to distinguish the causal effects of surgery and anesthesia via separable effects

The U.S. Food and Drug Administration has cautioned that prenatal exposure to anesthetic drugs during the third trimester may have neurotoxic effects; however, there is limited clinical evidence available to substantiate this recommendation. One major scientific question of interest is whether such neurotoxic effects might be due to surgery, anesthesia, or both. Isolating the effects of these two exposures is challenging because they are observationally equivalent, thereby inducing an extreme positivity violation. To address this, we adopt the separable effects framework of Robins and Richardson (2010) to identify the effect of anesthesia (alone) by blocking effects through variables that are assumed to completely mediate the causal pathway from surgery to the outcome. We apply this approach to data from the nationwide Medicaid Analytic eXtract (MAX) from 1999 through 2013, which linked 16,778,281 deliveries to mothers enrolled in Medicaid during pregnancy. Furthermore, we assess the sensitivity of our results to violations of our key identification assumptions.

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arXiv2024

Measurement Error-Robust Causal Inference via Constructed Instrumental Variables

Measurement error can often be harmful when estimating causal effects. Two scenarios in which this is the case are in the estimation of (a) the average treatment effect when confounders are measured with error and (b) the natural indirect effect when the exposure and/or confounders are measured with error. Methods adjusting for measurement error typically require external data or knowledge about the measurement error distribution. Here, we propose methodology not requiring any such information. Instead, we show that when the outcome regression is linear in the error-prone variables, consistent estimation of these causal effects can be recovered using constructed instrumental variables under certain conditions. These variables, which are functions of only the observed data, behave like instrumental variables for the error-prone variables. Using data from a study of the effects of prenatal exposure to heavy metals on growth and neurodevelopment in Bangladeshi mother-infant pairs, we apply our methodology to estimate (a) the effect of lead exposure on birth length while controlling for maternal protein intake, and (b) lead exposure's role in mediating the effect of maternal protein intake on birth length. Protein intake is calculated from food journal entries, and is suspected to be highly prone to measurement error.

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arXiv2023

On the Causal Interpretation of Randomized Interventional Indirect Effects

Identification of standard mediated effects such as the natural indirect effect relies on heavy causal assumptions. By circumventing such assumptions, so-called randomized interventional indirect effects have gained popularity in the mediation literature. Here, I introduce properties one might demand of an indirect effect measure in order for it to have a true mediational interpretation. For instance, the sharp null criterion requires an indirect effect measure to be null whenever no individual-level indirect effect exists. I show that without stronger assumptions, randomized interventional indirect effects do not satisfy such criteria. I additionally discuss alternative causal interpretations of such effects.

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arXiv2023

Sensitivity analysis for transportability in multi-study, multi-outcome settings

Existing work in data fusion has covered identification of causal estimands when integrating data from heterogeneous sources. These results typically require additional assumptions to make valid estimation and inference. However, there is little literature on transporting and generalizing causal effects in multiple-outcome setting, where the primary outcome is systematically missing on the study level but for which other outcome variables may serve as proxies. We review an identification result developed in ongoing work that utilizes information from these proxies to obtain more efficient estimators and the corresponding key identification assumption. We then introduce methods for assessing the sensitivity of this approach to the identification assumption.

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arXiv2022

All models are wrong, but which are useful? Comparing parametric and nonparametric estimation of causal effects in finite samples

There is a long-standing debate in the statistical, epidemiological and econometric fields as to whether nonparametric estimation that uses data-adaptive methods, like machine learning algorithms in model fitting, confer any meaningful advantage over simpler, parametric approaches in real-world, finite sample estimation of causal effects. We address the question: when trying to estimate the effect of a treatment on an outcome, across a universe of reasonable data distributions, how much does the choice of nonparametric vs.~parametric estimation matter? Instead of answering this question with simulations that reflect a few chosen data scenarios, we propose a novel approach evaluating performance across thousands of data-generating mechanisms drawn from non-parametric models with semi-informative priors. We call this approach a Universal Monte-Carlo Simulation. We compare performance of estimating the average treatment effect across two parametric estimators (a g-computation estimator that uses a parametric outcome model and an inverse probability of treatment weighted estimator) and two nonparametric estimators (Bayesian additive regression trees and a targeted minimum loss-based estimator that uses an ensemble of machine learning algorithms in model fitting). We summarize estimator performance in terms of bias, confidence interval coverage, and mean squared error. We find that the nonparametric estimators nearly always outperform the parametric estimators with the exception of having similar performance in terms of bias and similar-to-slightly-worse performance in terms of coverage under the smallest sample size of N=100.

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arXiv2021

Optimal tests of the composite null hypothesis arising in mediation analysis

The indirect effect of an exposure on an outcome through an intermediate variable can be identified by a product of two regression coefficients under certain causal and regression modeling assumptions. In this context, the null hypothesis of no indirect effect is a composite null hypothesis, as the null holds if either regression coefficient is zero. A consequence is that traditional hypothesis tests are severely underpowered near the origin (i.e., when both coefficients are small with respect to standard errors). We propose hypothesis tests that (i) preserve level alpha type 1 error, (ii) meaningfully improve power when both true underlying effects are small relative to sample size, and (iii) preserve power when at least one is not. One approach gives a closed-form test that is minimax optimal with respect to local power over the alternative parameter space. Another uses sparse linear programming to produce an approximately optimal test for a Bayes risk criterion. We discuss adaptations for performing large-scale hypothesis testing as well as modifications that yield improved interpretability. We provide an R package that implements our proposed methodology.

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arXiv2018

Causal Inference When Counterfactuals Depend on the Proportion of All Subjects Exposed

The assumption that no subject's exposure affects another subject's outcome, known as the no-interference assumption, has long held a foundational position in the study of causal inference. However, this assumption may be violated in many settings, and in recent years has been relaxed considerably. Often this has been achieved with either the aid of a known underlying network, or the assumption that the population can be partitioned into separate groups, between which there is no interference, and within which each subject's outcome may be affected by all the other subjects in the group via the proportion exposed (the stratified interference assumption). In this paper, we instead consider a complete interference setting, in which each subject affects every other subject's outcome. In particular, we make the stratified interference assumption for a single group consisting of the entire sample. This can occur when the exposure is a shared resource whose efficacy is modified by the number of subjects among whom it is shared. We show that a targeted maximum likelihood estimator for the i.i.d.~setting can be used to estimate a class of causal parameters that includes direct effects and overall effects under certain interventions. This estimator remains doubly-robust, semiparametric efficient, and continues to allow for incorporation of machine learning under our model. We conduct a simulation study, and present results from a data application where we study the effect of a nurse-based triage system on the outcomes of patients receiving HIV care in Kenyan health clinics.

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arXiv2017

On semiparametric estimation of a path-specific effect in the presence of mediator-outcome confounding

Path-specific effects are a broad class of mediated effects from an exposure to an outcome via one or more causal pathways with respect to some subset of intermediate variables. The majority of the literature concerning estimation of mediated effects has focused on parametric models with stringent assumptions regarding unmeasured confounding. We consider semiparametric inference of a path-specific effect when these assumptions are relaxed. In particular, we develop a suite of semiparametric estimators for the effect along a pathway through a mediator, but not some exposure-induced confounder of that mediator. These estimators have different robustness properties, as each depends on different parts of the observed data likelihood. One of our estimators may be viewed as combining the others, because it is locally semiparametric efficient and multiply robust. The latter property is illustrated in a simulation study. We apply our methodology to an HIV study, in which we estimate the effect comparing two drug treatments on a patient's average log CD4 count mediated by the patient's level of adherence, but not by previous experience of toxicity, which is clearly affected by which treatment the patient is assigned to, and may confound the effect of the patient's level of adherence on their virologic outcome.

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arXiv2016

A Class of Semiparametric Tests of Treatment Effect Robust to Confounder Classical Measurement Error

When assessing the presence of an exposure causal effect on a given outcome, it is well known that classical measurement error of the exposure can reduce the power of a test of the null hypothesis in question, although its type I error rate will generally remain at the nominal level. In contrast, classical measurement error of a confounder can inflate the type I error rate of a test of treatment effect. In this paper, we develop a large class of semiparametric test statistics of an exposure causal effect, which are completely robust to classical measurement error of a subset of confounders. A unique and appealing feature of our proposed methods is that they require no external information such as validation data or replicates of error-prone confounders. We present a doubly-robust form of this test that requires only one of two models to be correctly specified for the resulting test statistic to have correct type I error rate. We demonstrate validity and power within our class of test statistics through simulation studies. We apply the methods to a multi-U.S.-city, time-series data set to test for an effect of temperature on mortality while adjusting for atmospheric particulate matter with diameter of 2.5 micrometres or less (PM2.5), which is known to be measured with error.

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arXiv2015

On Partial Identification of the Pure Direct Effect

In causal mediation analysis, nonparametric identification of the pure (natural) direct effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called "cross-world-counterfactuals" independence and (ii) no exposure- induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient's adherence, and show that inference on this effect is somewhat sensitive to model assumptions.

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