arXiv subjects

Alex Luedtke

Publications and source records attributed to Alex Luedtke.

At least 37 records · Page 2Linked to original sources

arXiv2025

Efficient Estimation Under Data Fusion

We aim to make inferences about a smooth, finite-dimensional parameter by fusing data from multiple sources together. Previous works have studied the estimation of a variety of parameters in similar data fusion settings, including in the estimation of the average treatment effect and average reward under a policy, with the majority of them merging one historical data source with covariates, actions, and rewards and one data source of the same covariates. In this work, we consider the general case where one or more data sources align with each part of the distribution of the target population, for example, the conditional distribution of the reward given actions and covariates. We describe potential gains in efficiency that can arise from fusing these data sources together in a single analysis, which we characterize by a reduction in the semiparametric efficiency bound. We also provide a general means to construct estimators that achieve these bounds. In numerical experiments, we illustrate marked improvements in efficiency from using our proposed estimators rather than their natural alternatives. Finally, we illustrate the magnitude of efficiency gains that can be realized in vaccine immunogenicity studies by fusing data from two HIV vaccine trials.

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arXiv2024

Comparing HIV Vaccine Immunogenicity across Trials with Different Populations and Study Designs

Safe and effective preventive vaccines have the potential to help stem the HIV epidemic. The efficacy of such vaccines is typically measured in randomized, double-blind phase IIb/III trials and described as a reduction in newly acquired HIV infections. However, such trials are often expensive, time-consuming, and/or logistically challenging. These challenges lead to a great interest in immune responses induced by vaccination, and in identifying which immune responses predict vaccine efficacy. These responses are termed vaccine correlates of protection. Studies of vaccine-induced immunogenicity vary in size and design, ranging from small, early phase trials, to case-control studies nested in a broader late-phase randomized trial. Moreover, trials can be conducted in geographically diverse study populations across the world. Such diversity presents a challenge for objectively comparing vaccine-induced immunogenicity. To address these practical challenges, we propose a framework that is capable of identifying appropriate causal estimands and estimators, which can be used to provide standardized comparisons of vaccine-induced immunogenicity across trials. We evaluate the performance of the proposed estimands via extensive simulation studies. Our estimators are well-behaved and enjoy robustness properties. The proposed technique is applied to compare vaccine immunogenicity using data from three recent HIV vaccine trials.

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arXiv2024

Propensity Score Augmentation in Matching-based Estimation of Causal Effects

When assessing the causal effect of a binary exposure using observational data, confounder imbalance across exposure arms must be addressed. Matching methods, including propensity score-based matching, can be used to deconfound the causal relationship of interest. They have been particularly popular in practice, at least in part due to their simplicity and interpretability. However, these methods can suffer from low statistical efficiency compared to many competing methods. In this work, we propose a novel matching-based estimator of the average treatment effect based on a suitably-augmented propensity score model. Our procedure can be shown to have greater statistical efficiency than traditional matching estimators whenever prognostic variables are available, and in some cases, can nearly reach the nonparametric efficiency bound. In addition to a theoretical study, we provide numerical results to illustrate our findings. Finally, we use our novel procedure to estimate the effect of circumcision on risk of HIV-1 infection using vaccine efficacy trial data.

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arXiv2024

Estimation of subsidiary performance metrics under optimal policies

In policy learning, the goal is typically to optimize a primary performance metric, but other subsidiary metrics often also warrant attention. This paper presents two strategies for evaluating these subsidiary metrics under a policy that is optimal for the primary one. The first relies on a novel margin condition that facilitates Wald-type inference. Under this and other regularity conditions, we show that the one-step corrected estimator is efficient. Despite the utility of this margin condition, it places strong restrictions on how the subsidiary metric behaves for nearly optimal policies, which may not hold in practice. We therefore introduce alternative, two-stage strategies that do not require a margin condition. The first stage constructs a set of candidate policies and the second builds a uniform confidence interval over this set. We provide numerical simulations to evaluate the performance of these methods in different scenarios.

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arXiv2023

One-Step Estimation of Differentiable Hilbert-Valued Parameters

We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient, root-n rate estimators and corresponding confidence sets. These estimators correspond to generalizations of cross-fitted one-step estimators based on Hilbert-valued efficient influence functions. We give theoretical guarantees even when arbitrary estimators of nuisance functions are used, including those based on machine learning techniques. We show that these results naturally extend to Hilbert spaces that lack a reproducing kernel, as long as the parameter has an efficient influence function. However, we also uncover the unfortunate fact that, when there is no reproducing kernel, many interesting parameters fail to have an efficient influence function, even though they are pathwise differentiable. To handle these cases, we propose a regularized one-step estimator and associated confidence sets. We also show that pathwise differentiability, which is a central requirement of our approach, holds in many cases. Specifically, we provide multiple examples of pathwise differentiable parameters and develop corresponding estimators and confidence sets. Among these examples, four are particularly relevant to ongoing research by the causal inference community: the counterfactual density function, dose-response function, conditional average treatment effect function, and counterfactual kernel mean embedding.

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arXiv2023

Adversarial Meta-Learning of Gamma-Minimax Estimators That Leverage Prior Knowledge

Bayes estimators are well known to provide a means to incorporate prior knowledge that can be expressed in terms of a single prior distribution. However, when this knowledge is too vague to express with a single prior, an alternative approach is needed. Gamma-minimax estimators provide such an approach. These estimators minimize the worst-case Bayes risk over a set $Γ$ of prior distributions that are compatible with the available knowledge. Traditionally, Gamma-minimaxity is defined for parametric models. In this work, we define Gamma-minimax estimators for general models and propose adversarial meta-learning algorithms to compute them when the set of prior distributions is constrained by generalized moments. Accompanying convergence guarantees are also provided. We also introduce a neural network class that provides a rich, but finite-dimensional, class of estimators from which a Gamma-minimax estimator can be selected. We illustrate our method in two settings, namely entropy estimation and a prediction problem that arises in biodiversity studies.

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arXiv2023

Causal isotonic calibration for heterogeneous treatment effects

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

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arXiv2022

Individualized treatment rules under stochastic treatment cost constraints

Estimation and evaluation of individualized treatment rules have been studied extensively, but real-world treatment resource constraints have received limited attention in existing methods. We investigate a setting in which treatment is intervened upon based on covariates to optimize the mean counterfactual outcome under treatment cost constraints when the treatment cost is random. In a particularly interesting special case, an instrumental variable corresponding to encouragement to treatment is intervened upon with constraints on the proportion receiving treatment. For such settings, we first develop a method to estimate optimal individualized treatment rules. We further construct an asymptotically efficient plug-in estimator of the corresponding average treatment effect relative to a given reference rule.

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arXiv2022

Can the potential benefit of individualizing treatment be assessed using trial summary statistics alone?

Individualizing treatment assignment can improve outcomes for diseases with patient-to-patient variability in comparative treatment effects. When a clinical trial demonstrates that some patients improve on treatment while others do not, it is tempting to assume that treatment effect heterogeneity exists. However, if variability in response is mainly driven by factors other than treatment, investigating the extent to which covariate data can predict differential treatment response is a potential waste of resources. Motivated by recent meta-analyses assessing the potential of individualizing treatment for major depressive disorder using only summary statistics, we provide a method that uses summary statistics widely available in published clinical trial results to bound the benefit of optimally assigning treatment to each patient. We also offer alternate bounds for settings in which trial results are stratified by another covariate. We demonstrate our approach using summary statistics from a depression treatment trial. Our methods are implemented in the rct2otrbounds R package, which is available at https://github.com/ngalanter/rct2otrbounds .

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arXiv2022

Improved inference for vaccine-induced immune responses via shape-constrained methods

We study the performance of shape-constrained methods for evaluating immune response profiles from early-phase vaccine trials. The motivating problem for this work involves quantifying and comparing the IgG binding immune responses to the first and second variable loops (V1V2 region) arising in HVTN 097 and HVTN 100 HIV vaccine trials. We consider unimodal and log-concave shape-constrained methods to compare the immune profiles of the two vaccines, which is reasonable because the data support that the underlying densities of the immune responses could have these shapes. To this end, we develop novel shape-constrained tests of stochastic dominance and shape-constrained plug-in estimators of the Hellinger distance between two densities. Our techniques are either tuning parameter free, or rely on only one tuning parameter, but their performance is either better (the tests of stochastic dominance) or comparable with the nonparametric methods (the estimators of Hellinger distance). The minimal dependence on tuning parameters is especially desirable in clinical contexts where analyses must be prespecified and reproducible. Our methods are supported by theoretical results and simulation studies.

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arXiv2022

A general adaptive framework for multivariate point null testing

As a common step in refining their scientific inquiry, investigators are often interested in performing some screening of a collection of given statistical hypotheses. For example, they may wish to determine whether any one of several patient characteristics are associated with a health outcome of interest. Existing generic methods for testing a multivariate hypothesis -- such as multiplicity corrections applied to individual hypothesis tests -- can easily be applied across a variety of problems but can suffer from low power in some settings. Tailor-made procedures can attain higher power by building around problem-specific information but typically cannot be easily adapted to novel settings. In this work, we propose a general framework for testing a multivariate point null hypothesis in which the test statistic is adaptively selected to provide increased power. We present theoretical large-sample guarantees for our test under both fixed and local alternatives. In simulation studies, we show that tests created using our framework can perform as well as tailor-made methods when the latter are available, and we illustrate how our procedure can be used to create tests in two settings in which tailor-made methods are not currently available.

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arXiv2022

Improved Efficiency for Cross-Arm Comparisons via Platform Designs

Though platform trials have been touted for their flexibility and streamlined use of trial resources, their statistical efficiency is not well understood. We fill this gap by establishing their greater efficiency for comparing the relative efficacy of multiple interventions over using several separate, two-arm trials, where the relative efficacy of an arbitrary pair of interventions is evaluated by contrasting their relative risks as compared to control. In theoretical and numerical studies, we demonstrate that the inference of such a contrast using data from a platform trial enjoys identical or better precision than using data from separate trials, even when the former enrolls substantially fewer participants. This benefit is attributed to the sharing of controls among interventions under contemporaneous randomization, which is a key feature of platform trials. We further provide a novel procedure for establishing the non-inferiority of a given intervention relative to the most efficacious of the other interventions under evaluation, where this procedure is adaptive in the sense that it need not be \textit{a priori} known which of these other interventions is most efficacious. Our numerical studies show that this testing procedure can attain substantially better power when the data arise from a platform trial rather than multiple separate trials. Our results are illustrated using data from two monoclonal antibody trials for the prevention of HIV.

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arXiv2021

Efficient Estimation of the Maximal Association between Multiple Predictors and a Survival Outcome

This paper develops a new approach to post-selection inference for screening high-dimensional predictors of survival outcomes. Post-selection inference for right-censored outcome data has been investigated in the literature, but much remains to be done to make the methods both reliable and computationally-scalable in high-dimensions. Machine learning tools are commonly used to provide {\it predictions} of survival outcomes, but the estimated effect of a selected predictor suffers from confirmation bias unless the selection is taken into account. The new approach involves construction of semi-parametrically efficient estimators of the linear association between the predictors and the survival outcome, which are used to build a test statistic for detecting the presence of an association between any of the predictors and the outcome. Further, a stabilization technique reminiscent of bagging allows a normal calibration for the resulting test statistic, which enables the construction of confidence intervals for the maximal association between predictors and the outcome and also greatly reduces computational cost. Theoretical results show that this testing procedure is valid even when the number of predictors grows superpolynomially with sample size, and our simulations support that this asymptotic guarantee is indicative the performance of the test at moderate sample sizes. The new approach is applied to the problem of identifying patterns in viral gene expression associated with the potency of an antiviral drug.

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arXiv2021

Inference for treatment-specific survival curves using machine learning

In the absence of data from a randomized trial, researchers often aim to use observational data to draw causal inference about the effect of a treatment on a time-to-event outcome. In this context, interest often focuses on the treatment-specific survival curves; that is, the survival curves were the entire population under study to be assigned to receive the treatment or not. Under certain causal conditions, including that all confounders of the treatment-outcome relationship are observed, the treatment-specific survival can be identified with a covariate-adjusted survival function. Several estimators of this function have been proposed, including estimators based on outcome regression, inverse probability weighting, and doubly robust estimators. In this article, we propose a new cross-fitted doubly-robust estimator that incorporates data-adaptive (e.g. machine learning) estimators of the conditional survival functions. We establish conditions on the nuisance estimators under which our estimator is consistent and asymptotically linear, both pointwise and uniformly in time. We also propose a novel ensemble learner for combining multiple candidate estimators of the conditional survival estimators. Notably, our methods and results accommodate events occurring in discrete or continuous time (or both). We investigate the practical performance of our methods using numerical studies and an application to the effect of a surgical treatment to prevent metastases of parotid carcinoma on mortality.

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arXiv2021

Estimating the Efficiency Gain of Covariate-Adjusted Analyses in Future Clinical Trials Using External Data

We present a general framework for using existing data to estimate the efficiency gain from using a covariate-adjusted estimator of a marginal treatment effect in a future randomized trial. We describe conditions under which it is possible to define a mapping from the distribution that generated the existing external data to the relative efficiency of a covariate-adjusted estimator compared to an unadjusted estimator. Under conditions, these relative efficiencies approximate the ratio of sample size needed to achieve a desired power. We consider two situations where the outcome is either fully or partially observed and several treatment effect estimands that are of particular interest in most trials. For each such estimand, we develop a semiparametrically efficient estimator of the relative efficiency that allows for the application of flexible statistical learning tools to estimate the nuisance functions and an analytic form of a corresponding Wald-type confidence interval. We also propose a double bootstrap scheme for constructing confidence intervals. We demonstrate the performance of the proposed methods through simulation studies and apply these methods to data to estimate the relative efficiency of using covariate adjustment in Covid-19 therapeutic trials.

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arXiv2020

Discussion of Kallus (2020) and Mo, Qi, and Liu (2020): New Objectives for Policy Learning

We discuss the thought-provoking new objective functions for policy learning that were proposed in "More efficient policy learning via optimal retargeting" by Nathan Kallus and "Learning optimal distributionally robust individualized treatment rules" by Weibin Mo, Zhengling Qi, and Yufeng Liu. We show that it is important to take the curvature of the value function into account when working within the retargeting framework, and we introduce two ways to do so. We also describe more efficient approaches for leveraging calibration data when learning distributionally robust policies.

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arXiv2020

Adversarial Monte Carlo Meta-Learning of Optimal Prediction Procedures

We frame the meta-learning of prediction procedures as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated outcome, and the Predictor observes data sampled from a distribution drawn from this prior. The Predictor's objective is to learn a function that maps from a new feature to an estimate of the associated outcome. We establish that, under reasonable conditions, the Predictor has an optimal strategy that is equivariant to shifts and rescalings of the outcome and is invariant to permutations of the observations and to shifts, rescalings, and permutations of the features. We introduce a neural network architecture that satisfies these properties. The proposed strategy performs favorably compared to standard practice in both parametric and nonparametric experiments.

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arXiv2020

Sufficient and insufficient conditions for the stochastic convergence of Cesàro means

We study the stochastic convergence of the Cesàro mean of a sequence of random variables. These arise naturally in statistical problems that have a sequential component, where the sequence of random variables is typically derived from a sequence of estimators computed on data. We show that establishing a rate of convergence in probability for a sequence is not sufficient in general to establish a rate in probability for its Cesàro mean. We also present several sets of conditions on the sequence of random variables that are sufficient to guarantee a rate of convergence for its Cesàro mean. We identify common settings in which these sets of conditions hold.

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