arXiv subjects

Alan Hubbard

Publications and source records attributed to Alan Hubbard.

10 recordsLinked to original sources

arXiv2025

Constructing Confidence Intervals for Infinite-Dimensional Functional Parameters by Highly Adaptive Lasso

Estimating the conditional mean function is a central task in statistical learning. In this paper, we consider estimation and inference for a nonparametric class of real-valued cadlag functions with bounded sectional variation (Gill et al., 1995), using the Highly Adaptive Lasso (HAL) (van der Laan, 2015; Benkeser and van der Laan, 2016; van der Laan, 2023), a flexible empirical risk minimizer over linear combinations of tensor products of zero- or higher-order spline basis functions under an L1 norm constraint. Building on recent theoretical advances in asymptotic normality and uniform convergence rates for higher-order spline HAL estimators, this work focuses on constructing robust confidence intervals for HAL-based estimators of conditional means. First, we propose a targeted HAL with a debiasing step to remove the regularization bias of the targeted conditional mean and also consider a relaxed HAL estimator to reduce such bias within the working model. Second, we propose both global and local undersmoothing strategies to adaptively enlarge the working model and further reduce bias relative to variance. Third, we combine these estimation strategies with delta-method-based variance estimators to construct confidence intervals for the conditional mean. Through extensive simulation studies, we evaluate different combinations of our estimation procedures, model selection strategies, and confidence-interval constructions. The results show that our proposed approaches substantially reduce bias relative to variance and yield confidence intervals with coverage rates close to nominal levels across different scenarios. Finally, we demonstrate the general applicability of our framework by estimating conditional average treatment effect (CATE) functions, highlighting how HAL-based inference methods extend to other infinite-dimensional, non-pathwise-differentiable parameters.

stat.ME↗

arXiv2025

Targeted Learning Estimation of Sampling Variance for Improved Inference

For robust statistical inference it is crucial to obtain a good estimator of the variance of the proposed estimator of the statistical estimand. A commonly used estimator of the variance for an asymptotically linear estimator is the sample variance of the estimated influence function. This estimator has been shown to be anti-conservative in limited samples or in the presence of near-positivity violations, leading to elevated Type-I error rates and poor coverage. In this paper, capitalizing on earlier attempts at targeted variance estimators, we propose a one-step targeted variance estimator for the causal risk ratio (CRR) in scenarios involving treatment, outcome, and baseline covariates. While our primary focus is on the variance of log(CRR), our methodology can be extended to other causal effect parameters. Specifically, we focus on the variance of the IF for the log relative risk (log(CRR)) estimator, which requires deriving the efficient influence function for the variance of the IF as the basis for constructing the estimator. Several methods are available to develop efficient estimators of asymptotically linear parameters. In this paper, we concentrate on the so-called one-step targeted maximum likelihood estimator, which is a substitution estimator that utilizes a one-dimensional universal least favorable parametric submodel when updating the distribution. We conduct simulations with different effect sizes, sample sizes and levels of positivity to compare the estimator with existing methods in terms of coverage and Type-I error. Simulation results demonstrate that, especially with small samples and near-positivity violations, the proposed variance estimator offers improved performance, achieving coverage closer to the nominal level of 0.95 and a lower Type-I error rate.

stat.ME↗

arXiv2024

Data-Adaptive Identification of Effect Modifiers through Stochastic Shift Interventions and Cross-Validated Targeted Learning

In epidemiology, identifying subpopulations that are particularly vulnerable to exposures and those who may benefit differently from exposure-reducing interventions is essential. Factors such as age, gender-specific vulnerabilities, and physiological states such as pregnancy are critical for policymakers when setting regulatory guidelines. However, current semi-parametric methods for estimating heterogeneous treatment effects are often limited to binary exposures and can function as black boxes, lacking clear, interpretable rules for subpopulation-specific policy interventions. This study introduces a novel method that uses cross-validated targeted minimum loss-based estimation (TMLE) paired with a data-adaptive target parameter strategy to identify subpopulations with the most significant differential impact of simulated policy interventions that reduce exposure. Our approach is assumption-lean, allowing for the integration of machine learning while still yielding valid confidence intervals. We demonstrate the robustness of our methodology through simulations and application to data from the National Health and Nutrition Examination Survey. Our analysis of NHANES data on persistent organic pollutants (POPs) and leukocyte telomere length (LTL) identified age as a significant effect modifier. Specifically, we found that exposure to 3,3',4,4',5-pentachlorobiphenyl (PCNB) consistently had a differential impact on LTL, with a one-standard deviation reduction in exposure leading to a more pronounced increase in LTL among younger populations compared to older ones. We offer our method as an open-source software package, EffectXshift, enabling researchers to investigate the effect modification of continuous exposures. The EffectXshift package provides clear and interpretable results, informing targeted public health interventions and policy decisions.

stat.ME↗

arXiv2024

Bridging Binarization: Causal Inference with Dichotomized Continuous Exposures

The average treatment effect (ATE) is a common parameter estimated in causal inference literature, but it is only defined for binary exposures. Thus, despite concerns raised by some researchers, many studies seeking to estimate the causal effect of a continuous exposure create a new binary exposure variable by dichotomizing the continuous values into two categories. In this paper, we affirm binarization as a statistically valid method for answering causal questions about continuous exposures by showing the equivalence between the binarized ATE and the difference in the average outcomes of two specific modified treatment policies. These policies impose cut-offs corresponding to the binarized exposure variable and assume preservation of relative self-selection. Relative self-selection is the ratio of the probability density of an individual having an exposure equal to one value of the continuous exposure variable versus another. The policies assume that, for any two values of the exposure variable with non-zero probability density after the cut-off, this ratio will remain unchanged. Through this equivalence, we clarify the assumptions underlying binarization and discuss how to properly interpret the resulting estimator. Additionally, we introduce a new target parameter that can be computed after binarization that considers the observed world as a benchmark. We argue that this parameter addresses more relevant causal questions than the traditional binarized ATE parameter. We present a simulation study to illustrate the implications of these assumptions when analyzing data and to demonstrate how to correctly implement estimators of the parameters discussed. Finally, we present an application of this method to evaluate the effect of a law in the state of California which seeks to limit exposures to oil and gas wells on birth outcomes to further illustrate the underlying assumptions.

stat.ME↗

arXiv2023

Discovery of Critical Thresholds in Mixed Exposures and Estimation of Policy Intervention Effects using Targeted Learning

Traditional regulations of chemical exposure tend to focus on single exposures, overlooking the potential amplified toxicity due to multiple concurrent exposures. We are interested in understanding the average outcome if exposures were limited to fall under a multivariate threshold. Because threshold levels are often unknown a priori, we provide an algorithm that finds exposure threshold levels where the expected outcome is maximized or minimized. Because both identifying thresholds and estimating policy effects on the same data would lead to overfitting bias, we also provide a data-adaptive estimation framework, which allows for both threshold discovery and policy estimation. Simulation studies show asymptotic convergence to the optimal exposure region and to the true effect of an intervention. We demonstrate how our method identifies true interactions in a public synthetic mixture data set. Finally, we applied our method to NHANES data to discover metal exposures that have the most harmful effects on telomere length. We provide an implementation in the CVtreeMLE R package.

stat.ME↗

arXiv2021

Personalized Online Machine Learning

In this work, we introduce the Personalized Online Super Learner (POSL) -- an online ensembling algorithm for streaming data whose optimization procedure accommodates varying degrees of personalization. Namely, POSL optimizes predictions with respect to baseline covariates, so personalization can vary from completely individualized (i.e., optimization with respect to baseline covariate subject ID) to many individuals (i.e., optimization with respect to common baseline covariates). As an online algorithm, POSL learns in real-time. POSL can leverage a diversity of candidate algorithms, including online algorithms with different training and update times, fixed algorithms that are never updated during the procedure, pooled algorithms that learn from many individuals' time-series, and individualized algorithms that learn from within a single time-series. POSL's ensembling of this hybrid of base learning strategies depends on the amount of data collected, the stationarity of the time-series, and the mutual characteristics of a group of time-series. In essence, POSL decides whether to learn across samples, through time, or both, based on the underlying (unknown) structure in the data. For a wide range of simulations that reflect realistic forecasting scenarios, and in a medical data application, we examine the performance of POSL relative to other current ensembling and online learning methods. We show that POSL is able to provide reliable predictions for time-series data and adjust to changing data-generating environments. We further cultivate POSL's practicality by extending it to settings where time-series enter/exit dynamically over chronological time.

stat.ML↗

arXiv2021

Estimation of population size based on capture recapture designs and evaluation of the estimation reliability

We propose a modern method to estimate population size based on capture-recapture designs of K samples. The observed data is formulated as a sample of n i.i.d. K-dimensional vectors of binary indicators, where the k-th component of each vector indicates the subject being caught by the k-th sample, such that only subjects with nonzero capture vectors are observed. The target quantity is the unconditional probability of the vector being nonzero across both observed and unobserved subjects. We cover models assuming a single constraint (identification assumption) on the K-dimensional distribution such that the target quantity is identified and the statistical model is unrestricted. We present solutions for linear and non-linear constraints commonly assumed to identify capture-recapture models, including no K-way interaction in linear and log-linear models, independence or conditional independence. We demonstrate that the choice of constraint has a dramatic impact on the value of the estimand, showing that it is crucial that the constraint is known to hold by design. For the commonly assumed constraint of no K-way interaction in a log-linear model, the statistical target parameter is only defined when each of the $2^K - 1$ observable capture patterns is present, and therefore suffers from the curse of dimensionality. We propose a targeted MLE based on undersmoothed lasso model to smooth across the cells while targeting the fit towards the single valued target parameter of interest. For each identification assumption, we provide simulated inference and confidence intervals to assess the performance on the estimator under correct and incorrect identifying assumptions. We apply the proposed method, alongside existing estimators, to estimate prevalence of a parasitic infection using multi-source surveillance data from a region in southwestern China, under the four identification assumptions.

math.ST↗

arXiv2019

A Data-Adaptive Targeted Learning Approach of Evaluating Viscoelastic Assay Driven Trauma Treatment Protocols

Estimating the impact of trauma treatment protocols is complicated by the high dimensional yet finite sample nature of trauma data collected from observational studies. Viscoelastic assays are highly predictive measures of hemostasis. However, the effectiveness of thromboelastography(TEG) based treatment protocols has not been statistically evaluated.To conduct robust and reliable estimation with sparse data, we built an estimation "machine" for estimating causal impacts of candidate variables using the collaborative targeted maximum loss-based estimation(CTMLE) framework.The computational efficiency is achieved by using the scalable version of CTMLE such that the covariates are pre-ordered by summary statistics of their importance before proceeding to the estimation steps.To extend the application of the estimator in practice, we used super learning in combination with CTMLE to flexibly choose the best convex combination of algorithms. By selecting the optimal covariates set in high dimension and reducing constraints in choosing pre-ordering algorithms, we are able to construct a robust and data-adaptive model to estimate the parameter of interest.Under this estimation framework, CTMLE outperformed the other doubly robust estimators(IPW,AIPW,stabilized IPW,TMLE) in the simulation study. CTMLE demonstrated very accurate estimation of the target parameter (ATE). Applying CTMLE on the real trauma data, the treatment protocol (using TEG values immediately after injury) showed significant improvement in trauma patient hemostasis status (control of bleeding), and a decrease in mortality rate at 6h compared to standard care.The estimation results did not show significant change in mortality rate at 24h after arrival.

stat.AP↗

arXiv2018

A Fundamental Measure of Treatment Effect Heterogeneity

We offer a non-parametric plug-in estimator for an important measure of treatment effect variability and provide minimum conditions under which the estimator is asymptotically efficient. The stratum specific treatment effect function or so-called blip function, is the average treatment effect for a randomly drawn stratum of confounders. The mean of the blip function is the average treatment effect (ATE), whereas the variance of the blip function (VTE), the main subject of this paper, measures overall clinical effect heterogeneity, perhaps providing a strong impetus to refine treatment based on the confounders. VTE is also an important measure for assessing reliability of the treatment for an individual. The CV-TMLE provides simultaneous plug-in estimates and inference for both ATE and VTE, guaranteeing asymptotic efficiency under one less condition than for TMLE. This condition is difficult to guarantee a priori, particularly when using highly adaptive machine learning that we need to employ in order to eliminate bias. Even in defiance of this condition, CV-TMLE sampling distributions maintain normality, not guaranteed for TMLE, and have a lower mean squared error than their TMLE counterparts. In addition to verifying the theoretical properties of TMLE and CV-TMLE through simulations, we point out some of the challenges in estimating VTE, which lacks double robustness and might be unavoidably biased if the true VTE is small and sample size insufficient. We will provide an application of the estimator on a data set for treatment of acute trauma patients.

stat.ME↗

arXiv2018

A machine learning-based approach for estimating and testing associations with multivariate outcomes

We propose a method for summarizing the strength of association between a set of variables and a multivariate outcome. Classical summary measures are appropriate when linear relationships exist between covariates and outcomes, while our approach provides an alternative that is useful in situations where complex relationships may be present. We utilize ensemble machine learning to detect nonlinear relationships and covariate interactions and propose a measure of association that captures these relationships. A hypothesis test about the proposed associative measure can be used to test the strong null hypothesis of no association between a set of variables and a multivariate outcome. Simulations demonstrate that this hypothesis test has greater power than existing methods against alternatives where covariates have nonlinear relationships with outcomes. We additionally propose measures of variable importance for groups of variables, which summarize each groups' association with the outcome. We demonstrate our methodology using data from a birth cohort study on childhood health and nutrition in the Philippines.

stat.ME↗