arXiv subjects

Mark van der Laan

Publications and source records attributed to Mark van der Laan.

At least 37 records · Page 2Linked to original sources

arXiv2025

HAL-Based Plug-in Estimation with Pointwise Asymptotic Normality of the Causal Dose-Response Curve

Estimating and obtaining reliable inference for the marginally adjusted causal dose-response curve for continuous treatments without relying on parametric assumptions is a well-known statistical challenge. Parametric models risk introducing significant bias through model misspecification, compromising the accurate representation of the underlying data and dose-response relationship. On the other hand, nonparametric models face difficulties as the dose-response curve is not pathwise differentiable, preventing consistent estimation at standard rates. The Highly Adaptive Lasso (HAL) maximum likelihood estimator offers a promising approach to this issue. In this paper, we introduce a HAL-based plug-in estimator for the causal dose-response curve, bridge theoretical development and empirical application, and assess its empirical performance against other estimators. This work emphasizes not just theoretical proofs, but also demonstrates their application through comprehensive simulations, thereby filling an essential gap between theory and practice. Our comprehensive simulations demonstrate that the HAL-based estimator achieves pointwise asymptotic normality with valid inference and consistently outperforms existing approaches for estimating the causal dose-response curve.

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arXiv2025

Efficient Statistical Estimation for Sequential Adaptive Experiments with Implications for Adaptive Designs

Adaptive experimental designs have gained popularity in clinical trials and online experiments. Unlike traditional, fixed experimental designs, adaptive designs can dynamically adjust treatment randomization probabilities and other design features in response to data accumulated sequentially during the experiment. These adaptations are useful to achieve diverse objectives, including reducing uncertainty in the estimation of causal estimands or increasing participants' chances of receiving better treatments during the experiment. At the end of the experiment, it is often desirable to answer causal questions from the observed data. However, the adaptive nature of such experiments and the resulting dependence among observations pose significant challenges to providing valid statistical inference and efficient estimation of causal estimands. Building upon the Targeted Maximum Likelihood Estimator (TMLE) framework tailored for adaptive designs (van der Laan, 2008), we introduce a new Adaptive-Design-Likelihood-based TMLE (ADL-TMLE) to estimate a wide class of causal estimands from adaptive experiment data, including the average treatment effect as our primary example. We establish asymptotic normality and semiparametric efficiency of ADL-TMLE under relaxed positivity and design stabilization assumptions for adaptive experiments. Motivated by these results, we further propose a novel adaptive design aimed at minimizing the variance of the estimator based on data generated under that design. Simulations show that ADL-TMLE demonstrates superior variance-reduction performance across different types of adaptive experiments, and that the proposed adaptive design attains lower variance than the standard efficiency-oriented adaptive design. Finally, we generalize our framework to broader settings, including those with longitudinal structures.

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arXiv2025

Sensitivity Analysis for Unmeasured Confounding in Medical Product Development and Evaluation Using Real World Evidence

The American Statistical Association Biopharmaceutical Section (ASA BIOP) scientific working group on real-world evidence (RWE) has been making continuous, extended efforts towards a goal of supporting and advancing regulatory science with respect to clinical studies intended to use real-world data for evidence generation for the purpose of medical product development and evaluation (i.e., RWE studies). In 2023, the working group published a manuscript delineating challenges and opportunities in constructing estimands for RWE studies following the framework in ICH E9(R1) guidance on estimand and sensitivity analysis. As a follow-up task, we describe the other issue, sensitivity analysis. Although the FDA's definition of RWE studies includes randomized trials using RWD as a primary source of evidence generation such as pragmatic trials, here we focus on non-randomized RWE studies and the issue of unmeasured confounding which is a major source of bias for most RWE studies. We review the availability and applicability of sensitivity analysis methods for different types of unmeasured confounding. We also provide some practical and regulatory considerations on using sensitivity analysis for such RWE studies. Then, we use a plasmode case study to demonstrate realistic ways to interpret sensitivity analysis results in supporting regulatory decision-making. We conclude with a brief discussion.

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arXiv2025

Super Ensemble Learning Using the Highly-Adaptive-Lasso

We introduce the Meta Highly-Adaptive-Lasso Minimum Loss Estimator (M-HAL-MLE), a novel ensemble approach for estimating functional parameters of realistically modeled data distribution from independent and identically distributed observations. Given $J$ initial estimators, candidate ensembles are generated by finite-sectional-variation cadlag functions. Using $V$-fold cross-validation, the M-HAL-MLE selects the optimal cadlag ensemble minimizing the cross-validated empirical risk, with the sectional variation bound as a tuning parameter. The final estimator, M-HAL super-learner, is obtained by averaging ensemble compositions across folds. In contrast, the oracle ensemble and oracle estimator are defined by minimizing the population excess risk relative to the true function. We establish following theoretical properties: 1) the M-HAL super-learner converges to the oracle estimator at rate $n^{-2/3}$ in excess risk, up to log-n factors; 2) by appropriate undersmoothing, target features of the M-HAL super-learner are asymptotically linear for corresponding target features of the oracle estimator; 3) the excess risk between the oracle estimator and true function, along with the difference between their target features, is generally second-order. Simulations validate the theoretical results, demonstrating effectiveness in high-dimensional settings. We further illustrate the method in a real-data application involving mediation analysis of functional MRI from human pain studies.

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arXiv2025

Targeted Deep Architectures: A TMLE-Based Framework for Robust Causal Inference in Neural Networks

Modern deep neural networks are powerful predictive tools yet often lack valid inference for causal parameters, such as treatment effects or entire survival curves. While frameworks like Double Machine Learning (DML) and Targeted Maximum Likelihood Estimation (TMLE) can debias machine-learning fits, existing neural implementations either rely on "targeted losses" that do not guarantee solving the efficient influence function equation or computationally expensive post-hoc "fluctuations" for multi-parameter settings. We propose Targeted Deep Architectures (TDA), a new framework that embeds TMLE directly into the network's parameter space with no restrictions on the backbone architecture. Specifically, TDA partitions model parameters - freezing all but a small "targeting" subset - and iteratively updates them along a targeting gradient, derived from projecting the influence functions onto the span of the gradients of the loss with respect to weights. This procedure yields plug-in estimates that remove first-order bias and produce asymptotically valid confidence intervals. Crucially, TDA easily extends to multi-dimensional causal estimands (e.g., entire survival curves) by merging separate targeting gradients into a single universal targeting update. Theoretically, TDA inherits classical TMLE properties, including double robustness and semiparametric efficiency. Empirically, on the benchmark IHDP dataset (average treatment effects) and simulated survival data with informative censoring, TDA reduces bias and improves coverage relative to both standard neural-network estimators and prior post-hoc approaches. In doing so, TDA establishes a direct, scalable pathway toward rigorous causal inference within modern deep architectures for complex multi-parameter targets.

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arXiv2025

Regularized Targeted Maximum Likelihood Estimation in Highly Adaptive Lasso Implied Working Models

We address the challenge of performing Targeted Maximum Likelihood Estimation (TMLE) after an initial Highly Adaptive Lasso (HAL) fit. Existing approaches that utilize the data-adaptive working model selected by HAL-such as the relaxed HAL update-can be simple and versatile but may become computationally unstable when the HAL basis expansions introduce collinearity. Undersmoothed HAL may fail to solve the efficient influence curve (EIC) at the desired level without overfitting, particularly in complex settings like survival-curve estimation. A full HAL-TMLE, which treats HAL as the initial estimator and then targets in the nonparametric or semiparametric model, typically demands costly iterative clever-covariate calculations in complex set-ups like survival analysis and longitudinal mediation analysis. To overcome these limitations, we propose two new HAL-TMLEs that operate within the finite-dimensional working model implied by HAL: Delta-method regHAL-TMLE and Projection-based regHAL-TMLE. We conduct extensive simulations to demonstrate the performance of our proposed methods.

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arXiv2025

Longitudinal Targeted Minimum Loss-based Estimation with Temporal-Difference Heterogeneous Transformer

We propose Deep Longitudinal Targeted Minimum Loss-based Estimation (Deep LTMLE), a novel approach to estimate the counterfactual mean of outcome under dynamic treatment policies in longitudinal problem settings. Our approach utilizes a transformer architecture with heterogeneous type embedding trained using temporal-difference learning. After obtaining an initial estimate using the transformer, following the targeted minimum loss-based likelihood estimation (TMLE) framework, we statistically corrected for the bias commonly associated with machine learning algorithms. Furthermore, our method also facilitates statistical inference by enabling the provision of 95% confidence intervals grounded in asymptotic statistical theory. Simulation results demonstrate our method's superior performance over existing approaches, particularly in complex, long time-horizon scenarios. It remains effective in small-sample, short-duration contexts, matching the performance of asymptotically efficient estimators. To demonstrate our method in practice, we applied our method to estimate counterfactual mean outcomes for standard versus intensive blood pressure management strategies in a real-world cardiovascular epidemiology cohort study.

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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.

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arXiv2025

The impact of job stability on monetary poverty in Italy: causal small area estimation

Job stability - encompassing secure contracts, adequate wages, social benefits, and career opportunities - is a critical determinant in reducing monetary poverty, as it provides households with reliable income and enhances economic well-being. This study leverages EU-SILC survey and census data to estimate the causal effect of job stability on monetary poverty across Italian provinces, quantifying its influence and analyzing regional disparities. We introduce a novel causal small area estimation (CSAE) framework that integrates global and local estimation strategies for heterogeneous treatment effect estimation, effectively addressing data sparsity at the provincial level. Furthermore, we develop a general bootstrap scheme to construct reliable confidence intervals, applicable regardless of the method used for estimating nuisance parameters. Extensive simulation studies demonstrate that our proposed estimators outperform classical causal inference methods in terms of stability while maintaining computational scalability for large datasets. Applying this methodology to real-world data, we uncover significant relationships between job stability and poverty across six Italian regions, offering critical insights into regional disparities and their implications for evidence-based policy design.

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arXiv2025

Score-Preserving Targeted Maximum Likelihood Estimation

Targeted maximum likelihood estimators (TMLEs) are asymptotically optimal among regular, asymptotically linear estimators. In small samples, however, we may be far from "asymptopia" and not reap the benefits of optimality. Here we propose a variant (score-preserving TMLE; SP-TMLE) that leverages an initial estimator defined as the solution of a large number of possibly data-dependent score equations. Instead of targeting only the efficient influence function in the TMLE update to knock out the plug-in bias, we also target the already-solved scores. Solving additional scores reduces the remainder term in the von-Mises expansion of our estimator because these scores may come close to spanning higher-order influence functions. The result is an estimator with better finite-sample performance. We demonstrate our approach in simulation studies leveraging the (relaxed) highly adaptive lasso (HAL) as our initial estimator. These simulations show that in small samples SP-TMLE has reduced bias relative to plug-in HAL and reduced variance relative to vanilla TMLE, blending the advantages of the two approaches. We also observe improved estimation of standard errors in small samples.

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arXiv2025

Adaptive-TMLE for the Average Treatment Effect based on Randomized Controlled Trial Augmented with Real-World Data

We consider the problem of estimating the average treatment effect (ATE) when both randomized control trial (RCT) data and external real-world data (RWD) are available. We decompose the ATE estimand as the difference between a pooled-ATE estimand that integrates RCT and RWD and a bias estimand that captures the conditional effect of RCT enrollment on the outcome. We introduce an adaptive targeted maximum likelihood estimation (A-TMLE) framework to estimate them. We prove that the A-TMLE estimator is root-n-consistent and asymptotically normal. Moreover, in finite sample, it achieves the super-efficiency one would obtain had one known the oracle model for the conditional effect of the RCT enrollment on the outcome. Consequently, the smaller and more parsimonious the working model of the bias induced by the RWD is, the greater our estimator's efficiency, while our estimator will always be at least as efficient as an efficient estimator that uses the RCT data only. A-TMLE outperforms existing methods in simulations by having smaller mean-squared-error and 95% confidence intervals. We apply A-TMLE to augment the DEVOTE trial with external data from the Optum Clinformatics Data Mart, demonstrating its potential to establish treatment superiority in noninferiority trials. A-TMLE could utilize external RWD to help improve the power of randomized trials without biasing the estimates of intervention effects. This approach could allow for smaller, faster trials, decreasing the time until patients can receive effective treatments.

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arXiv2025

Technical Note: Targeted Maximum Likelihood Estimator for an ATE Standardized for New Target Population

In this technical note we present a targeted maximum likelihood estimator (TMLE) for a previously studied target parameter that aims to transport an average treatment effect (ATE) on a clinical outcome in a source population to what the ATE would have been in another target population. It is assumed that one only observes baseline covariates in the target population, while we assume that one can learn the conditional treatment effect on the outcome of interest in the source population. We also allow that one might observe only a subset of the covariates in the target population while all covariates are measured in the source population. We consider the case that the outcome is a clinical outcome at some future time point that is subject to missingness, or that our outcome of interest is a time to event that is subject to right-censoring. We derive the canonical gradients and present the corresponding TMLEs for these two cases.

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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.

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arXiv2024

Challenges and Possible Strategies to Address Them in Rare Disease Drug Development: A Statistical Perspective

Developing drugs for rare diseases presents unique challenges from a statistical perspective. These challenges may include slowly progressive diseases with unmet medical needs, poorly understood natural history, small population size, diversified phenotypes and geneotypes within a disorder, and lack of appropriate surrogate endpoints to measure clinical benefits. The Real-World Evidence (RWE) Scientific Working Group of the American Statistical Association Biopharmaceutical Section has assembled a research team to assess the landscape including challenges and possible strategies to address these challenges and the role of real-world data (RWD) and RWE in rare disease drug development. This paper first reviews the current regulations by regulatory agencies worldwide and then discusses in more details the challenges from a statistical perspective in the design, conduct, and analysis of rare disease clinical trials. After outlining an overall development pathway for rare disease drugs, corresponding strategies to address the aforementioned challenges are presented. Other considerations are also discussed for generating relevant evidence for regulatory decision-making on drugs for rare diseases. The accompanying paper discusses how RWD and RWE can be used to improve the efficiency of rare disease drug development.

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arXiv2024

Use of Real-World Data and Real-World Evidence in Rare Disease Drug Development: A Statistical Perspective

Real-world data (RWD) and real-world evidence (RWE) have been increasingly used in medical product development and regulatory decision-making, especially for rare diseases. After outlining the challenges and possible strategies to address the challenges in rare disease drug development (see the accompanying paper), the Real-World Evidence (RWE) Scientific Working Group of the American Statistical Association Biopharmaceutical Section reviews the roles of RWD and RWE in clinical trials for drugs treating rare diseases. This paper summarizes relevant guidance documents and frameworks by selected regulatory agencies and the current practice on the use of RWD and RWE in natural history studies and the design, conduct, and analysis of rare disease clinical trials. A targeted learning roadmap for rare disease trials is described, followed by case studies on the use of RWD and RWE to support a natural history study and marketing applications in various settings.

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arXiv2024

Highly Adaptive Ridge

In this paper we propose the Highly Adaptive Ridge (HAR): a regression method that achieves a $n^{-1/3}$ dimension-free L2 convergence rate in the class of right-continuous functions with square-integrable sectional derivatives. This is a large nonparametric function class that is particularly appropriate for tabular data. HAR is exactly kernel ridge regression with a specific data-adaptive kernel based on a saturated zero-order tensor-product spline basis expansion. We use simulation and real data to confirm our theory. We demonstrate empirical performance better than state-of-the-art algorithms for small datasets in particular.

stat.ML↗

arXiv2024

Large Language Models as Co-Pilots for Causal Inference in Medical Studies

The validity of medical studies based on real-world clinical data, such as observational studies, depends on critical assumptions necessary for drawing causal conclusions about medical interventions. Many published studies are flawed because they violate these assumptions and entail biases such as residual confounding, selection bias, and misalignment between treatment and measurement times. Although researchers are aware of these pitfalls, they continue to occur because anticipating and addressing them in the context of a specific study can be challenging without a large, often unwieldy, interdisciplinary team with extensive expertise. To address this expertise gap, we explore the use of large language models (LLMs) as co-pilot tools to assist researchers in identifying study design flaws that undermine the validity of causal inferences. We propose a conceptual framework for LLMs as causal co-pilots that encode domain knowledge across various fields, engaging with researchers in natural language interactions to provide contextualized assistance in study design. We provide illustrative examples of how LLMs can function as causal co-pilots, propose a structured framework for their grounding in existing causal inference frameworks, and highlight the unique challenges and opportunities in adapting LLMs for reliable use in epidemiological research.

cs.AI↗

arXiv2024

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.

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