arXiv subjects

Mark van der Laan

Publications and source records attributed to Mark van der Laan.

At least 19 recordsLinked to original sources

arXiv2026

Considerations for the Integration of Randomized Controlled Trials and Real-World Data

As clinical decision-making increasingly moves toward individualized and context-specific treatment recommendations, reliance on any single evidence source, randomized or observational, may be insufficient. Principled integration of randomized controlled trials and real-world data, grounded in explicit causal frameworks, offers a path toward evidence that is both internally credible and externally relevant. In this article, we describe distinct objectives for the integration of randomized controlled trials and real-world data and discuss how these objectives shape key design and analytic considerations, illustrating the resulting choices through example estimands. We highlight practical issues that commonly arise in applied settings, including data relevance and curation, cross-source comparability, estimand specification, and sensitivity analysis. We aim for this article to help readers evaluate and implement principled approaches to integrating randomized controlled trials and real-world data in ways that can support more reliable treatment recommendations while maintaining regulatory-grade evidentiary standards.

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arXiv2026

A Causal Inference Approach for Evaluating Diagnostic Tests and AI-Enabled Medical Devices: From Effect Modification to Information-Augmented Decision-Making

Diagnostic medical tests and devices provide useful information for evaluating the potential benefits and risks of therapeutic treatments. However, unlike treatments, their impact on health outcomes is generally indirect because measuring diagnostic information typically does not itself affect patient outcomes, which complicates evaluation of their effectiveness. In this work, we develop a causal inference approach for evaluating diagnostic tests by distinguishing explanatory and pragmatic effectiveness. Explanatory effectiveness evaluates whether a diagnostic test result provides treatment-relevant information beyond baseline covariates by explaining additional treatment-effect heterogeneity, which we characterize using a variance-based treatment-effect variable importance measure. Pragmatic effectiveness evaluates whether incorporating this information into personalized treatment decisions improves expected outcomes, a question central to decision-making for patients, clinicians, and other health care stakeholders. We formalize pragmatic effectiveness as a contrast between expected outcomes under optimal personalized treatment rules defined with and without access to the diagnostic test result. We establish identification of the proposed estimand and provide Targeted Maximum Likelihood Estimation (TMLE) and cross-validated TMLE procedures for nonparametric estimation and inference. Simulation studies and a synthetic colorectal cancer application illustrate the proposed estimands and estimation performance. More broadly, this approach provides a causal inference perspective for evaluating AI-enabled devices by distinguishing their dual roles as information-enrichment and personalized decision-optimization tools, clarifying whether AI improves outcomes by expanding information for downstream decisions, improving the decision rule used to act on that information, or through both pathways.

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arXiv2026

Longitudinal Adaptive Experimental Design for Learning Multiple Target Estimands with Semiparametric Efficient Inference

Adaptive designs are increasingly used in clinical trials and digital experiments to improve estimation efficiency by updating treatment randomization probabilities as data accumulate. While most existing work focuses on settings with a single-stage treatment, adaptive designs for longitudinal studies with multi-stage, time-varying treatments remain relatively underexplored. In this work, we develop a general semiparametric efficiency framework for designing longitudinal adaptive experiments to optimize the estimation efficiency of a broad class of target estimands of interest. An efficiency-oriented design criterion is proposed to accommodate both single-estimand targets and joint optimization across multiple estimands. We demonstrate that optimal randomization at earlier stages depends on later-stage allocations, yielding a backward-recursive strategy for deriving the oracle design, and propose a longitudinal adaptive design to sequentially learn and target the oracle design using accumulating data. We further develop an adaptive-design-likelihood-based longitudinal targeted maximum likelihood estimator (ADL-LTMLE) for asymptotically normal and semiparametric efficient estimation of statistical estimands from dependent data collected from adaptive experiments, without relying on parametric model assumptions. Applying the framework to time-to-treatment-initiation effects that compare initiating treatment at a given stage with delaying initiation until a subsequent stage, we show that designs optimized for a particular stage-specific effect can substantially compromise estimation efficiency for effects defined at other stages, highlighting the design trade-offs addressed by our framework. Simulation studies show the proposed design and estimation approaches achieve substantial variance reductions relative to non-adaptive designs, with performance close to that of the oracle design.

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arXiv2026

Towards Best Practices for Covariate Adjustment in Regulatory Trials: From Fixed to Data-Adaptive Approaches

While randomization justifies the use of unadjusted effect estimators in randomized trials, there is growing interest in covariate adjustment to improve precision. Adjusting for baseline variables that are prognostic of the outcome can reduce estimator variance, resulting in narrower confidence intervals and increased statistical power. Recent guidance by the U.S. Food and Drug Administration supports fixed adjustment for prognostic covariates using parametric regression models. However, this guidance does not address more flexible approaches using data-adaptive or machine learning methods. We offer our perspectives on covariate adjustment to improve analytic precision. We focus on estimating the average effect for the target population in trials with minimal outcome missingness. We provide a non-technical overview of effect estimators that are unadjusted and effect estimators using fixed versus data-adaptive adjustment. We offer practical suggestions for conducting adjusted analyses that are data-adaptive, fully pre-specified, transparently and reproducibly implemented, robust to model misspecification, and guaranteed to improve precision relative to unadjusted analyses --- all while preserving statistical validity and the causal effect of interest. We hope that sharing our perspectives will foster broader discussion and eventual acceptance of principled, pre-specified, data-adaptive covariate adjustment in randomized trials.

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arXiv2026

The V-fold jackknife for semiparametric inference: variance estimation, confidence intervals, and simultaneous confidence bands

For decades, the bootstrap has been a default tool for statistical inference because of its broad applicability and minimal analytic requirements. Although its validity is well understood for smooth parametric estimators, its theoretical properties for many modern semiparametric and machine-learning estimators remain largely unstudied. Nevertheless, bootstrap procedures are often used routinely in such settings, even when their validity is unknown and their computational cost is substantial. We develop the $V$-fold jackknife as a computationally efficient and theoretically justified alternative for semiparametric inference. It requires only $V$ leave-fold-out refits and uses the empirical dispersion of jackknife pseudo-values to quantify uncertainty, without deriving or evaluating an influence function. For regular asymptotically linear estimators of pathwise differentiable parameters, we show that, for fixed $V$, the Studentized $V$-fold jackknife statistic converges to a $t$-distribution with $V-1$ degrees of freedom, giving valid confidence intervals even though the jackknife variance estimator does not converge in probability. When $V\to\infty$, we establish consistency of the variance estimator at rate $V^{-1/2}$, allowing $V$ to diverge slowly, for example at rate $\log n$. We also develop simultaneous confidence bands based on the correct componentwise-Studentized limiting distribution. Finally, we extend the theory to generalized asymptotically linear estimators with diverging influence-function variance and slower-than-$\sqrt n$ convergence; scale invariance of Studentization eliminates the need to know the effective convergence rate. Simulations on the average treatment effect, Kaplan--Meier survival curve, and highly adaptive lasso dose-response curves confirm reliable inference, including where influence-function-based standard errors are anti-conservative or unstable.

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arXiv2026

An Estimator-Robust Design for Augmenting Randomized Controlled Trials with External Real-World Data

Augmenting randomized controlled trials (RCTs) with external real-world data (RWD) has the potential to improve the finite sample efficiency of treatment effect estimators. We describe using adaptive targeted maximum likelihood estimation (A-TMLE) for estimating the average treatment effect (ATE) by decomposing the ATE estimand into two components: a pooled-ATE estimand that combines data from both the RCT and external sources, and a bias estimand that captures the conditional effect of RCT enrollment on the outcome. This approach views the RCT data as the reference and corrects for inconsistencies of any kind between the RCT and the external data source. Given the growing abundance of external RWD from modern electronic health records, determining the optimal strategy to select candidate external patients for data integration remains an open yet critical problem. In this work, we begin by studying the robustness property of the A-TMLE estimator and then propose a matching-based sampling strategy that attempts to improve the robustness of the estimator with respect to the target estimand. Our proposed strategy is outcome-blind and involves matching based on two one-dimensional scores: the trial enrollment score and the propensity score in the external data. We demonstrate in simulations that our sampling strategy improves the coverage and narrows the widths of confidence intervals produced by A-TMLE. We illustrate our method with a case study of augmenting the DEVOTE cardiovascular safety trial by using the Optum Clinformatics claims database.

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arXiv2026

Improving the Efficiency of Subgroup Analysis in Randomized Controlled Trials with TMLE

Subgroup analyses within randomized controlled trials are often underpowered due to limited sample sizes. We address this challenge by leveraging trial participants outside the subgroup of interest to augment estimation within the subgroup. Specifically, we study two Targeted Maximum Likelihood Estimators (TMLEs) that borrow information from non-subgroup participants within the same trial: a TMLE with pooled regression (TMLE-PR) and an Adaptive Targeted Maximum Likelihood Estimator (A-TMLE). Both estimators enable information sharing without relying on any external real-world data, thereby capitalizing on key strengths of the trial: most importantly, the protection against bias afforded by the randomized treatment, but also harmonized data collection, and consistent treatment and outcome definitions. The general strategy proposed here directly advances the priorities of key regulatory agencies, including the FDA, by improving the precision of subgroup-specific treatment effect estimates without introducing external sources of bias, thereby facilitating rigorous inference to support equitable labeling, access, and post-market evaluation. In a case study based on analysis of data from a cardiovascular outcome trial (LEADER, NCT01179048), we estimate the risk reduction of major adverse cardiac events (MACE) under liraglutide treatment among Black and Asian subgroups -- each comprising less than 10\% of the trial population -- using the proposed estimators that borrow information from the remainder of the trial. Using A-TMLE, in particular, we find estimated absolute MACE risk reductions of 1.6, 1.5, and 1.5 percentage points among Asian participants and 2.1, 2.0, and 2.1 percentage points among Black participants at 365, 540, and 730 days, respectively, with 95\% confidence intervals excluding the null at each time point.

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arXiv2026

Highly Adaptive Principal Component Regression

The Highly Adaptive Lasso (HAL) is a nonparametric regression method that achieves almost dimension-free convergence rates under minimal smoothness assumptions, but its implementation can be computationally prohibitive in high dimensions due to the large design matrix it requires. The Highly Adaptive Ridge (HAR) has been proposed as a related ridge-regularized analogue. Building on both procedures, we introduce the Principal Component Highly Adaptive Lasso (PCHAL) and Principal Component Highly Adaptive Ridge (PCHAR). These estimators use an outcome-blind principal-component reduction of the HAL basis, offering substantial computational gains over HAL while achieving empirical performance comparable to HAL and HAR. We also describe an early-stopped gradient descent variant, which provides a convenient form of smooth spectral regularization without explicitly selecting a hard principal-component cutoff. Finally, we uncover that under special circumstances, the HAL kernel is identical to the covariance function of Brownian motion.

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arXiv2026

Externally Controlled Trials: A Review of Design and Borrowing Through a Causal Lens

Externally controlled trials (ECTs) are increasingly used when randomized controls are infeasible, unethical, or insufficient, including applications in rare diseases, oncology, pediatrics, and post-approval effectiveness research. Although methodological work has expanded rapidly across causal inference, Bayesian dynamic borrowing, and hybrid trial designs, the literature remains fragmented. We adopt a six-step scientific roadmap to organize modern ECT methodology in two primary settings: (i) single-arm trials that evaluate efficacy through comparison with external controls, and (ii) hybrid controlled trials that augment the internal control arm with external controls drawn from real-world data or historical studies. The roadmap clarifies causal estimands, identifiability assumptions, and how statistical parameters arise from identification, and shows how modeling and borrowing strategies trade off efficiency and robustness, especially under covariate shift and outcome drift. Within this framework, we synthesize and evaluate recent Bayesian and frequentist developments, compare their strengths, limitations, operating characteristics, and available software, and emphasize the role of sensitivity analysis. By re-framing ECT methodology through a causal lens, this work establishes a coherent foundation for integrating external data into regulatory and clinical decision-making and highlights core challenges and opportunities for future research.

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arXiv2026

A CV-TMLE global test approach to improve power in rare disease clinical studies with multiple-component endpoints

Rare disease trials face unique statistical challenges due to limited patient populations and heterogeneous clinical manifestations among patients. Multiple endpoints are often necessary to comprehensively capture treatment benefits. A global test is an approach for evaluating whether a treatment has any beneficial effect across multiple endpoints. We propose a new global test based on a weighted composite endpoint. The proposed global test employs shrinkage-based cross-validated targeted maximum likelihood estimation (CV-TMLE) to learn data-adaptive weights that maximize power while maintaining Type I error control. Shrinkage can be tailored to incorporate existing domain knowledge, such as anticipated relative effect sizes. In simulation studies designed to reflect real rare disease trial settings, the proposed procedure demonstrated improved power over standard multiplicity adjustments and classical global tests (such as the O'Brien test), while maintaining nominal Type I error, when effects are heterogeneous across endpoints. The proposed method simultaneously learns an optimal weighted composite outcome and provides an unbiased and efficient targeted maximum likelihood estimator (TMLE) for the average treatment effect (ATE) on that weighted outcome, with valid inference taking into account that the ATE is data dependent.

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arXiv2026

An Online Meta-Level Adaptive Design Framework with Targeted Learning Inference: Applications to Evaluating and Utilizing Surrogate Outcomes in Adaptive Designs

Adaptive designs are increasingly used in clinical trials and online experiments to improve participant outcomes by dynamically updating treatment allocation as data accumulate. In practice, experimenters often consider multiple candidate designs, each with distinct trade-offs. However, typically only one design is implemented at a time, leaving benefits and costs of alternative designs unobserved and unquantified. To address this, we propose a novel meta-level adaptive design framework that enables real-time, data-driven evaluation and selection among candidate adaptive designs. Specifically, we define a new class of causal estimands to evaluate adaptive designs and propose Targeted Maximum Likelihood Estimators for these estimands. These estimators are asymptotically normal while accommodating dependence in adaptive-design data without parametric assumptions, enabling online selection among candidate designs. We further apply this framework to a motivating example where multiple surrogates of a long-term outcome are considered for updating randomization probabilities in adaptive experiments. Unlike existing surrogate evaluation methods, our approach comprehensively quantifies surrogates' utility to accelerate detection of heterogeneous treatment effects, expedite updates to treatment randomization, and improve participant outcomes, facilitating dynamic selection among surrogate-guided designs. Overall, our framework provides a unified approach for evaluating opportunities and costs of various adaptive designs and guiding real-time decision-making in adaptive experiments.

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arXiv2026

Adaptive debiased machine learning using data-driven model selection techniques

Debiased machine learning estimators for smooth functionals in nonparametric models can exhibit substantial variability and instability, often leading practitioners to instead rely on parametric or semiparametric working models. Such models, however, may be misspecified and can therefore introduce bias. We study how data-driven model selection can be combined with debiased machine learning to construct estimators that adapt to structure in the data-generating distribution. To this end, we propose Adaptive Debiased Machine Learning (ADML), a nonparametric framework for constructing superefficient estimators of pathwise differentiable parameters. The framework unifies a broad class of previously proposed adaptive estimators, including methods based on variable selection, learned feature representations, and collaborative targeted learning. It requires only high-level conditions and approximate validity of the selection procedure, which are implied by lower-level conditions already assumed in important settings, including sieve-based selection, sparsity-based methods such as the Lasso, and data-adaptive feature representations. We show that ADML estimators yield regular and efficient root-$n$ inference for an oracle projection parameter induced by a data-adaptive oracle submodel. This oracle parameter coincides with the target parameter at the true distribution but typically has a smaller efficiency bound, thereby yielding superefficiency for the target parameter. As a practical illustration, we introduce a broad class of automatic ADML estimators for continuous linear functionals of the outcome regression, in which model selection is performed directly on the regression itself. Motivated by overlap challenges in causal inference, we develop new superefficient plug-in estimators for the average treatment effect based on calibration in semiparametric regression models.

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arXiv2026

Targeted Learning on Variable Importance Measure for Heterogeneous Treatment Effect

Quantifying the heterogeneity of treatment effect is important for understanding how a commercial product or medical treatment affects different population subgroups. While much of treatment effect heterogeneity analysis focuses on the conditional average treatment effect, an alternative parameter that captures treatment effect heterogeneity is the variance of treatment effect across different covariate groups. One can also derive variable importance parameters that measure (and rank) how much of treatment effect heterogeneity is explained by a targeted subset of covariates. In this article, we propose a new targeted maximum likelihood estimator (TMLE) for a treatment effect variable importance measure, in the form of the difference of the variances of conditional average treatment effect. This TMLE is a pure plug-in estimator that consists of two steps: 1) the initial estimation of relevant components to plug in and 2) an iterative updating step to optimize the bias-variance tradeoff. Simulation results show that the proposed estimator has competitive performance in terms of lower bias and better confidence interval coverage compared to a simple substitution estimator and an estimating equation estimator. We apply these methods to data from a randomized clinical trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults. We find that the estimating equation estimator and the proposed TMLE suggest similar rankings of variable importance. The application of this method also demonstrates the advantage of a plug-in estimator, which always respects the global constraints on the data distribution and that the estimand is a particular function of the distribution.

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arXiv2026

HAL-MLE Log-Splines Density Estimation (Part I: Univariate)

We study nonparametric maximum likelihood estimation of probability densities under a total variation (TV) type penalty, sectional variation norm (also named as Hardy-Krause variation). TV regularization has a long history in regression and density estimation, including results on $L^2$ and KL divergence convergence rates. Here, we revisit this task using the Highly Adaptive Lasso (HAL) framework. We formulate a HAL-based maximum likelihood estimator (HAL-MLE) using the log-spline link function from \citet{kooperberg1992logspline}, and show that in the univariate setting the bounded sectional variation norm assumption underlying HAL coincides with the classical bounded TV assumption. This equivalence directly connects HAL-MLE to existing TV-penalized approaches such as local adaptive splines \citep{mammen1997locally}. We establish three new theoretical results: (i) the univariate HAL-MLE is asymptotically linear, (ii) it admits pointwise asymptotic normality, and (iii) it achieves uniform convergence at rate $n^{-(k+1)/(2k+3)}$ up to logarithmic factors for the smoothness order $k \geq 1$. These results extend existing results from \citet{van2017uniform}, which previously guaranteed only uniform consistency without rates when $k=0$. We will include the uniform convergence for general dimension $d$ in the follow-up work of this paper. The intention of this paper is to provide a unified framework for the TV-penalized density estimation methods, and to connect the HAL-MLE to the existing TV-penalized methods in the univariate case, despite that the general HAL-MLE is defined for multivariate cases.

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arXiv2026

Causal inference for calibrated scaling interventions on time-to-event processes

This work develops a flexible inferential framework for nonparametric causal inference in time-to-event settings, based on stochastic interventions defined through multiplicative scaling of the intensity governing an intermediate event process. These interventions induce a family of estimands indexed by a scalar parameter α, representing effects of modifying event rates while preserving the temporal and covariate-dependent structure of the observed data generating mechanism. To enhance interpretability, we introduce calibrated interventions, where α is chosen to achieve a pre-specified goal, such as a desired level of cumulative risk of the intermediate event, and define corresponding composite target parameters capturing the downstream effects on the outcome process. This yields clinically meaningful contrasts while avoiding unrealistic deterministic intervention regimes. Under a nonparametric model, we derive efficient influence curves for α-indexed, calibrated, and composite target parameters and establish their double robustness properties. We further sketch a targeted maximum likelihood estimation (TMLE) strategy that accommodates flexible, machine learning based nuisance estimation. The proposed framework applies broadly to (causal) questions involving time-to-event treatments or mediators and is illustrated through different examples event-history settings. A simulation study demonstrates finite-sample inferential properties, and highlights the implications of practical positivity violations when interventions extend beyond observed data support.

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arXiv2026

Experiment-selector cross-validated targeted maximum likelihood estimator for hybrid RCT-external data studies

Augmenting a randomized controlled trial (RCT) with external data may increase power at the risk of introducing bias. To select and analyze the experiment (RCT alone or combined with external data) with the optimal bias-variance tradeoff, we develop a novel experiment-selector cross-validated targeted maximum likelihood estimator for randomized-external data studies (ES-CVTMLE). This estimator utilizes two estimates of bias to determine whether to integrate external data based on 1) a function of the difference in conditional mean outcome under control between the RCT and combined experiments and 2) an estimate of the average treatment effect on a negative control outcome (NCO). We define the asymptotic distribution of the ES-CVTMLE under varying magnitudes of bias and construct confidence intervals by Monte Carlo simulation. We evaluate ES-CVTMLE compared to three other data fusion estimators in simulations and demonstrate the ability of ES-CVTMLE to distinguish biased from unbiased external controls in a real data analysis of the effect of liraglutide on glycemic control from the LEADER trial. The ES-CVTMLE has the potential to improve power while providing relatively robust inference for future hybrid RCT-external data studies.

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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.

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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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