arXiv subjects

Lars van der Laan

Publications and source records attributed to Lars van der Laan.

29 records · Page 2Linked to original sources

arXiv2025

Undersmoothed LASSO Models for Propensity Score Weighting and Synthetic Negative Control Exposures for Bias Detection

The propensity score (PS) is often used to control for large numbers of covariates in high-dimensional healthcare database studies. The least absolute shrinkage and selection operator (LASSO) has become the most widely used tool for fitting large-scale PS models in these settings. LASSO uses L1 regularized regression to prevent overfitting by shrinking coefficients toward zero (setting some exactly to zero). The degree of regularization is typically selected using cross-validation to minimize out-of-sample prediction error. Both theory and simulations have shown, however, that when using LASSO models for PS weighting, less regularization is needed to minimize bias in PS weighted estimators. This is referred to as undersmoothing the LASSO model, where the optimal degree of undersmoothing can be derived from the target causal parameter's efficient influence function. In many settings, however, the efficient influence function is unknown or difficult to derive. Here, we consider the use of balance metrics as a simple and generally applicable approach to select the degree of undersmoothing when the efficient influence function is unknown. Because LASSO models that are tuned using balance metrics alone are not assured to minimize bias in PS weighted estimators -- as such metrics are blind to the efficient influence function -- we propose a framework to generate synthetic negative control exposures for bias detection. We show that synthetic negative control exposures can identify analyses that likely violate partial exchangeability due to lack of control for measured confounding. Finally, we use a series of numerical studies to investigate the finite sample performance of using balance criteria to undersmooth LASSO PS-weighted estimators, and the use of synthetic negative control exposures to detect biased analyses.

stat.ME↗

arXiv2025

Generalized Venn and Venn-Abers Calibration with Applications in Conformal Prediction

Ensuring model calibration is critical for reliable prediction, yet popular distribution-free methods such as histogram binning and isotonic regression offer only asymptotic guarantees. We introduce a unified framework for Venn and Venn-Abers calibration that extends Vovk's approach beyond binary classification to a broad class of prediction problems defined by generic loss functions. Our method transforms any perfectly in-sample calibrated predictor into a set-valued predictor that, in finite samples, outputs at least one marginally calibrated point prediction. These set predictions shrink asymptotically and converge to a single conditionally calibrated prediction, capturing epistemic uncertainty. We further propose Venn multicalibration, a new approach for achieving finite-sample calibration across subpopulations. For quantile loss, our framework recovers group-conditional and multicalibrated conformal prediction as special cases and yields novel prediction intervals with quantile-conditional coverage.

stat.ML↗

arXiv2025

Stabilized Inverse Probability Weighting via Isotonic Calibration

Inverse weighting with an estimated propensity score is widely used by estimation methods in causal inference to adjust for confounding bias. However, directly inverting propensity score estimates can lead to instability, bias, and excessive variability due to large inverse weights, especially when treatment overlap is limited. In this work, we propose a post-hoc calibration algorithm for inverse propensity weights that generates well-calibrated, stabilized weights from user-supplied, cross-fitted propensity score estimates. Our approach employs a variant of isotonic regression with a loss function specifically tailored to the inverse propensity weights. Through theoretical analysis and empirical studies, we demonstrate that isotonic calibration improves the performance of doubly robust estimators of the average treatment effect.

stat.ME↗

arXiv2025

Semiparametric logistic regression for inference on relative vaccine efficacy in case-only studies with informative missingness

We develop semiparametric methods for estimating subgroup-specific relative vaccine efficacy against multiple viral strains in a partially vaccinated population. Focusing on observational case-only studies, we address informative missingness in strain type due to vaccination status, pre-vaccination characteristics, and post-infection factors such as viral load. We establish general conditions for the nonparametric identification of relative conditional vaccine efficacy between strains using covariate-adjusted conditional odds ratio parameters. Assuming a log-linear parametric form for strain-specific conditional vaccine efficacy, we propose targeted maximum likelihood estimators based on partially linear logistic regression, leveraging machine learning for flexible confounding adjustment. Finally, we apply our methods to estimate relative strain-specific conditional vaccine efficacy in the ENSEMBLE COVID-19 vaccine trial.

stat.ME↗

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.

stat.ME↗

arXiv2024

Self-Calibrating Conformal Prediction

In machine learning, model calibration and predictive inference are essential for producing reliable predictions and quantifying uncertainty to support decision-making. Recognizing the complementary roles of point and interval predictions, we introduce Self-Calibrating Conformal Prediction, a method that combines Venn-Abers calibration and conformal prediction to deliver calibrated point predictions alongside prediction intervals with finite-sample validity conditional on these predictions. To achieve this, we extend the original Venn-Abers procedure from binary classification to regression. Our theoretical framework supports analyzing conformal prediction methods that involve calibrating model predictions and subsequently constructing conditionally valid prediction intervals on the same data, where the conditioning set or conformity scores may depend on the calibrated predictions. Real-data experiments show that our method improves interval efficiency through model calibration and offers a practical alternative to feature-conditional validity.

stat.ML↗

arXiv2023

Estimating Uncertainty in Multimodal Foundation Models using Public Internet Data

Foundation models are trained on vast amounts of data at scale using self-supervised learning, enabling adaptation to a wide range of downstream tasks. At test time, these models exhibit zero-shot capabilities through which they can classify previously unseen (user-specified) categories. In this paper, we address the problem of quantifying uncertainty in these zero-shot predictions. We propose a heuristic approach for uncertainty estimation in zero-shot settings using conformal prediction with web data. Given a set of classes at test time, we conduct zero-shot classification with CLIP-style models using a prompt template, e.g., "an image of a ", and use the same template as a search query to source calibration data from the open web. Given a web-based calibration set, we apply conformal prediction with a novel conformity score that accounts for potential errors in retrieved web data. We evaluate the utility of our proposed method in Biomedical foundation models; our preliminary results show that web-based conformal prediction sets achieve the target coverage with satisfactory efficiency on a variety of biomedical datasets.

cs.AI↗

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.

stat.ML↗

arXiv2023

Targeted Maximum Likelihood Based Estimation for Longitudinal Mediation Analysis

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted maximum likelihood estimation (TMLE) of longitudinal natural direct and indirect effects defined with random interventions. The proposed estimators are multiply robust, locally efficient, and directly estimate and update the conditional densities that factorize data likelihoods. We utilize the highly adaptive lasso (HAL) and projection representations to derive new estimators (HAL-EIC) of the efficient influence curves of longitudinal mediation problems and propose a fast one-step TMLE algorithm using HAL-EIC while preserving the asymptotic properties. The proposed method can be generalized for other longitudinal causal parameters that are smooth functions of data likelihoods, and thereby provides a novel and flexible statistical toolbox.

stat.ME↗

arXiv2023

Efficient nonparametric estimation of the covariate-adjusted threshold-response function, a support-restricted stochastic intervention

Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. This risk, viewed as a function of thresholds and possibly adjusted for covariates, we call the threshold-response function. Extending the work of Donovan, Hudgens and Gilbert (2019), we propose a nonparametric efficient estimator for the covariate-adjusted threshold-response function, which utilizes machine learning and Targeted Minimum-Loss Estimation (TMLE). We additionally propose a more general estimator, based on sequential regression, that also applies when there is outcome missingness. We show that the threshold-response for a given threshold may be viewed as the expected outcome under a stochastic intervention where all participants are given a treatment dose above the threshold. We prove the estimator is efficient and characterize its asymptotic distribution. A method to construct simultaneous 95% confidence bands for the threshold-response function and its inverse is given. Furthermore, we discuss how to adjust our estimator when the treatment or biomarker is missing-at-random, as is the case in clinical trials with biased sampling designs, using inverse-probability-weighting. The methods are assessed in a diverse set of simulation settings with rare outcomes and cumulative case-control sampling. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.

stat.ME↗

arXiv2021

Higher Order Targeted Maximum Likelihood Estimation

Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed Highly Adaptive Lasso (HAL) which parametrizes the relevant functional of the data distribution in terms of a multivariate real valued cadlag function that is assumed to have finite variation norm. We showed that the HAL-MLE converges in Kullback-Leibler dissimilarity at a rate n-1/3 up till logn factors. Therefore, by using HAL as initial density estimator in the TMLE, the resulting HAL-TMLE is an asymptotically efficient estimator only assuming that the relevant nuisance functions of the data density are cadlag and have finite variation norm. However, in finite samples, the second order remainder can dominate the sampling distribution so that inference based on asymptotic normality would be anti-conservative. In this article we propose a new higher order TMLE, generalizing the regular first order TMLE. We prove that it satisfies an exact linear expansion, in terms of efficient influence functions of sequentially defined higher order fluctuations of the target parameter, with a remainder that is a k+1th order remainder. As a consequence, this k-th order TMLE allows statistical inference only relying on the k+1th order remainder being negligible. We also provide a rationale for the higher order TMLE that it will be superior to the first order TMLE by (iteratively) locally minimizing the exact finite sample remainder of the first order TMLE. The second order TMLE is demonstrated for nonparametric estimation of the integrated squared density and for the treatment specific mean outcome. We also provide an initial simulation study for the second order TMLE of the treatment specific mean confirming the theoretical analysis.

math.ST↗