arXiv subjects

Thomas A. Gerds

Publications and source records attributed to Thomas A. Gerds.

8 recordsLinked to original sources

arXiv2026

Nonparametric inference for sublevel-set probabilities of conditional average treatment effect functions

The average treatment effect can obscure important heterogeneity when individuals respond differently to a treatment. While the conditional average treatment effect (CATE) function captures such heterogeneity, it is difficult to communicate when it depends on many covariates. Sublevels sets of a multivariate CATE function are equally complicated objects, but the probability of a sublevel set of a CATE function is a single number with a simple interpretation as the proportion of individuals whose expected treatment effect does not exceed a prespecified threshold. By varying the threshold, a univariate monotone curve appears which can be used to visualize the overall type and degree of heterogeneity in a population. We formalize this curve as a target parameter and show that it is not pathwise differentiable under a nonparametric model. To address this nonstandard estimation problem, we leverage recent advances in monotone function estimation and develop a Grenander-type estimator that incorporates machine learning. We also show that the best piecewise linear approximation to the curve of interest is a pathwise differentiable parameter, and we develop a debiased machine learning estimator of this approximation. We investigate our proposed estimators' finite sample performance in a sequence of numerical studies based on data synthesized from a randomized trial. The methods are illustrated in data from a randomized trial on diabetes medication.

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arXiv2026

Estimation of treatment effects in presence of differential use of post-randomization concomitant medication with time-to-event outcomes

In placebo-controlled randomized trials, the post-randomization use of concomitant medications may be higher in the placebo arm than in the treatment arm. This may dilute the full benefits of the randomized drug as estimated by the intention-to-treat analysis. We focus on cardiovascular outcomes trials in type-2 diabetes patients of glucose-lowering treatments where patients in the placebo arm are more likely to add other glucose-lowering agents with established cardio-protective properties. As a supplement to the intention-to-treat analysis, we propose a class of estimands within a causal framework that isolates the specific impact of the treatment being studied from that of concomitant treatment use. These estimands are defined under time-dependent treatment interventions to balance exposure to additional medications across intervention arms. We advocate for specific stochastic interventions to achieve this balance while minimizing positivity violations, which arise when certain treatment combinations or characteristics are not sufficiently represented in the data. We employ targeted minimum loss-based estimation (TMLE) to optimize the estimation procedure for our estimands while allowing for flexible adjustments for time-dependent covariates from follow-up visits. Finally, we demonstrate the application of the methods through a simulation study and a real-world example from the LEADER cardiovascular outcomes trial, which assessed cardiovascular risk for liraglutide versus placebo.

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arXiv2025

The joint survival super learner: A super learner for right-censored data

Risk prediction models are widely used to guide real-world decision-making in areas such as healthcare and economics, and they also play a key role in estimating nuisance parameters in semiparametric inference. The super learner is a machine learning framework that combines a library of prediction algorithms into a meta-learner using cross-validated loss. In the context of right-censored data, careful consideration must be given to both the choice of loss function and the estimation of expected loss. Moreover, estimators such as inverse probability of censoring weighting require accurate modeling and an estimator of the censoring distribution. We propose a novel approach to super learning for survival analysis that jointly evaluates candidate learners for both the event-time distribution and the censoring distribution. Our method imposes no restrictions on the algorithms included in the library, accommodates competing risks, and does not rely on a single pre-specified estimator of the censoring distribution. We establish a finite-sample bound on the average price we pay for using cross-validation, and show that this price vanishes asymptotically, up to poly-logarithmic terms, provided that the size of the library does not grow faster than at a polynomial rate in the sample size. We demonstrate the practical utility of our method using prostate cancer data and compare it to existing super learner algorithms for survival analysis using synthesized data.

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arXiv2025

concrete: Targeted Estimation of Survival and Competing Risks in Continuous Time

This article introduces the R package concrete, which implements a recently developed targeted maximum likelihood estimator (TMLE) for the cause-specific absolute risks of time-to-event outcomes measured in continuous time. Cross-validated Super Learner machine learning ensembles are used to estimate propensity scores and conditional cause-specific hazards, which are then targeted to produce robust and efficient plug-in estimates of the effects of static or dynamic interventions on a binary treatment given at baseline quantified as risk differences or risk ratios. Influence curve-based asymptotic inference is provided for TMLE estimates and simultaneous confidence bands can be computed for target estimands spanning multiple multiple times or events. In this paper we review the one-step continuous-time TMLE methodology as it is situated in an overarching causal inference workflow, describe its implementation, and demonstrate the use of the package on the PBC dataset.

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arXiv2024

Estimating conditional hazard functions and densities with the highly-adaptive lasso

We consider estimation of conditional hazard functions and densities over the class of multivariate càdlàg functions with uniformly bounded sectional variation norm when data are either fully observed or subject to right-censoring. We demonstrate that the empirical risk minimizer is either not well-defined or not consistent for estimation of conditional hazard functions and densities. Under a smoothness assumption about the data-generating distribution, a highly-adaptive lasso estimator based on a particular data-adaptive sieve achieves the same convergence rate as has been shown to hold for the empirical risk minimizer in settings where the latter is well-defined. We use this result to study a highly-adaptive lasso estimator of a conditional hazard function based on right-censored data. We also propose a new conditional density estimator and derive its convergence rate. Finally, we show that the result is of interest also for settings where the empirical risk minimizer is well-defined, because the highly-adaptive lasso depends on a much smaller number of basis function than the empirical risk minimizer.

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arXiv2023

Nonparametric estimation of the interventional disparity indirect effect among the exposed

In situations with non-manipulable exposures, interventions can be targeted to shift the distribution of intermediate variables between exposure groups to define interventional disparity indirect effects. In this work, we present a theoretical study of identification and nonparametric estimation of the interventional disparity indirect effect among the exposed. The targeted estimand is intended for applications examining the outcome risk among an exposed population for which the risk is expected to be reduced if the distribution of a mediating variable was changed by a (hypothetical) policy or health intervention that targets the exposed population specifically. We derive the nonparametric efficient influence function, study its double robustness properties and present a targeted minimum loss-based estimation (TMLE) procedure. All theoretical results and algorithms are provided for both uncensored and right-censored survival outcomes. With offset in the ongoing discussion of the interpretation of non-manipulable exposures, we discuss relevant interpretations of the estimand under different sets of assumptions of no unmeasured confounding and provide a comparison of our estimand to other related estimands within the framework of interventional (disparity) effects. Small-sample performance and double robustness properties of our estimation procedure are investigated and illustrated in a simulation study.

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arXiv2021

Continuous-time targeted minimum loss-based estimation of intervention-specific mean outcomes

This paper studies the generalization of the targeted minimum loss-based estimation (TMLE) framework to estimation of effects of time-varying interventions in settings where both interventions, covariates, and outcome can happen at subject-specific time-points on an arbitrarily fine time-scale. TMLE is a general template for constructing asymptotically linear substitution estimators for smooth low-dimensional parameters in infinite-dimensional models. Existing longitudinal TMLE methods are developed for data where observations are made on a discrete time-grid. We consider a continuous-time counting process model where intensity measures track the monitoring of subjects, and focus on a low-dimensional target parameter defined as the intervention-specific mean outcome at the end of follow-up. To construct our TMLE algorithm for the given statistical estimation problem we derive an expression for the efficient influence curve and represent the target parameter as a functional of intensities and conditional expectations. The high-dimensional nuisance parameters of our model are estimated and updated in an iterative manner according to separate targeting steps for the involved intensities and conditional expectations. The resulting estimator solves the efficient influence curve equation. We state a general efficiency theorem and describe a highly adaptive lasso estimator for nuisance parameters that allows us to establish asymptotic linearity and efficiency of our estimator under minimal conditions on the underlying statistical model.

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arXiv2021

Ranking of average treatment effects with generalized random forests for time-to-event outcomes

In this paper we present a data-adaptive estimation procedure for estimation of average treatment effects in a time-to-event setting based on generalized random forests. In these kinds of settings, the definition of causal effect parameters are complicated by competing risks; here we distinguish between treatment effects on the crude and the net probabilities, respectively. To handle right-censoring, and to switch between crude and net probabilities, we propose a two-step procedure for estimation, applying inverse probability weighting to construct time-point specific weighted outcomes as input for the forest. The forest adaptively handles confounding of the treatment assigned by applying a splitting rule that targets a causal parameter. We demonstrate that our method is effective for a causal search through a list of treatments to be ranked according to the magnitude of their effect. We further apply our method to a dataset from the Danish health registries where it is of interest to discover drugs with an unexpected protective effect against relapse of severe depression.

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