arXiv subjects

Anders Munch

Publications and source records attributed to Anders Munch.

4 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.

stat.ME↗

arXiv2025

Cheap Subsampling bootstrap confidence intervals for fast and robust inference

Bootstrapping is often applied to get confidence limits for semiparametric inference of a target parameter in the presence of nuisance parameters. Bootstrapping with replacement can be computationally expensive and problematic when cross-validation is used in the estimation algorithm due to duplicate observations in the bootstrap samples. We provide a valid, fast, easy-to-implement subsampling bootstrap method for constructing confidence intervals for asymptotically linear estimators and discuss its application to semiparametric causal inference. Our method, inspired by the Cheap Bootstrap (Lam, 2022), leverages the quantiles of a t-distribution and has the desired coverage with few bootstrap replications. We show that the method is asymptotically valid if the subsample size is chosen appropriately as a function of the sample size. We illustrate our method with data from the LEADER trial (Marso et al., 2016), obtaining confidence intervals for a longitudinal targeted minimum loss-based estimator (van der Laan and Gruber, 2012). Through a series of empirical experiments, we also explore the impact of subsample size, sample size, and the number of bootstrap repetitions on the performance of the confidence interval.

stat.ME↗

arXiv2024

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.

stat.ME↗

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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