arXiv subjects

Manuel M. Müller

Publications and source records attributed to Manuel M. Müller.

3 recordsLinked to original sources

arXiv2026

Data-driven controlled subgroup selection in clinical trials

Subgroup selection in clinical trials is essential for identifying patient groups that react differently to a treatment, thereby enabling personalised medicine. In particular, subgroup selection can identify patient groups that respond particularly well to a treatment or that encounter adverse events more often. However, this is a post-selection inference problem, which may pose challenges for traditional techniques used for subgroup analysis, such as increased Type I error rates and potential biases from data-driven subgroup identification. In this paper, we present two methods for subgroup selection in regression problems: one based on generalised linear modelling and another on isotonic regression. We demonstrate how these methods can be used for data-driven subgroup identification in the analysis of clinical trials, focusing on two distinct tasks: identifying patient groups that are safe from manifesting adverse events and identifying patient groups with high treatment effect, while controlling for Type I error in both cases. A thorough simulation study is conducted to evaluate the strengths and weaknesses of each method, providing detailed insight into the sensitivity of the Type I error rate control to modelling assumptions.

stat.ME↗

arXiv2025

Are all models wrong? Fundamental limits in distribution-free empirical model falsification

In statistics and machine learning, when we train a fitted model on available data, we typically want to ensure that we are searching within a model class that contains at least one accurate model -- that is, we would like to ensure an upper bound on the model class risk (the lowest possible risk that can be attained by any model in the class). However, it is also of interest to establish lower bounds on the model class risk, for instance so that we can determine whether our fitted model is at least approximately optimal within the class, or, so that we can decide whether the model class is unsuitable for the particular task at hand. Particularly in the setting of interpolation learning where machine learning models are trained to reach zero error on the training data, we might ask if, at the very least, a positive lower bound on the model class risk is possible -- or are we unable to detect that "all models are wrong"? In this work, we answer these questions in a distribution-free setting by establishing a model-agnostic, fundamental hardness result for the problem of constructing a lower bound on the best test error achievable over a model class, and examine its implications on specific model classes such as tree-based methods and linear regression.

math.ST↗

arXiv2023

Isotonic subgroup selection

Given a sample of covariate-response pairs, we consider the subgroup selection problem of identifying a subset of the covariate domain where the regression function exceeds a pre-determined threshold. We introduce a computationally-feasible approach for subgroup selection in the context of multivariate isotonic regression based on martingale tests and multiple testing procedures for logically-structured hypotheses. Our proposed procedure satisfies a non-asymptotic, uniform Type I error rate guarantee with power that attains the minimax optimal rate up to poly-logarithmic factors. Extensions cover classification, isotonic quantile regression and heterogeneous treatment effect settings. Numerical studies on both simulated and real data confirm the practical effectiveness of our proposal, which is implemented in the R package ISS.

math.ST↗