Replica analysis of overfitting in regression models for time-to-event data

ACC Coolen; JE Barrett; P Paga; CJ Perez-Vicente

doi:10.1088/1751-8121/aa812f

Home/Archive/arXiv

arXiv · 1705.01730

Replica analysis of overfitting in regression models for time-to-event data

ACC Coolen·JE Barrett·P Paga·CJ Perez-Vicente

View original source ↗Read source document ↗Export metadata ↓

Abstract

Overfitting, which happens when the number of parameters in a model is too large compared to the number of data points available for determining these parameters, is a serious and growing problem in survival analysis. While modern medicine presents us with data of unprecedented dimensionality, these data cannot yet be used effectively for clinical outcome prediction. Standard error measures in maximum likelihood regression, such as p-values and z-scores, are blind to overfitting, and even for Cox's proportional hazards model (the main tool of medical statisticians), one finds in literature only rules of thumb on the number of samples required to avoid overfitting. In this paper we present a mathematical theory of overfitting in regression models for time-to-event data, which aims to increase our quantitative understanding of the problem and provide practical tools with which to correct regression outcomes for the impact of overfitting. It is based on the replica method, a statistical mechanical technique for the analysis of heterogeneous many-variable systems that has been used successfully for several decades in physics, biology, and computer science, but not yet in medical statistics. We develop the theory initially for arbitrary regression models for time-to-event data, and verify its predictions in detail for the popular Cox model.

Explore related subjects

stat.AP cond-mat.dis-nn physics.data-an

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

ACC Coolen, JE Barrett, P Paga, CJ Perez-Vicente. 2017-07-20. Replica analysis of overfitting in regression models for time-to-event data. https://doi.org/10.1088/1751-8121%2Faa812f

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Online activity prediction via generalized Indian buffet process models

Online A/B tests are the standard tool for data-driven decision-making at scale. Among the design choices with the largest impact on statistical power is the triggering mechanism: how many users to expose and for how long. This often requires forecasting user engagement, i.e., whether enough users will trigger, and when a target participation level will be reached, from limited pilot data. We introduce a Bayesian nonparametric model for predicting both new-user counts and total triggers, accommodating the heavy-tailed engagement patterns typical of web experiments. All predictive quantities can be computed without intensive numerical procedures such as Markov chain Monte Carlo (MCMC) or variational inference. We evaluate on three public datasets (over 450 public benchmark evaluations) and a proprietary benchmark drawn from 759 production A/B tests comprising 1,774 arms. Across the benchmark analyses, our models are competitive and frequently improve accuracy in forecasting new users, total triggers, and time to reach a target sample size compared with state-of-the-art competitors, especially when only a few pilot days are observed.

stat.AP↗

arXiv2026

Spending Scarce Confirmatory PET Measurements: Target-Aligned Validation in A4/LEARN

Anti-amyloid therapies and blood-based biomarkers are changing Alzheimer disease workups into a two-stage measurement workflow: screen broadly with cheaper information, then spend scarce confirmatory amyloid measurements where they support the decision that will be reported. Amyloid positron-emission tomography (PET) remains one such protocol measurement for amyloid burden, but PET slots, trial budgets, and payer-facing evidence packages are finite. This paper asks a deliberately operational question: when is simple transparent PET validation enough, and when is a fitted residual-uncertainty score worth the added complexity? For a weighted protocol target, the first-order value of validating subject i is the product of target influence and residual protocol uncertainty. Generic uncertainty sampling uses only the second factor and can spend PET measurements on subjects that are hard to predict but weak for the scientific, clinical, or commercial claim. We apply this rule to the A4/LEARN PET archive, treating observed PET as a design laboratory for scarce-confirmation studies. For the primary APOE4 carrier versus non-carrier contrast in Centiloid 24-or-higher PET positivity, simple APOE4-balanced validation recovers nearly all of the target-specific gain: at PET budget 200, the confidence-interval width ratio relative to random validation is 0.923 for APOE4 balancing and 0.914 for target-specific scoring, while generic uncertainty sampling is 0.980. Other targets behave differently: target-specific scoring gives larger gains for an age-slope analysis and for cutoff-indexed PET positivity. The practical message is simple: spend scarce protocol measurements according to the claim being validated, not only according to prediction uncertainty.

stat.AP↗

arXiv2026

Identifying Damage Pathways Linking Sequence Composition to Storage Failure in DNA Data Storage via High-Dimensional Mediation Analysis

DNA data storage offers extraordinary information density and long-term durability, but its reliability is limited by sequence-dependent errors introduced during synthesis and accumulated during storage. It remains unclear how sequence composition is associated with storage failure through specific molecular damage components. We develop a high-dimensional semiparametric mediation framework for survival outcomes. GC content is treated as the exposure, a high-dimensional baseline damage spectrum (a vector of per-read damage counts stratified by trinucleotide context and error type) as the mediator, and storage-quality failure as the outcome. Nonlinear covariate effects in both the mediator and survival models are approximated using deep neural networks. A three-step procedure combining product-of-coefficients screening, Smoothly Clipped Absolute Deviation (SCAD) penalized estimation, and joint significance testing is developed for mediator selection and inference. Applied to an aging experiment on electrochemically synthesized DNA, the method identifies 14 significant mediators, all corresponding to single-base deletions, with estimated mediated effects concentrated in trinucleotide contexts ending in C. These results reveal deletion-type damage as a major pathway linking sequence composition to reduced archival reliability and suggest candidate sequence features for future optimization and error-control strategies. The proposed framework thus offers a mechanism-oriented statistical approach for understanding and improving the reliability of DNA data storage.

stat.AP↗