arXiv subjects

Johan Steen

Publications and source records attributed to Johan Steen.

7 recordsLinked to original sources

arXiv2025

On the additive image of 0th persistent homology

For $X$ a finite category and $F$ a finite field, we study the additive image of the functor $\operatorname{H}_0(-,F) \colon \operatorname{rep}(X, \mathbf{Top}) \to \operatorname{rep}(X, \mathbf{Vect}_F)$, or equivalently, of the free functor $\operatorname{rep}(X, \mathbf{Set}) \to \operatorname{rep}(X, \mathbf{Vect}_F)$. We characterize all finite categories $X$ for which the indecomposables in the additive image coincide with the indecomposable indicator representations and provide examples of quivers of wild representation type where the additive image contains only finitely many indecomposables. Motivated by questions in topological data analysis, we conduct a detailed analysis of the additive image for finite grids. In particular, we show that for grids of infinite representation type, there exist infinitely many indecomposables both within and outside the additive image. We develop an algorithm for determining if a representation of a finite category is in the additive image. In addition, we investigate conditions for realizability and the effect of modifications of the source category and the underlying field. The paper concludes with a discussion of the additive image of $\operatorname{H}_n(-,F)$ for an arbitrary field $F$, extending previous work for prime fields.

math.RT↗

arXiv2021

On Estimation and Cross-validation of Dynamic Treatment Regimes with Competing Risks

The optimal moment to start renal replacement therapy in a patient with acute kidney injury (AKI) remains a challenging problem in intensive care nephrology. Multiple randomised controlled trials have tried to answer this question, but these can, by definition, only analyse a limited number of treatment initiation strategies. In view of this, we use routinely collected observational data from the Ghent University Hospital intensive care units (ICUs) to investigate different pre-specified timing strategies for renal replacement therapy initiation based on time-updated levels of serum potassium, pH and fluid balance in critically ill patients with AKI with the aim to minimize 30-day ICU mortality. For this purpose, we apply statistical techniques for evaluating the impact of specific dynamic treatment regimes in the presence of ICU discharge as a competing event. We discuss two approaches, a non-parametric one - using an inverse probability weighted Aalen-Johansen estimator - and a semiparametric one - using dynamic-regime marginal structural models. Furthermore, we suggest an easy to implement cross-validation technique that can be used for the out-of-sample performance assessment of the optimal dynamic treatment regime. Our work illustrates the potential of data-driven medical decision support based on routinely collected observational data.

stat.AP↗

arXiv2020

Handling time-dependent exposures and confounders when estimating attributable fractions -- bridging the gap between multistate and counterfactual modeling

The population-attributable fraction (PAF) expresses the proportion of events that can be ascribed to a certain exposure in a certain population. It can be strongly time-dependent because either exposure incidence or excess risk may change over time. Competing events may moreover hinder the outcome of interest from being observed. Occurrence of either of these events may, in turn, prevent the exposure of interest. Estimation approaches therefore need to carefully account for the timing of events in such highly dynamic settings. The use of multistate models has been widely encouraged to eliminate preventable yet common types of time-dependent bias. Even so, it has been pointed out that proposed multistate modeling approaches for PAF estimation fail to fully eliminate such bias. In addition, assessing whether patients die from rather than with a certain exposure not only requires adequate modeling of the timing of events but also of their confounding factors. While proposed multistate modeling approaches for confounding adjustment may adequately accommodate baseline imbalances, unlike g-methods, these proposals are not generally equipped to handle time-dependent confounding. However, the connection between multistate modeling and g-methods (e.g. inverse probability of censoring weighting) for PAF estimation is not readily apparent. In this paper, we provide a weighting-based characterization of both approaches to illustrate this connection, to pinpoint current shortcomings of multistate modeling, and to enhance intuition into simple modifications to overcome these. R code is made available to foster the uptake of g-methods for PAF estimation.

stat.ME↗

arXiv2019

Cotorsion torsion triples and the representation theory of filtered hierarchical clustering

We give a full classification of representation types of the subcategories of representations of an $m \times n$ rectangular grid with monomorphisms (dually, epimorphisms) in one or both directions, which appear naturally in the context of clustering as two-parameter persistent homology in degree zero. We show that these subcategories are equivalent to the category of all representations of a smaller grid, modulo a finite number of indecomposables. This equivalence is constructed from a certain cotorsion torsion triple, which is obtained from a tilting subcategory generated by said indecomposables.

math.RT↗

arXiv2018

Graphical models for mediation analysis

Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These express how a change in exposure affects those intermediate variables (along certain pathways), and how the resulting changes in those variables in turn affect the outcome (along subsequent pathways). However, unlike identification of total effects, adjustment for confounding is insufficient for identification of path-specific effects because their magnitude is also determined by the extent to which individuals who experience large exposure effects on the mediator, tend to experience relatively small or large mediator effects on the outcome. This chapter therefore provides an accessible review of identification strategies under general nonparametric structural equation models (with possibly unmeasured variables), which rule out certain such dependencies. In particular, it is shown which path-specific effects can be identified under such models, and how this can be done.

stat.ME↗

arXiv2016

Enrichment and representability for triangulated categories

Given a fixed tensor triangulated category S we consider triangulated categories T together with an S-enrichment which is compatible with the triangulated structure of T. It is shown that, in this setting, an enriched analogue of Brown representability holds when both S and T are compactly generated. A natural class of examples of such enriched triangulated categories categories are module categories over separable monoids in S. In this context we prove a version of the Eilenberg-Watts theorem for exact coproduct and copower preserving S-functors, i.e., we show that any such functor between the module categories of separable monoids in S is given by tensoring with a bimodule.

math.CT↗

arXiv2014

Strong generators in tensor triangulated categories

We show that in an essentially small rigid tensor triangulated category with connected Balmer spectrum there are no proper non-zero thick tensor ideals admitting strong generators. This proves, for instance, that the category of perfect complexes over a commutative ring without non-trivial idempotents has no proper non-zero thick subcategories that are strongly generated.

math.CT↗