title: A balanced hazard ratio for risk group evaluation from survival data.
abstract: Common clinical studies assess the quality of prognostic factors, such as gene expression signatures, clinical variables or environmental factors, and cluster patients into various risk groups. Typical examples include cancer clinical trials where patients are clustered into high or low risk groups. Whenever applied to survival data analysis, such groups are intended to represent patients with similar survival odds and to select the most appropriate therapy accordingly. The relevance of such risk groups, and of the related prognostic factors, is typically assessed through the computation of a hazard ratio. We first stress three limitations of assessing risk groups through the hazard ratio: (1) it may promote the definition of arbitrarily unbalanced risk groups; (2) an apparently optimal group hazard ratio can be largely inconsistent with the p-value commonly associated to it; and (3) some marginal changes between risk group proportions may lead to highly different hazard ratio values. Those issues could lead to inappropriate comparisons between various prognostic factors. Next, we propose the balanced hazard ratio to solve those issues. This new performance metric keeps an intuitive interpretation and is as simple to compute. We also show how the balanced hazard ratio leads to a natural cut-off choice to define risk groups from continuous risk scores. The proposed methodology is validated through controlled experiments for which a prescribed cut-off value is defined by design. Further results are also reported on several cancer prognosis studies, and the proposed methodology could be applied more generally to assess the quality of any prognostic markers.
authors.forename: Samuel
authors.identifier: http://orcid.org/0000-0002-2405-0753
authors.initials: S
authors.lastname: Branders
authors.affiliation: Université catholique de Louvain - ICTEAM/Machine Learning Group, Place Sainte Barbe 2, Louvain-la-Neuve, B-1348, Belgium.
authors.forename: Pierre
authors.identifier: http://orcid.org/0000-0003-4835-6519
authors.initials: P
authors.lastname: Dupont
mesh_terms: D056808:Biostatistics / Q000379:methods; D001943:Breast Neoplasms / Q000235:genetics / Q000401:mortality / Q000628:therapy; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data; D005260:Female; D006801:Humans; D011379:Prognosis; D016016:Proportional Hazards Models; D012307:Risk Factors; D016019:Survival Analysis; D059467:Transcriptome
keywords: hazard ratio; prognostic factors; risk groups; survival data