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The median hazard ratio: a useful measure of variance and general contextual effects in multilevel survival analysis
Inst Clin Evaluat Sci, G106,2075 Bayview Ave, Toronto, ON M4N 3M5, Canada.;Univ Toronto, Inst Hlth Management Policy & Evaluat, Toronto, ON, Canada.;Sunnybrook Res Inst, Schulich Heart Res Program, Toronto, ON, Canada..
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Medicinska och farmaceutiska vetenskapsområdet, centrumbildningar mm, Centre for Clinical Research, County of Västmanland. Lund Univ, Unit Social Epidemiol, Fac Med, Malmo, Sweden..
Lund Univ, Unit Social Epidemiol, Fac Med, Malmo, Sweden.;Region Skane, Ctr Primary Hlth Care Res, Malmo, Sweden..
2017 (English)In: Statistics in Medicine, ISSN 0277-6715, E-ISSN 1097-0258, Vol. 36, no 6, p. 928-938Article in journal (Refereed) Published
Abstract [en]

Multilevel data occurs frequently in many research areas like health services research and epidemiology. A suitable way to analyze such data is through the use of multilevel regression models (MLRM). MLRM incorporate cluster-specific random effects which allow one to partition the total individual variance into between-cluster variation and between-individual variation. Statistically, MLRM account for the dependency of the data within clusters and provide correct estimates of uncertainty around regression coefficients. Substantively, the magnitude of the effect of clustering provides a measure of the General Contextual Effect (GCE). When outcomes are binary, the GCE can also be quantified by measures of heterogeneity like the Median Odds Ratio (MOR) calculated from a multilevel logistic regression model. Time-to-event outcomes within a multilevel structure occur commonly in epidemiological and medical research. However, the Median Hazard Ratio (MHR) that corresponds to the MOR in multilevel (i.e., 'frailty') Cox proportional hazards regression is rarely used. Analogously to the MOR, the MHR is the median relative change in the hazard of the occurrence of the outcome when comparing identical subjects from two randomly selected different clusters that are ordered by risk. We illustrate the application and interpretation of the MHR in a case study analyzing the hazard of mortality in patients hospitalized for acute myocardial infarction at hospitals in Ontario, Canada. We provide R code for computing the MHR. The MHR is a useful and intuitive measure for expressing cluster heterogeneity in the outcome and, thereby, estimating general contextual effects in multilevel survival analysis.

Place, publisher, year, edition, pages
WILEY , 2017. Vol. 36, no 6, p. 928-938
Keywords [en]
Median Hazard Ratio, Median Odds Ratio, clustered data, multilevel analysis, frailty models, survival analysis
National Category
Bioinformatics (Computational Biology) Public Health, Global Health, Social Medicine and Epidemiology
Identifiers
URN: urn:nbn:se:uu:diva-320927DOI: 10.1002/sim.7188ISI: 000394781600004PubMedID: 27885709OAI: oai:DiVA.org:uu-320927DiVA, id: diva2:1091601
Funder
Swedish Research Council, 2013-2484Available from: 2017-04-27 Created: 2017-04-27 Last updated: 2018-01-13Bibliographically approved

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