Open Access
March 2019 Modeling biomarker ratios with gamma distributed components
Moritz Berger, Michael Wagner, Matthias Schmid
Ann. Appl. Stat. 13(1): 548-572 (March 2019). DOI: 10.1214/18-AOAS1207


We propose a regression model termed “extended GB2 model”, which is designed to analyze ratios of biomarkers in epidemiological and medical research. Typical examples of biomarker ratios are given by the LDL/HDL cholesterol ratio in cardiovascular research and the amyloid-$\beta$ 42/40 ratio in dementia research. Unlike regression modeling with a log-transformed response, which is often used to describe ratio outcomes in observational studies, the extended GB2 model directly links the expectation of the untransformed biomarker ratio to a set of covariates. This strategy allows for a simple interpretation of the predictor-response relationships in terms of multiplicative increases/decreases of the expected outcome, similar to Poisson and Cox regression. In the theoretical part of the paper, we derive the log-likelihood of the proposed model, analyze its properties, and provide details on confidence intervals and hypothesis testing. We will also present the results of a simulation study demonstrating the robustness of the proposed modeling approach against model misspecification. The usefulness of the method is demonstrated by two applications on the aforementioned LDL/HDL cholesterol and amyloid-$\beta$ 42/40 ratios. For this, we analyze data from a cohort study on kidney disease and from a large observational database on neurodegenerative diseases.


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Moritz Berger. Michael Wagner. Matthias Schmid. "Modeling biomarker ratios with gamma distributed components." Ann. Appl. Stat. 13 (1) 548 - 572, March 2019.


Received: 1 January 2018; Revised: 1 August 2018; Published: March 2019
First available in Project Euclid: 10 April 2019

zbMATH: 07057439
MathSciNet: MR3937440
Digital Object Identifier: 10.1214/18-AOAS1207

Keywords: Biomarker ratio , gamma distribution , generalized beta distribution of the second kind , generalized linear model , regression

Rights: Copyright © 2019 Institute of Mathematical Statistics

Vol.13 • No. 1 • March 2019
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