Modeling biomarker ratios with gamma distributed components. (English) Zbl 1417.62304

Berger, Moritz; Wagner, Michael; Schmid, Matthias

Ann. Appl. Stat. 13, No. 1, 548-572 (2019); corrigendum ibid. 17, No. 3, 2700 (2023).

Summary: 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.

MSC:

62P10	Applications of statistics to biology and medical sciences; meta analysis
62J12	Generalized linear models (logistic models)

Keywords:

biomarker ratio; gamma distribution; generalized beta distribution of second kind; generalized linear model; regression