Tree-based, hybrid regression for modeling biomedical data

• Applicant: Privatdozent Dr. Moritz Berger
• Subject Area: Epidemiology and Medical Biometry/Statistics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 456235587

Regression models play an increasingly important role for analysing data from clinical and epidemiological studies. They allow to describe and quantify the association between a dependent variable of interest (outcome variable) and a set of explanatory variables. Generalized linear regression models (GLMs) relate the expected value of the outcome variable to a linear combination of the explanatory variables via a suitable link function. The linear effects can easily be interpreted independently of the values of other variables. The simple form of a GLM however comes at the price that the parametric structure often does not sufficiently describe the more complex relationships in biomedical applications. As a seminal extension of GLMs, Hastie & Tibshirani introduced the class of varying coefficient models, which allow to adjust for interactions in a very flexibel way. The specific variant of varying coefficient models dealt with in this project are so-called tree-based varying coefficient models, abbreviated to ‘TSVC’ (Tree Structured Varying Coefficients). Building upon the developements in the first phase of the project (April 2021 - April 2025) the main objective now is to further extend the class of TSVC models. The subject of the second project phase is the developement in three largely unexplored areas, namely (i) the modelling of hierarchical data (longitudinal data or grouped cross-sectional data), (ii) the extension to distributional regression approaches, and (iii) the combination of the TSVC algorithm with variable selection by gradient boosting. In the course of the methodological developments, it is planned to make the implementations freely available by suitable software (supplementing the existing TSVC programme package). Furthermore, the added value of the proposed methods, as in the preliminary work, will be investigated by means of extensive simulations and by using selected clinical and epidemiological data (in cooperation with partners from the DZNE Bonn, ICH Hamburg and the TU Munich).

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr. Matthias Schmid