Boosting Structured Additive Quantile Regression for Longitudinal Childhood Obesity Data

Fenske Nora (), Fahrmeir Ludwig (), Hothorn Torsten (), Rzehak Peter () and Höhle Michael ()
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Fenske Nora: Institut für Statistik, Ludwigs-Maximilians-Universität München, Ludwigstr. 33, München 80539, Germany
Fahrmeir Ludwig: Institut für Statistik, Ludwigs-Maximilians-Universität München, Germany
Hothorn Torsten: Abteilung Biostatistik, Universität Zürich, Switzerland
Rzehak Peter: Division of Metabolic and Nutritional Medicine, Dr. von Hauner Children’s Hospital, Ludwig-Maximilians-Universität München, Germany
Höhle Michael: Department of Mathematics, Stockholm University, Sweden

The International Journal of Biostatistics, 2013, vol. 9, issue 1, 1-18

Abstract: Childhood obesity and the investigation of its risk factors has become an important public health issue. Our work is based on and motivated by a German longitudinal study including 2,226 children with up to ten measurements on their body mass index (BMI) and risk factors from birth to the age of 10 years. We introduce boosting of structured additive quantile regression as a novel distribution-free approach for longitudinal quantile regression. The quantile-specific predictors of our model include conventional linear population effects, smooth nonlinear functional effects, varying-coefficient terms, and individual-specific effects, such as intercepts and slopes. Estimation is based on boosting, a computer intensive inference method for highly complex models. We propose a component-wise functional gradient descent boosting algorithm that allows for penalized estimation of the large variety of different effects, particularly leading to individual-specific effects shrunken toward zero. This concept allows us to flexibly estimate the nonlinear age curves of upper quantiles of the BMI distribution, both on population and on individual-specific level, adjusted for further risk factors and to detect age-varying effects of categorical risk factors. Our model approach can be regarded as the quantile regression analog of Gaussian additive mixed models (or structured additive mean regression models), and we compare both model classes with respect to our obesity data.

Keywords: longitudinal quantile regression; additive mixed models; body mass index; overweight (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1515/ijb-2012-0035

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