title: Prediction intervals for future BMI values of individual children: a non-parametric approach by quantile boosting.
abstract: BACKGROUND
  The construction of prediction intervals (PIs) for future body mass index (BMI) values of individual children based on a recent German birth cohort study with n = 2007 children is problematic for standard parametric approaches, as the BMI distribution in childhood is typically skewed depending on age.
  
  
  METHODS
  We avoid distributional assumptions by directly modelling the borders of PIs by additive quantile regression, estimated by boosting. We point out the concept of conditional coverage to prove the accuracy of PIs. As conditional coverage can hardly be evaluated in practical applications, we conduct a simulation study before fitting child- and covariate-specific PIs for future BMI values and BMI patterns for the present data.
  
  
  RESULTS
  The results of our simulation study suggest that PIs fitted by quantile boosting cover future observations with the predefined coverage probability and outperform the benchmark approach. For the prediction of future BMI values, quantile boosting automatically selects informative covariates and adapts to the age-specific skewness of the BMI distribution. The lengths of the estimated PIs are child-specific and increase, as expected, with the age of the child.
  
  
  CONCLUSIONS
  Quantile boosting is a promising approach to construct PIs with correct conditional coverage in a non-parametric way. It is in particular suitable for the prediction of BMI patterns depending on covariates, since it provides an interpretable predictor structure, inherent variable selection properties and can even account for longitudinal data structures.
authors.affiliation: Institut für Medizininformatik, Biometrie und Epidemiologie, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany. andreas.mayr@imbe.med.uni-erlangen.de
authors.forename: Andreas
authors.initials: A
authors.lastname: Mayr
authors.forename: Torsten
authors.initials: T
authors.lastname: Hothorn
authors.forename: Nora
authors.initials: N
authors.lastname: Fenske
mesh_terms: D000293:Adolescent; D017677:Age Distribution; D015992:Body Mass Index; D002648:Child; D002675:Child, Preschool; D005260:Female; D005858:Germany; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D015233:Models, Statistical; D012016:Reference Values; D012044:Regression Analysis; D017678:Sex Distribution; D018709:Statistics, Nonparametric