title: Predicting birth weight with conditionally linear transformation models.
abstract: Low and high birth weight (BW) are important risk factors for neonatal morbidity and mortality. Gynecologists must therefore accurately predict BW before delivery. Most prediction formulas for BW are based on prenatal ultrasound measurements carried out within one week prior to birth. Although successfully used in clinical practice, these formulas focus on point predictions of BW but do not systematically quantify uncertainty of the predictions, i.e. they result in estimates of the conditional mean of BW but do not deliver prediction intervals. To overcome this problem, we introduce conditionally linear transformation models (CLTMs) to predict BW. Instead of focusing only on the conditional mean, CLTMs model the whole conditional distribution function of BW given prenatal ultrasound parameters. Consequently, the CLTM approach delivers both point predictions of BW and fetus-specific prediction intervals. Prediction intervals constitute an easy-to-interpret measure of prediction accuracy and allow identification of fetuses subject to high prediction uncertainty. Using a data set of 8712 deliveries at the Perinatal Centre at the University Clinic Erlangen (Germany), we analyzed variants of CLTMs and compared them to standard linear regression estimation techniques used in the past and to quantile regression approaches. The best-performing CLTM variant was competitive with quantile regression and linear regression approaches in terms of conditional coverage and average length of the prediction intervals. We propose that CLTMs be used because they are able to account for possible heteroscedasticity, kurtosis, and skewness of the distribution of BWs.
authors.affiliation: Institut für Statistik, Ludwig-Maximilians-Universität, München, Germany.
authors.forename: Lisa
authors.initials: L
authors.lastname: Möst
authors.affiliation: Institut für Medizinische Biometrie, Informatik und Epidemiologie, Bonn, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Schmid
authors.affiliation: Frauenklinik, Geburtshilfe und Pränataldiagnostik, Universitätsklinikum Erlangen, Universitätsstraße, Erlangen, Germany.
authors.forename: Florian
authors.initials: F
authors.lastname: Faschingbauer
authors.affiliation: Institut für Epidemiologie, Biostatistik und Prävention, Abteilung Biostatistik, Universität Zürich, Zürich, Switzerland Torsten.Hothorn@uzh.ch.
authors.forename: Torsten
authors.initials: T
authors.lastname: Hothorn
mesh_terms: D001724:Birth Weight; D005260:Female; D005333:Fetus / Q000033:anatomy & histology; D005858:Germany; D006801:Humans; D007231:Infant, Newborn; D016014:Linear Models; D011247:Pregnancy; D035501:Uncertainty
keywords: component-wise boosting; conditional coverage; conditional transformation models; prediction intervals