Resumen de Growth curves for multiple-output response variables via Bayesian quantile regression models

Thomas Kneib, Bruno Santos, Agatha Rodrigues

• Reference fetal growth curves play an important role in identifying fetal growth restriction, macrosomia and other fetal malformations. This is veri ed based on percentiles of some biometric measurements at a speci c gestational age using obstetric ultrasound. As an example, the diagnosis of microcephaly is based on a biparietal diameter smaller than the 10th percentile based on the reference curve. In practice, each biometric measurement reference curve is constructed independently of other measurements, even if they are correlated and some information about dependencies among them might be lost. Here we use these measurements to de ne growth curves modelling jointly more than one measurement.

  We consider structured additive quantile regression models for multipleoutput response variables, where we are able to specify a nonlinear e ect of time.

  We de ne a Markov Chain Monte Carlo (MCMC) procedure for model estimation, using ideas previously discussed in the literature. We examine four di erent ultrasound measurements and we show how one can retrieve more information when modelling these response variables jointly instead of individually. We illustrate the method with data from pregnancies from the University Hospital of the University of S~ao Paulo (HU / USP) in the city of S~ao Paulo, Brazil.