Estimating onset time from longitudinal data in the presence of measurement error with application to estimating gestational age from maternal anthropometry during pregnancy.

Accurate assessment of gestational age at birth is necessary for optimal pediatric care. In high resource countries, several methods using ultrasound have been proposed to assess gestational age at birth; however, these methods are not easily accessible for low-resource populations. We develop a shared random parameter model for estimating gestational age at birth from longitudinal maternal anthropometry that incorporates additional maternal information from the last menstrual period, a measure of gestational age collected with sizable measurement error. The proposed methodology is evaluated using simulation studies under a training-test set paradigm. In addition, we propose methodology to validate prediction when some measurements of the gold standard are collected with measurement error. We illustrate the proposed methodologies with data from the NICHD Fetal Growth Studies.