Predicting large fetuses at birth is of great interest to obstetricians. Using an NICHD Scandinavian Study that collected longitudinal ultrasound examination data during pregnancy, we estimate diagnostic accuracy parameters of estimated fetal weight (EFW) at various times during pregnancy in predicting large-for-gestational-age. We adopt a placement value based Bayesian regression model with random effects to estimate ROC curves. The use of placement values allows us to model covariate effects directly on the ROC curves and the adoption of a Bayesian approach accommodates the a priori constraint that an ROC curve of EFW near delivery should dominate another further away. The proposed methodology is shown to perform better than some alternative approaches in simulations and its application to the Scandinavian Study data suggests that diagnostic accuracy of EFW can improve about 65% from week 17 to 37 of gestation.