The impact of random-effect misspecification on percentile estimation for longitudinal growth data

Identifying unusual growth-related measurements or longitudinal patterns in growth is often the focus in fetal and pediatric medicine. For example, the goal of the ongoing National Fetal Growth Study is to develop both cross-sectional and longitudinal reference curves for ultrasound fetal growth measurements that can be used for this purpose. Current methodology for estimating cross-sectional and longitudinal reference curves relies mainly on the linear mixed model. The focus of this paper is on examining the robustness of percentile estimation to the assumptions with respect to the Gaussian random-effect assumption implicitly made in the standard linear mixed model. We also examine a random-effects distribution based on mixtures of normals and compare the two approaches under both correct and misspecified random-effects distributions. In general, we find that the standard linear mixed model is relatively robust for cross-sectional percentile estimation but less robust for longitudinal or 'personalized' reference curves based on the conditional distribution given prior ultrasound measurements. The methodology is illustrated with data from a longitudinal fetal growth study.