Individual predictions based on nonlinear mixed modeling: application to prenatal twin growth

The assessment of growth during fetal life and childhood commonly relies upon cross'sectional reference ranges or centiles. However, individual sequential predictions may help the timewise assessment of a growth process. In twin pregnancies for example, which are at risk of growth restriction, such predictions may improve the detection of abnormal trajectories. In this article, we present a simple forecasting method, assuming that a given normal individual behaves in the same way as a reference population. We consider, as a prediction in a given individual, the forecast of a future observation conditional to any previous observation and a set of population parameters obtained by nonlinear mixed modeling in a reference population. We suggest an estimator for this prediction without resorting to linear approximation and show that it enjoys interesting asymptotics when the amount of observations increases over time. We use two independent real datasets of twin pregnancies with normal growth and outcome to illustrate the application of such predictions in prenatal growth. We consider the first dataset as a reference dataset and model it using a two'level nonlinear model. We perform illustration and validation of predictions on the second dataset.