Prediction Accuracy in Multivariate Repeated-Measures Bayesian Forecasting Models with Examples Drawn from Research on Sleep and Circadian Rhythms

In study designs with repeated measures for multiple subjects, population models capturing within-and between-subjects variances enable efficient individualized prediction of outcome measures (response variables) by incorporating individuals response data through Bayesian forecasting. When measurement constraints preclude reasonable levels of prediction accuracy, additional (secondary) response variables measured alongside the primary response may help to increase prediction accuracy. We investigate this for the case of substantial between-subjects correlation between primary and secondary response variables, assuming negligible within-subjects correlation. We show how to determine the accuracy of primary response predictions as a function of secondary response observations. Given measurement costs for primary and secondary variables, we determine the number of observations that produces, with minimal cost, a fixed average prediction accuracy for a model of subject means. We illustrate this with estimation of subject-specific sleep parameters using polysomnography and wrist actigraphy. We also consider prediction accuracy in an example time-dependent, linear model and derive equations for the optimal timing of measurements to achieve, on average, the best prediction accuracy. Finally, we examine an example involving a circadian rhythm model and show numerically that secondary variables can improve individualized predictions in this time-dependent nonlinear model as well.