Kogan Clark, Kalachev Leonid, Van Dongen Hans P A
Sleep and Performance Research Center, Washington State University, Spokane, WA 99210, USA.
Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA.
Comput Math Methods Med. 2016;2016:4724395. doi: 10.1155/2016/4724395. Epub 2016 Jan 14.
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.
在针对多个受试者的重复测量研究设计中，通过贝叶斯预测纳入个体反应数据，能够捕捉受试者内和受试者间方差的总体模型实现了对结果测量（反应变量）的高效个体化预测。当测量限制妨碍了合理水平的预测准确性时，与主要反应一起测量的额外（次要）反应变量可能有助于提高预测准确性。我们针对主要和次要反应变量之间存在显著受试者间相关性且假设受试者内相关性可忽略不计的情况进行研究。我们展示了如何根据次要反应观测值确定主要反应预测的准确性。考虑到主要和次要变量的测量成本，我们确定了以最小成本为受试者均值模型产生固定平均预测准确性所需的观测次数。我们通过使用多导睡眠图和手腕活动记录仪估计受试者特定的睡眠参数对此进行说明。我们还在一个示例随时间变化的线性模型中考虑预测准确性，并推导了平均而言实现最佳预测准确性的测量最佳时间的方程。最后，我们研究了一个涉及昼夜节律模型的示例，并通过数值表明次要变量在这个随时间变化的非线性模型中也可以改善个体化预测。
