School of Mathematics and Statistics, Newcastle University, Newcastle, NE1 7RU, U.K.
Stat Med. 2012 Nov 20;31(26):3165-77. doi: 10.1002/sim.4502. Epub 2012 Aug 3.
We propose a new semiparametric model for functional regression analysis, combining a parametric mixed-effects model with a nonparametric Gaussian process regression model, namely a mixed-effects Gaussian process functional regression model. The parametric component can provide explanatory information between the response and the covariates, whereas the nonparametric component can add nonlinearity. We can model the mean and covariance structures simultaneously, combining the information borrowed from other subjects with the information collected from each individual subject. We apply the model to dose-response curves that describe changes in the responses of subjects for differing levels of the dose of a drug or agent and have a wide application in many areas. We illustrate the method for the management of renal anaemia. An individual dose-response curve is improved when more information is included by this mechanism from the subject/patient over time, enabling a patient-specific treatment regime.
我们提出了一种新的半参数模型用于功能回归分析，将参数混合效应模型与非参数高斯过程回归模型相结合，即混合效应高斯过程功能回归模型。参数成分可以提供响应和协变量之间的解释信息，而非参数成分可以添加非线性。我们可以同时对均值和协方差结构进行建模，将从其他受试者那里借来的信息与从每个个体受试者那里收集的信息结合起来。我们将该模型应用于剂量-反应曲线，该曲线描述了药物或药物剂量不同水平下受试者反应的变化，在许多领域都有广泛的应用。我们以肾性贫血的管理为例来说明这种方法。当通过这种机制从受试者/患者那里随时间获得更多信息时，个体剂量-反应曲线会得到改善，从而实现个体化的治疗方案。
