Lee Dominic S, Rudge Andrew D, Chase J Geoffrey, Shaw Geoffrey M
Department of Mathematics and Statistics and Centre for Bioengineering, University of Canterbury, Christchurch, New Zealand.
Comput Methods Programs Biomed. 2005 Oct;80(1):75-87. doi: 10.1016/j.cmpb.2005.06.004.
In physiological system modelling for control or decision support, model validation is a critical element. A nonparametric approach for assessing the validity of deterministic dynamic models against empirical data is developed, based on kernel regression and kernel density estimation, yielding visual graphical assessment tools as well as numerical metrics of compatibility between the model and the data. Nonparametric regression has been suggested for assessing a parametric statistical model by constructing a confidence band for the proposed model and then checking whether the nonparametric regression curve lies within the band. However, for deterministic models, there is no confidence band that can be constructed. A reversal of roles is therefore suggested--construct a probability band for the nonparametric regression curve and check whether the proposed model lies within the band. This approach extends the utility of nonparametric regression for model assessment to deterministic models. Weighted kernel density estimation is incorporated to derive a density profile for the regression curve, creating a local graphical validation tool. In addition, the density profile is used to define and compute two numerical measures--average normalized density (AND) and relative average normalized density (RAND), representing global statistical validity measures. These tools are demonstrated using a biomedical system model for agitation-sedation and sedation management control.
在用于控制或决策支持的生理系统建模中，模型验证是一个关键要素。基于核回归和核密度估计，开发了一种用于根据经验数据评估确定性动态模型有效性的非参数方法，产生了可视化图形评估工具以及模型与数据之间兼容性的数值指标。有人建议通过为所提出的模型构建一个置信带，然后检查非参数回归曲线是否位于该带内，来评估参数统计模型。然而，对于确定性模型，无法构建置信带。因此建议角色反转——为非参数回归曲线构建一个概率带，并检查所提出的模型是否位于该带内。这种方法将非参数回归在模型评估中的效用扩展到了确定性模型。纳入加权核密度估计以得出回归曲线的密度分布，创建一个局部图形验证工具。此外，密度分布用于定义和计算两个数值度量——平均归一化密度（AND）和相对平均归一化密度（RAND），它们代表全局统计有效性度量。使用用于躁动 - 镇静和镇静管理控制的生物医学系统模型对这些工具进行了演示。
