Fattinger K E, Verotta D
Department of Pharmacy and Pharmaceutical Chemistry, University of California San Francisco 94143, USA.
J Pharmacokinet Biopharm. 1995 Dec;23(6):581-610. doi: 10.1007/BF02353463.
In a pharmacokinetics context deconvolution facilitates the following: (i) Given data obtained after intravascular (generally intravenous) input one may estimate the disposition function; (ii) given the disposition function and data obtained after extravascular administration one may estimate the extravascular to vascular input rate function. In general if the data can be represented by the convolution of two functions, of which one is unknown, deconvolution allows the estimation of the unknown one. Attention has been given in the past to deconvolution and in particular to its nonparametric variants. However, in a population context (multiple observations collected in each of a group of subjects) the use of nonparametric deconvolution is limited to either analyzing each subject separately or to analyzing the aggregate response from the population without specifying subject-specific characteristics. To our knowledge a fully nonparametric deconvolution method in which subject specificity is explicitly taken into account has not been reported. To do so we use so-called "longitudinal splines." A longitudinal spline is a nonparametric function composed of a template spline, in common to all subjects, and of a distortion spline representing the difference of the subject's function from the template. Using longitudinal splines for input rate or disposition function one obtains a solution to the problem of taking subject specificity into account in a nonparametric deconvolution context. To obtain estimates of longitudinal splines we consider three different methods: (1) parametric nonlinear mixed effect, (2) least squares, and (3) two-stage. Results obtained in one simulated and two real data analyses are shown.
在药代动力学背景下，反卷积有助于以下几点：(i) 给定血管内（通常为静脉内）输入后获得的数据，可以估计处置函数；(ii) 给定处置函数和血管外给药后获得的数据，可以估计血管外到血管的输入速率函数。一般来说，如果数据可以由两个函数的卷积表示，其中一个是未知的，反卷积可以估计未知的那个函数。过去人们已经关注到反卷积，特别是其非参数变体。然而，在群体背景下（在一组受试者中的每一个受试者上收集多个观察值），非参数反卷积的使用仅限于分别分析每个受试者，或者在不指定受试者特异性特征的情况下分析群体的总体反应。据我们所知，尚未报道一种明确考虑受试者特异性的完全非参数反卷积方法。为此，我们使用所谓的“纵向样条”。纵向样条是一种非参数函数，由所有受试者共有的模板样条和表示受试者函数与模板差异的变形样条组成。使用纵向样条来估计输入速率或处置函数，可以在非参数反卷积背景下解决考虑受试者特异性的问题。为了获得纵向样条的估计值，我们考虑三种不同的方法：(1) 参数非线性混合效应，(2) 最小二乘法，以及(3) 两阶段法。展示了在一次模拟分析和两次真实数据分析中获得的结果。
