A Weighted Least‐Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal 133Xenon Washout in Dogs and Man
A Weighted Least‐Squares Technique for the Analysis of Kinetic Data and Its Application to the Study of Renal 133Xenon Washout in Dogs and Man
复制标题
动力学数据分析的加权最小二乘技术及其在狗和人肾 133Xenon 冲刷研究中的应用
DOI：
10.1161/01.res.32.1.71
复制
发表时间：
1973
影响因子：
20.1
通讯作者：
P. Cannon
中科院分区：
文献类型：
--
作者：
R. Dell;R. Sciacca;Kenneth R. Lieberman;D. Case;P. Cannon
用PL/1编写了一个计算机程序，通过迭代最小二乘技术，使用最陡下降法和牛顿-拉夫逊收敛方法的组合，依次拟合数据的二、三、四指数项的和。假设误差服从泊松分布，每个数据点通过其方差的倒数加权。一个隔室，即一个指数项，如果它没有显著地减少拟合线的最小二乘误差，则由F检验判断为不显著。通过“运行”测试和数据点落在95%置信范围之外的频率来评估数据的有效性。分析结果表明：(1)12例正常人肾133Xe洗脱曲线中有9例最适合用四室模型描述；(2)38例原发性高血压患者的研究中有18例得出四室曲线，1室血流显著减少；(3)9例充血性心力衰竭患者均有三室洗脱曲线。(4)两例少尿性肾衰竭患者的洗脱曲线用双指数方程描述得最好（其中一名患者对注射速尿有反应，出现第三个更快的隔室）。显然，这种形式的分析可以很容易地应用于用非线性方程描述的其他数据集。
A computer program was written in PL/1 to successively fit the sum of two, three, and four exponential terms to data by an iterative least-squares technique, using a combination of the steepest-descent and the Newton-Raphson methods for convergence. Each data point was weighted by the reciprocal of its variance, assuming that the errors followed a Poisson distribution. A compartment, i.e., an exponential term, was declared nonsignificant if it did not significantly reduce the least-squares error about the fitted line as judged by an F test. Validity of the data was assessed by a “runs” test and by the frequency with which data points fell outside the 95% confidence range. Results of the analysis showed that (1) 9 of 12 normal human kidney 133Xe washout curves were best described by a four-compartment model, (2) 18 of 38 studies in patients with essential hypertension yielded a four-compartment curve with significant reduction in compartment-1 flow, (3) nine patients with congestive heart failure all had three-compartment washout curves, (4) two patients with oliguric renal failure had washout curves described best by a two-exponential equation (one of these patients responded to an injection of furosemide with the appearance of a third, more rapid compartment). Obviously, this form of analysis can be easily applied to other sets of data which are described by nonlinear equations.