De Beer Jacques O, De Beer Thomas R, Goeyens Leo
Scientific Institute of Public Health, Department of Pharmacobromatology, J. Wytsmanstraat 14, B-1050 Brussels, Belgium.
Anal Chim Acta. 2007 Feb 12;584(1):57-65. doi: 10.1016/j.aca.2006.11.032. Epub 2006 Nov 17.
In validation of quantitative analysis methods, knowledge of the response function is essential as it describes, within the range of application, the existing relationship between the response (the measurement signal) and the concentration or quantity of the analyte in the sample. The most common response function used is obtained by simple linear regression, estimating the regression parameters slope and intercept by the least squares method as general fitting method. The assumption in this fitting is that the response variance is a constant, whatever the concentrations within the range examined. The straight calibration line may perform unacceptably due to the presence of outliers or unexpected curvature of the line. Checking the suitability of calibration lines might be performed by calculation of a well-defined quality coefficient based on a constant standard deviation. The concentration value for a test sample calculated by interpolation from the least squares line is of little value unless it is accompanied by an estimate of its random variation expressed by a confidence interval. This confidence interval results from the uncertainty in the measurement signal, combined with the confidence interval for the regression line at that measurement signal and is characterized by a standard deviation s(x0) calculated by an approximate equation. This approximate equation is only valid when the mathematical function, calculating a characteristic value g from specific regression line parameters as the slope, the standard error of the estimate and the spread of the abscissa values around their mean, is below a critical value as described in literature. It is mathematically demonstrated that with respect to this critical limit value for g, the proposed value for the quality coefficient applied as a suitability check for the linear regression line as calibration function, depends only on the number of calibration points and the spread of the abscissa values around their mean.
在定量分析方法的验证中，响应函数的知识至关重要，因为它在应用范围内描述了响应（测量信号）与样品中分析物浓度或量之间的现有关系。最常用的响应函数是通过简单线性回归获得的，采用最小二乘法估计回归参数斜率和截距作为一般拟合方法。这种拟合的假设是，无论在所研究范围内的浓度如何，响应方差都是一个常数。由于存在异常值或直线出现意外的曲率，直线校准曲线可能表现不佳。可以通过基于恒定标准偏差计算一个定义明确的质量系数来检查校准曲线的适用性。通过从最小二乘线插值计算得到的测试样品浓度值价值不大，除非它伴有由置信区间表示的随机变化估计值。这个置信区间源于测量信号的不确定性，再加上该测量信号处回归线的置信区间，其特征是由一个近似方程计算出的标准偏差s(x0)。这个近似方程仅在从特定回归线参数（如斜率、估计标准误差和横坐标值围绕其均值的离散度）计算特征值g的数学函数低于文献中描述的临界值时才有效。从数学上证明，就g的这个临界极限值而言，用作校准函数的线性回归线适用性检查的质量系数提议值仅取决于校准点数和横坐标值围绕其均值的离散度。
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