Duer Wayne C, Ogren Paul J, Meetze Alison, Kitchen Chester J, Von Lindern Ryan, Yaworsky Dustin C, Boden Christopher, Gayer Jeffery A
Hillsborough County Medical Examiner Department, College of Medicine, University of South Florida, 401 South Morgan Street, Tampa, Florida 33602, USA.
J Anal Toxicol. 2008 Jun;32(5):329-38. doi: 10.1093/jat/32.5.329.
The impact of experimental errors in one or both variables on the use of linear least-squares was investigated for method calibrations (response = intercept plus slope times concentration, or equivalently, Y = a(1) + a(2)X ) frequently used in analytical toxicology. In principle, the most reliable calibrations should consider errors from all sources, but consideration of concentration (X) uncertainties has not been common due to complex fitting algorithm requirements. Data were obtained for liquid chromatography-tandem mass spectrometry, gas chromatography-mass spectrometry, high-performance liquid chromatography, gas chromatography, and enzymatic assay. The required experimental uncertainties in response were obtained from replicate measurements. The required experimental uncertainties in concentration were determined from manufacturers' furnished uncertainties in stock solutions coupled with uncertainties imparted by dilution techniques. The mathematical fitting techniques used in the investigation were ordinary least-squares, weighted least-squares (WOLS), and generalized least-squares (GLS). GLS best-fit results, obtained with an efficient iteration algorithm implemented in a spreadsheet format, are used with a modified WOLS-based formula to derive reliable uncertainties in calculated concentrations. It was found that while the values of the intercepts and slopes were not markedly different for the different techniques, the derived uncertainties in parameters were different. Such differences can significantly affect the predicted uncertainties in concentrations derived from the use of the different linear least-squares equations.
针对分析毒理学中常用的方法校准（响应值=截距加斜率乘以浓度，或等效地，Y = a(1) + a(2)X），研究了一个或两个变量中的实验误差对线性最小二乘法使用的影响。原则上，最可靠的校准应考虑所有来源的误差，但由于复杂的拟合算法要求，浓度（X）不确定度的考虑并不常见。获得了液相色谱-串联质谱、气相色谱-质谱、高效液相色谱、气相色谱和酶法分析的数据。响应值所需的实验不确定度通过重复测量获得。浓度所需的实验不确定度由制造商提供的储备溶液不确定度以及稀释技术带来的不确定度确定。研究中使用的数学拟合技术为普通最小二乘法、加权最小二乘法（WOLS）和广义最小二乘法（GLS）。通过电子表格格式实现的高效迭代算法获得的GLS最佳拟合结果，与基于WOLS的修正公式一起用于推导计算浓度中的可靠不确定度。结果发现，虽然不同技术的截距和斜率值没有明显差异，但推导的参数不确定度不同。这种差异会显著影响使用不同线性最小二乘方程得出的预测浓度不确定度。
