Doyle M L, Ackers G K
Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, St. Louis, MO 63110.
Biophys Chem. 1992 Apr;42(3):271-81. doi: 10.1016/0301-4622(92)80019-2.
Parameter resolvability and bias has been investigated for weighted nonlinear regression of data where the independent variable is subject to instrumental uncertainty. The specific example of cooperative oxygenation of hemoglobin was studied, where fractional saturation is determined spectrophotometrically and the oxygen activity is measured with a Clark polarographic electrode. For this system the instrumental uncertainty in the oxygen electrode was measured directly and the influence of the uncertainties on resolution of oxygen binding parameters was determined by Monte Carlo simulations. Four weighting functions were tested for their ability to minimize parameter uncertainty and bias: (1) uniform weighting; (2) "propagated weighting" whereby uncertainties in the independent variable are propagated into and added to uncertainties of the dependent variable; (3) Hill plot transform, or "end weighting"; and (4) maximum likelihood analysis, where deviations between fitting function and data are minimized as weighted horizontal and vertical distance vectors. Results of the Monte Carlo simulations favor the use of either uniform weighting, propagated weighting, or maximum likelihood weighting methods. Use of the Hill transform as a weighting function produced poorer parameter resolvability and inaccurate representation of the data in general. Bias error was negligible for all weighting functions.
对于自变量存在仪器不确定性的数据的加权非线性回归，已对参数可分辨性和偏差进行了研究。研究了血红蛋白协同氧合的具体实例，其中通过分光光度法测定分数饱和度，并使用克拉克极谱电极测量氧活性。对于该系统，直接测量了氧电极中的仪器不确定性，并通过蒙特卡罗模拟确定了不确定性对氧结合参数分辨率的影响。测试了四种加权函数将参数不确定性和偏差最小化的能力：(1) 均匀加权；(2) “传播加权”，即将自变量中的不确定性传播到因变量的不确定性中并与之相加；(3) 希尔图变换，或“末端加权”；(4) 最大似然分析，即将拟合函数与数据之间的偏差作为加权水平和垂直距离向量最小化。蒙特卡罗模拟结果支持使用均匀加权、传播加权或最大似然加权方法。一般来说，使用希尔变换作为加权函数会导致较差的参数可分辨性和对数据的不准确表示。所有加权函数的偏差误差均可忽略不计。
