Plikaytis B D, Turner S H, Gheesling L L, Carlone G M
Biostatistics and Information Management Branch, Centers for Disease Control, Atlanta, Georgia 30333.
J Clin Microbiol. 1991 Jul;29(7):1439-46. doi: 10.1128/jcm.29.7.1439-1446.1991.
We examined several of the more commonly used models (log-log, two forms of the logit-log, and the four-parameter logistic-log transformations) for forming standard or calibration curves by using a standardized enzyme-linked immunosorbent assay (ELISA). Assay range, accuracy, and error for each function were measured and compared. Antibody levels to Neisseria meningitidis group A polysaccharide were estimated by calculating antibody concentrations of a serially diluted standard reference serum of known concentration. Each function achieved a high squared correlation coefficient (r2 greater than 0.97), indicating a high degree of accuracy in forming the standard curves. However, when predicted antibody concentrations were compared with the known values, the log-log function exhibited the least precision, with extreme percentages of error occurring at several dilutions. A partially specified logit-log transformation performed better than the log-log model over a reduced range of standard dilutions. This indicated that a high r2 alone was not a reliable measure of the accuracy of the standard curve. Of the methods surveyed, the logistic-log and fully specified logit-log functions were the most accurate models for forming standard curves and for interpolating antibody concentrations from the standard curve. The accuracy of the fully specified logit-log function is highly dependent on the precise specification of two unknown quantities, the optical densities at zero and infinite concentrations, prior to fitting the model to a typical set of calibration data. The four-parameter logistic-log function was the preferred choice for quantitating N. meningitidis group A total polysaccharide antibody by using a standardized ELISA. The function does not require prespecification of any parameters before estimating the standard curve, and the four parameters are readily interpretable in terms of identifiable physical quantities. This model also has the advantage that it is easiest to visualize since it does not incorporate complex transformations of the optical density scale.
我们使用标准化酶联免疫吸附测定（ELISA），研究了几种更常用的用于形成标准曲线或校准曲线的模型（对数-对数模型、两种形式的对数几率-对数模型以及四参数逻辑对数变换模型）。测量并比较了每个函数的检测范围、准确性和误差。通过计算已知浓度的系列稀释标准参考血清的抗体浓度，来估计针对A群脑膜炎奈瑟菌多糖的抗体水平。每个函数都获得了较高的平方相关系数（r2大于0.97），这表明在形成标准曲线方面具有高度准确性。然而，当将预测的抗体浓度与已知值进行比较时，对数-对数函数的精度最低，在几个稀释度下出现了极高的误差百分比。在较窄的标准稀释范围内，部分指定的对数几率-对数变换模型比对数-对数模型表现更好。这表明仅高r2并不是标准曲线准确性的可靠度量。在所调查的方法中，逻辑对数模型和完全指定的对数几率-对数函数是形成标准曲线以及从标准曲线内插抗体浓度的最准确模型。完全指定的对数几率-对数函数的准确性高度依赖于在将模型拟合到一组典型校准数据之前，对两个未知量（零浓度和无限浓度下的光密度）的精确指定。四参数逻辑对数函数是使用标准化ELISA定量A群脑膜炎奈瑟菌总多糖抗体的首选。该函数在估计标准曲线之前不需要预先指定任何参数，并且这四个参数根据可识别的物理量很容易解释。该模型的另一个优点是，由于它不包含光密度标度的复杂变换，所以最容易可视化。
