Yamada H, Kuroda A, Yatabe T, Inaba T, Chiba K, Iio M
Radioisotopes. 1981 Jun;30(6):311-7.
In order to improve goodness-of-fit in RIA standard analysis, programs for computing log-logistic and cubic log-logit were written in BASIC using personal computer P-6060 (Olivetti). Iterative least square method of Taylor series was applied for non-linear estimation of logistic and log-logistic. Here "log-logistic" represents Y = (a--d)/(1+log(X)/c)b)+d As weights either 1, 1/var(Y) or 1/sigma 2 were used in logistic or log-logistic and either Y2(1--Y)2, Y2(1-Y)2/var(Y), or Y2(1--Y)2/sigma 2 were used in logistic or log-logistic and either Y2(1--Y)2, Y2(1--Y)2/var(Y), or Y2(1--Y)2/sigma 2 were used in quadratic or cubic log-logit. The term var(Y) represents squares of pure error and sigma 2 represents estimated variance calculated using a following equation log(sigma 2 + 1) = log(A)+J log(y). As indicators for goodness-of-fit, MSL/Se2, CMD% and WRV (see text) were used. Better regression was obtained in case of alpha-fetoprotein by log-logistic than by logistic. Cortisol standard curve was much better fitted with cubic log-logit than quadratic log-logit. Predicted precision of AFP standard curve was below 5% in log-logistic instead of 8% in logistic analysis. Predicted precision obtained using cubic log-logit was about five times lower than that with quadratic log-logit. Importance of selecting good models in RIA data processing was stressed in conjunction with intrinsic precision of radioimmunoassay system indicated by predicted precision.
为了提高放射免疫分析（RIA）标准分析中的拟合优度，使用个人计算机P - 6060（好利获得公司），用BASIC语言编写了计算对数-逻辑斯蒂和三次对数-对数单位变换的程序。采用泰勒级数的迭代最小二乘法对逻辑斯蒂和对数-逻辑斯蒂进行非线性估计。这里“对数-逻辑斯蒂”表示为Y = (a - d)/(1 + (log(X)/c)^b) + d。在逻辑斯蒂或对数-逻辑斯蒂分析中，权重分别使用1、1/var(Y)或1/σ²，在二次或三次对数-对数单位变换中，分别使用Y²(1 - Y)²、Y²(1 - Y)²/var(Y)或Y²(1 - Y)²/σ²。术语var(Y)表示纯误差的平方，σ²表示使用以下方程计算得到的估计方差log(σ² + 1) = log(A) + J log(y)。作为拟合优度的指标，使用了MSL/Se²、CMD%和WRV（见正文）。在甲胎蛋白的情况下，对数-逻辑斯蒂回归比逻辑斯蒂回归更好。皮质醇标准曲线用三次对数-对数单位变换比二次对数-对数单位变换拟合得好得多。在对数-逻辑斯蒂分析中，甲胎蛋白标准曲线的预测精度低于5%，而在逻辑斯蒂分析中为8%。使用三次对数-对数单位变换获得的预测精度比二次对数-对数单位变换低约五倍。结合放射免疫分析系统的内在精度（由预测精度表示），强调了在RIA数据处理中选择良好模型的重要性。
