四参数log-logistic模型在生物活性测定研究中的应用

目的: 利用数学模型拟合生物反应与药物浓度的S曲线关系，比较不同模型的拟合效果。方法: 分别利用logistic模型与四参数log-logistic模型对目前常见体外生物活性测定中反应液吸光度与药物浓度的S曲线关系进行拟合。结果和结论: 四参数log-logistic模型拟合效果要优于传统的logistic模型，R²分别为1.000和0.9975，误差均方根分别为0.00968和0.1030。在拟合S型曲线方面，四参数log-logistic模型比logistic模型拟合效果更优，且其4个参数更具现实意义，即D和A分别代表S曲线的下限和上限，C代表半数反应浓度，B代表吸光度增长速率参数，相当于S曲线的斜率。

Objective: To fit the sigmoid relationship between the bioassay reaction and drug concentration and to compare the effectiveness of fit of different models. Methods: The logistic model and 4 parameter log-logistic model were used to fit the relationship between absorbance of reaction and concentration which was commonly found in in-vitro bioassay. Results and Conclusion: The 4 parameter log-logistic model had a superior goodness of fit compared to logistic model,the R² was 1.000 and 0.9975,respectively,and the root MSE was 0.00968 and 0.1030,respectively.The 4 parameter log-logistic model fits better than logistic model for the S-shape curves,and are more practical for understanding,i.e.,D,A,C and B represent the lower asymptote,upper asymptote,50% effective concentration (EC₅₀) and steepness (related to the slope of the curve at the EC₅₀) respectively.