Analysis of RIA standard curve by log-logistic and cubic log-logit models (author's transl)

Abstract

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.