Small values of | b | result in a gradual transition from one asymptotic region to the other, while large values of | b | result in fast transitions. For 5PL curves, all 4 cases produce distinct functional forms. For 4PL curves, case #1 and case #4 or case #2 and case #3 generate the same functional forms, and both conventions are used in the industry. Note that when g = 1 and the curve is actually a 4PL curve, two pairs of the cases can be combined into single cases. The relationship between the order of a and d, the sign of b, and the slope of the monotonic 5PL and 4PL functions can be seen in the 4 cases above. See Tech Note: Curve Weighting for more information. Sample concentrations computed from unweighted curve fitting procedures can differ from properly weighted curves by hundreds of percent.

This produces the most accurate concentration estimates. Weighting the squared residual errors with the estimated variances at each point allows the responses from the noisier and less noisy points to contribute equally to the regression curve. The reaction kinetics of the assay are also a major factor in the response variances of each dose, and the reaction kinetics vary widely between different tests. It is common for the variances of points at the high-response end of a curve to be three or four orders of magnitude larger than variances of points at the low response end. Because immunoassay and bioassay data are quite heteroscedastic (unequal variances), each response is weighted by the inverse of the estimated variance of that response: This distribution of responses is approximately normal for most immunoassay and bioassay data.Ĭritical to obtaining the best curve fit are the estimated variances used to compute the weighted squared residual at each point. Initial variance estimates can be made from one assay, and more reliable variance estimates can be obtained from a pool of 6 or more historical assays. The estimated variance is obtained from a distribution of responses at specific concentrations. A weighted squared residual is the vertical distance between the observed point and the curve, squared, divided by the estimated variance at that point. Least squares regression derives the one set of coefficients that has the smallest sum of squared residuals (RSSE, or residual sum of squares error) for that curve model. Statistical curve fitting uses a method called least squares regression fitting.

Graphpad prism 5 logistic regression