Analysis of concentration-response relationships by seemingly unrelated nonlinear regression (SUNR) technique

In performing statistical evaluation of concentration-response relationship in pharmacological studies, all the commercially available statistical packages assume each data point is an independent measure of the drug response, and do not account for the dependence between the multiple measurements taken from the same subject (tissue, animal, or sample). Seemingly unrelated nonlinear regression (SUNR) is a statistical technique that takes into account both within-and between-subject variance. This technique has been implemented in an SAS-based interactive program called SUNR. The statistical analyses are based upon the original work by Gallant (Gallant, 1975, J Econometrics 3:35-50; Gallant and Goebel, 1976, JASA 71:961-967), which has been further developed by Muller and Helms (1984) (Presented at ASA meeting in Washington, D.C.) To test this program, we have analyzed both simulated and actual data with SUNR, comparing our results to those of several popular statistical programs. All the programs yielded essentially the same estimates for the EC50, minimum and maximum response in both the simulated and experimental data sets. However, our results differed markedly from the commercial packages in the estimates of standard errors associated with the estimated maxima. When analyzing simulated data, which were far less noisy than the experimental data, differences between the analyses were minimal. However, in the analyses of experimental data, the standard errors calculated by the commercial programs appear to significantly underestimate the standard error. Using SUNR, however, the 95% confidence limits on the maxima are markedly wider, and, importantly, always cover the observed actual data range.