Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
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Resulting from a clinical consulting case in urology we developed a software tool for determining nonlinear dose-response relationships. Unlike most existing statistical software packages, we directly compute and display analytical pointwise 95% confidence intervals for the prediction result. Furthermore, user-defined changepoints with 95% confidence interval can be calculated in order to estimate the dosage for a 50% response rate, for instance. This is necessary to compare the effect of different retinoids, tumor cell lines, etc. In this way we supplement the clinical software-equipment in our laboratory and encourage the evaluation of dose-response data. The numerical and computational problems arising with nonlinear regression, 4-parameter logistic as well as log-logit modelling and the respective confidence intervals are addressed in particular. Analysis of real data and an example data set demonstrate the approach. A demo version of the software tool can be downloaded from the first author's homepage.