Confidence Regions on Optimal Drug or Treatment Combination
With Toxic drugs, to find the optimal dosage levels, when two or more drugs are combined in the treatment, is a rather complex problem. The best way to analyse this kind of problem is to apply Response Surface Methodologies (RSM) which can be presented through Contours of Continuous Response. In theses contours, the darker shade or the higher digits represent the optimal treatment region and whithin its bondaries will lie the best dosage levels for each drug in the combination. However, some constrains must be set in order to avoid significant toxicity. And a confident region of 100(1-α)%, which includes the optimal treament level, is indeed the best solution to help the analysis of the problem. In this paper, we are concerned mainly how to calculate such confidence regions. But a brief explanation about the whole process will be given.
KeywordsResponse surface methodologies Optimization methods Multi Logistic Regression Asymptotic properties Maximum-likelihood estimation
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