Optimal Bayesian design applied to logistic regression experiments

• Published in: Journal of statistical planning and inference 1989-02, Vol.21 (2), p.191-208
• Main Authors: Chaloner, Kathryn, Larntz, Kinley
• Format: Article
• Language: English
• Subjects: A-optimality; Algorithm; Bayesian design; binary data; D-optimality; equivalence theorem; Exact sciences and technology; Experimental design; logistic regression; Mathematics; Nelder–Mead algorithm; non-linear models; optimal design; optimization; Probability and statistics; reliability experiments; Sciences and techniques of general use; simplex method; Statistics; stress testing
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/0378-3758(89)90004-9

A traditional way to design a binary response experiment is to design the experiment to be most efficient for a best guess of the parameter values. A design which is optimal for a best guess however may not be efficient for parameter values close to that best guess. We propose designs which formally account for the prior uncertainty in the parameter values. A design for a situation where the best guess has substantial uncertainty attached to itis very different from a design for a situation where approximate values of the parameters are known. We derive a general theory for concave design critria for non-linear models and then apply the theory to logistic regression. Designs found by numerical optimization are examined for a range of prior distributions and a range of criteria. The theoretical results are used to verify that the designs are indeed optimal.