# zbMATH — the first resource for mathematics

Minimax D-optimal designs for the logistic model. (English) Zbl 1060.62545
Summary: We propose an algorithm for constructing minimax D-optimal designs for the logistic model when only the ranges of the values for both parameters are assumed known. Properties of these designs are studied and compared with optimal Bayesian designs and R. R. Sitter’s [Biometrics, 48, 1145–1155 (1992)] minimax D-optimal $$kk$$-designs. Examples of minimax D-optimal designs are presented for the logistic and power logistic models, including a dose-response design for rheumatoid arthritis patients.

##### MSC:
 62K05 Optimal statistical designs 62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text:
##### References:
 [1] Brown, Planning a quantal assay of potency, Biometrics 22 pp 322– (1966) [2] Burges, Microbial Control of Insects and Mites pp 591– (1971) [3] Chaloner, Optimal Bayesian design applied to logistic regression experiments, Journal of Statistical Planning and Inference 21 pp 191– (1989) · Zbl 0666.62073 [4] Chernoff, Locally optimal designs for estimating parameters, Annals of Mathematical Statistics 24 pp 586– (1953) · Zbl 0053.10504 [5] Fedorov, Convex design theory, Mathematische Operationsforschung und Statistik 11 pp 403– (1980) · Zbl 0471.62075 [6] Gaudard, Efficient designs for estimation in the power logistic quantal response model, Statistica Sinica 3 pp 233– (1993) · Zbl 0823.62087 [7] Heise, Optimal designs for bivariate logistic regression, Biometrics 52 pp 613– (1996) · Zbl 0925.62328 [8] King , J. 1996 Minimax optimal designs Ph.D. dissertation School of Public Health, Department of Biostatistics, University of California [9] Minkin, Likelihood-based experimental design for estimation of ED50, Biometrics 55 pp 1030– (1999) · Zbl 1059.62679 [10] Silvey, Optimal Design (1980) [11] Sitter, Robust designs for binary data, Biometrics 48 pp 1145– (1992) · Zbl 0760.62013 [12] Strijbosch, Limiting dilution assays: Experimental design and statistical analysis, Journal of Immunological Methods 97 pp 133– (1987) [13] Wong, A unified approach to the construction of minimax designs, Biometrika 79 pp 611– (1992) · Zbl 0762.62019 [14] Zeng, Dual objective Bayesian optimal designs for a dose-ranging study using ACR responder index, Drug Information Journal 34 pp 421– (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.