Optimal designs for criteria involving log(potency) in comparative binary bioassays

Journal of Statistical Planning and Inference

Volumn 113, Issue 2, 2003, Pages 617-632

  Smith, D M ^a   Ridout, M S ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF KENT   (United Kingdom)

Author keywords

Dose response; General equivalence theorem; Generalized linear models

Indexed keywords

EID: 0037408764     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(02)00112-X     Document Type: Article

References (32)

1. Ashton, W.D., 1972. The Logit Transformation. Charles Griffin & Company Ltd.
2. Atkinson, A.C., Donev, A.N., 1992. Optimum Experimental Designs. Oxford University Press, Oxford.
3. Atwood, C.L., 1969. Optimal and efficient designs of experiments. Ann. Math. Statist. 40, 1570-1602.
4. Benyon, P.R., 1976. ASR15 A remark on AS47 "Function minimization using a simplex procedure". Appl. Statist. 25, 97.
5. Burridge, J., Sebastiani, P., 1994. D-optimal designs for generalised linear models with variance proportional to the square of the mean. Biometrika 81, 295-304.
6. Chaloner, K., 1993. A note on optimal Bayesian design for nonlinear problems. J. Statist. Plann. Inference 37, 229-235.
7. Chaloner, K., Larntz, K., 1988. Software for logistic regression experiment design. In: Dodge, Y., Fedorov, V.V., Wynn, H.P. (Eds.), Optimal Design and Analysis of Experiments. Elsevier, North-Holland, Amsterdam, pp. 207-211.
8. Chaloner, K., Larntz, K., 1989. Optimal Bayesian design applied to logistic regression experiments. J. Statist. Plann. Inference 21, 191-208.
9. Chaloner, K., Verdinelli, I., 1995. Bayesian experimental design: a review Statist. Sci. 10, 273-304.
10. Chambers, J.M., Ertel, J.E., 1974. ASR11 A remark on AS47. Appl. Statist. 23, 250-251.
11. Cook, R.D., Nachtsheim, C.J., 1980. A comparison of algorithms for constructing exact D-optimal designs. Technometrics 22, 315-324.
12. Fan, S., Chaloner, K., 1999. Geometric methods for singular C-optimal designs. Technical Report No. 629, University of Minnesota.
13. Finney, D.J., 1971. Statistical Method in Biological Assay, 2nd Edition. Charles Griffin & Company Ltd.
14. Firth, D., Hinde, J.P., 1997. Parameter neutral optimum design. J. Roy. Statist. Soc. B 59, 799-811.
15. Ford, I., Titterington, D.M., Kitsos, C.P., 1989. Recent advances in non-linear experimental design. Technometrics 31, 49-60.
16. Ford, I., Torsney, B., Wu, C.F.J., 1992. The use of a canonical form in the construction of locally optimal designs for non-linear problems. J. Roy. Statist. Soc. B 54, 569-583.
17. Haines, L.M., 1987. The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models. Technometrics 29, 439-447.
18. Haines, L.M., 1995. A geometric approach to optimal design for one-parameter non-linear models. J. Roy. Statist. Soc. B 57, 575-598.
19. Healy, M.J.R., 1968a. Triangular decomposition of a symmetric matrix. Algorithm AS6. Appl. Statist. 17, 195-197.
20. Healy, M.J.R., 1968b. Inversion of a positive semi-definite symmetric matrix. Algorithm AS7. Appl. Statist. 17, 198-199.
21. Hill, I.D., 1978. ASR28 Remark on AS47. Appl. Statist. 27, 380-382.
22. Macleod, A.J., 1989. A robust and reliable algorithm for the logarithm of the gamma function. Algorithm AS245. Appl. Statist. 38, 397-402.
23. Matthews, J.N.S., 1999. Effect of prior specification on Bayesian design for two-sample comparison of a binary outcome. Amer. Statist. 53, 254-256.
24. Morgan, B.J.T., 1992. Analysis of Quantal Response Data. Chapman & Hall, London.
25. O'Neill, R., 1971. Function minimization using a simplex procedure. Algorithm AS47. Appl. Statist. 20, 338-345. Corrigendum (1974). Appl. Statist. 23, 252.
26. Pukelsheim, F., Rieder, S., 1992. Efficient rounding of approximate designs. Biometrika 79, 763-770.
27. Silvey, S.D., 1978. Optimal design measures with singular information matrices. Biometrika 65, 553-559.
28. Silvey, S.D., 1980. Optimal Design. Chapman & Hall, London.
29. Sitter, R.R., Torsney, B., 1995. Optimal designs for binary response experiments with two design variables. Statist. Sinica 5, 405-419.
30. Sitter, R.R., Wu, C.F.J., 1993. Optimal designs for binary response experiments: Fieller, D and A criteria Scand. J. Statist. 20, 329-341.
31. Smith, D.M., Ridout, M.S., 1998. Locally and Bayesian optimal designs for binary dose-response models with various link functions. In: Payne, R., Green, P. (Eds.), COMPSTAT98. Physica-Verlag, Wurzburg, pp. 455-460.
32. Wichura, M.J., 1988. The percentage points of the normal distribution. Algorithm AS241. Appl. Statist. 37, 477-484.