Optimizing a Unimodal Response Function for Binary Variables
- 239 Downloads
Several allocation rules are examined for the problem of optimizing a response function for a set of Bernoulli populations, where the population means are assumed to have a strict unimodal structure. This problem arises in dose response settings in clinical trials. The designs are evaluated both on their efficiency in identifying a good population at the end of the experiment, and in their efficiency in sampling from good populations during the trial. A new design, that adapts multi-arm bandit strategies to this unimodal structure, is shown to be superior to the designs previously proposed. The bandit design utilizes approximate Gittin’s indices and shape constrained regression.
Keywordsadaptive clinical trial dose-response experimental design multi-arm bandit nonparametric Polya urn random walk sequential sampling stochastic approximation unimodal regression up and down
Unable to display preview. Download preview PDF.
- Gittins, J.C. and Jones, D.M. (1974). A dynamic allocation index for the sequential design of experiments. In Progress in Statistics Eds J. Gani et al., pp. 241–266. Amsterdam: North Holland.Google Scholar
- Hardwick, J. (1995). A modified bandit as an approach to ethical allocation in clinical trials. In Adaptive Designs: Institute Math. Stat. Lecture Notes 25, Eds B. Rosenberger & N. Flournoy, pp. 223–237. Hayward CA: Institute of Mathematical Statistics.Google Scholar
- Hardwick, J., Meyer, M. and Stout, Q.F. (2000). Adaptive designs for dose response problems with competing failure modes. Submitted.Google Scholar
- Hardwick, J. and Stout, Q.F. (2000). Bandit designs for optimizing a unimodal response function. In preparation.Google Scholar
- Keifer, J. and Wolfowitz, J. (1952). Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. 25, 529–532.Google Scholar
- Stout, Q.F. and Hardwick, J. (2000). Optimal algorithms for univariate unimodal regression. Computing Science and Statistics 32. To appear.Google Scholar
- Ivanova, A. and Flournoy, N. (2000). A birth and death urn for ternary outcomes: stochastic processes applied to urn models. In A Volume in Honor of Theophilos Cacoulous Eds C.A. Charalambides, M.V. Koutras and N. Balakr-ishnan. Florida: CRC Press/Chapman and Hall. (In press).Google Scholar
- Ivanova, A., Rosenberger, W.F., Durham, S.D. and Flournoy, N. (2000). A birth and death urn for randomized clinical trials: asymptotic methods. Sankhya. (To appear).Google Scholar
- Kpamegan, E.E. (2000). An Optimizing Up-and-Down Design. Dissertation in progress, American University.Google Scholar