Abstract
This paper is concerned with a closed adaptive sequential procedure for selecting a random-size subset containing experimental treatments that are better than a standard. All the k treatments under considerations are measured by two endpoints accounting for treatment efficacy and treatment safety respectively. The selection is made with regard to the two binary endpoints. An experimental treatment is considered to be better than the standard if its both endpoints have successful rates higher than the standard ones. We provide a step-by-step sampling rule, stopping rule, and decision rule for the proposed procedure. We show that the proposed sequential procedure achieves the same requirements for the probability of a correct selection as does the fixed-sample-size procedure, but requires fewer observations. We use simulations to evaluate the sample size savings of the proposed procedure over the corresponding fixed-sample-size procedure.
Similar content being viewed by others
References
Bechhofer, R.E. and Kulkarni, R.V. (1982). Closed adaptive sequential procedures for selecting the best of k ≥ 2 Bernoulli populations.. In Proceedings of Third Purdue Symposium in Statistical Decision Theory and Related Topics (S.S. Gupta and J. Berger) I pp. 61–108.
Bryant, J. and Day, R. (1995). Incorporating toxicity considerations into the design of two-stage phase II clinical trials. Biometrics 51, 1372–1383.
Buzaianu, E.M. and Chen, P. (2008). Curtailment procedure for selecting among Bernoulli populations. Commun Stat Theory Methods 37, 1085–1102.
Buzaianu, E.M., Chen, P. and Hsu, L. (2020). Selecting among treatments with two Bernoulli endpoints. Manuscript submitted for publication.
Carsten, C. and Chen, P. (2016). Curtailed two-stage matched pairs design in double-arm phase II clinical trials. J Biopharm Stat 26, 816–822.
Conway, M.R. and Petroni, G.R. (1995). Bivariate sequential designs for phase II trials. Biometrics 51, 656–664.
Chen, C.M. and Chi, Y. (2012). Curtailed two-stage designs with two dependent binary endpoints. Pharm Stat 11, 57–62.
Dunnett, C.M. (1984). Selection of the best treatment in comparison to a control with an application to a medical trial. In Design of Experiments, Ranking, and Selection (T.J. Santner and A.C. Tamhane) Marcel Dekker Inc., New York 47–66.
Gupta, S.S. and Sobel, M. (1958). On selecting a subset which contains all populations better than a standard. Ann Math Stat 29, 235–244.
Jennison, C. (1983). Equal probability of correct selection for Bernoulli selection procedures. Commun Stat Theory Methods 12, 2887–2896.
Jennison, C. and Turnbull, B.W. (1993). Group sequential tests for bivariate response: interim analysis of clinical trials with both efficacy and safety endpoints. Biometrics 49, 741–752.
Sobel, M. and Hyuett, M.J. (1957). Selecting the best one of several binomial populations. Bell Syst Tech J 36, 537–576.
Royzman, I. (2017). Hurdles for Neulasta biosimilars. Available from: https://www.biologicsblog.com/hurdles-for-neulasta-biosimilars/.
Thall, P.F., Simon, R. and Ellenberg, S.S. (1988). Two-stage designs for comparative clinical trials. Biometrika 75, 303–310.
Wikipedia (2020). Pegfilgrastim. Available from: https://en.wikipedia.org/wiki/Pegfilgrastim.
Acknowledgements
The first author was partly funded by a faculty scholarship developmental grant from the University of North Florida.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Buzaianu, E.M., Chen, P. & Hsu, L. A Curtailed Procedure for Selecting Among Treatments With Two Bernoulli Endpoints. Sankhya B 84, 320–339 (2022). https://doi.org/10.1007/s13571-021-00261-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13571-021-00261-2