On Testing Hypotheses in Response-Adaptive Designs Targeting the Best Treatment
We considerer a sequential, response-adaptive design for clinical trials which is characterized by the fact that it assigns patients to the best treatment with a probability converging to one. This property is optimal from an ethical point of view; in this paper we analyze some inferential problems related to the design. In particular, we want to establish, by means of a test of hypothesis, which treatment is superior, in the sense that it has greater mean response. Together with the natural generalization of the classical t-statistic, we introduce a statistic based on the probability of assigning patients to a treatment conditional on past observations. Theoretical properties of the tests are studied, together with numerical evaluations of the power for dichotomous responses.
KeywordsSuccess Probability Empirical Power Ethical Point Dichotomous Response Simulated Clinical Trial
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Thanks to Piercesare Secchi and Anna Maria Paganoni for the ideas and discussions which have stimulated this work.
- Baldi Antognini, A. and A. Giovagnoli (2009). Ethics and inference in binary clinical trials: admissible allocations and response-adaptive randomization. Preprint. Google Scholar
- Hu, F. and W. F. Rosenberger (2006). The Theory of Response-Adaptive Randomization in Clinical Trials. Wiley Series in Probability and Statistics. New York: Wiley.Google Scholar
- Ivanova, A and N. Flournoy (2001). A birth and death urn for ternary outcomes: stochastic processes applied to urn models. In: Charalambides C, Koutras MV, Balakrishnan (eds) Probability and Statistical Models with Applications., 583–600. Boca Raton: Chapman and Hall/CRC.Google Scholar
- Li, W., S. D. Durham, and N. Flournoy (1996). Randomized Polya urn designs. Proceedings of the Biometric Section of the American Statistical Association, 166–170.Google Scholar
- May, C. and N. Flournoy, N. (2009). Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn. The Annals of Statistics 32, 1058–1078.Google Scholar
- May, C., A. Paganoni, and P. Secchi (2007). Response-adaptive designs targeting the best treatment for clinical trials with continuous responses. In S.Co.2007 Fifth Conference - Complex Models and Computational intensive methods for estimation and prediction - Book of short papers, pp. 326–331. Cluep.Google Scholar