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.

[1]  W. Rosenberger,et al.  The theory of response-adaptive randomization in clinical trials , 2006 .

[2]  Narayanaswamy Balakrishnan,et al.  Probability and Statistical Models with Applications , 2000 .

[3]  Stefano Federico Tonellato,et al.  S.CO.2007 Fifth Conference. Complex Models and Computational Intensive Methods for Estimation and Prediction. Book of short papers. , 2007 .

[4]  Nancy Flournoy,et al.  A Birth and Death Urn for Ternary Outcomes: Stochastic Processes Applied to Urn Models , 2000 .

[5]  William F. Rosenberger,et al.  Randomization in Clinical Trials , 2003 .

[6]  Anastasia Ivanova,et al.  A play-the-winner-type urn design with reduced variability , 2003 .

[7]  P. Milano,et al.  A response-adaptive design targeting the best treatment for clinical trials with continuous responses , 2007 .

[8]  A. B. Antognini,et al.  Ethics and inference in binary clinical trials: admissible allocations and response-adaptive randomization , 2008 .

[9]  William F. Rosenberger,et al.  RANDOMIZED URN MODELS AND SEQUENTIAL DESIGN , 2002 .

[10]  S. D. Durham,et al.  Randomized Play-the-Leader Rules for Sequential Sampling from Two Populations , 1990, Probability in the engineering and informational sciences (Print).

[11]  S. D. Durham,et al.  A sequential design for maximizing the probability of a favourable response , 1998 .

[12]  N. Flournoy,et al.  Asymptotics in response-adaptive designs generated by a two-color, randomly reinforced urn , 2009, 0904.0350.

[13]  William F Rosenberger,et al.  Response‐Adaptive Randomization for Clinical Trials with Continuous Outcomes , 2006, Biometrics.

[14]  Anna Maria Paganoni,et al.  A randomly reinforced urn , 2006 .