An urn model to construct an efficient test procedure for response adaptive designs

Ghiglietti, Andrea; Paganoni, Anna Maria

doi:10.1007/s10260-015-0314-y

Stat Methods Appl

2015

DOI: 10.1007/s10260-015-0314-y

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An urn model to construct an efficient test procedure for response adaptive designs

Andrea Ghiglietti

Anna Maria Paganoni

Abstract: We study the statistical performance of different tests for comparing the mean effect of two treatments. Given a reference classical test T 0 , we determine which sample size and proportion allocation guarantee to a test T , based on response-adaptive design, to be better than T 0 , in terms of (a) higher power and (b) fewer subjects assigned to the inferior treatment. The adoption of a response-adaptive design to implement the random allocation procedure is necessary to ensure that both (a) and (b) are satisf… Show more

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Cited by 2 publications

References 22 publications

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Urn models for response-adaptive randomized designs: a simulation study based on a non-adaptive randomized trial

Ghiglietti

Scarale

Miceli

et al. 2018

Journal of Biopharmaceutical Statistics

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Recently, response-adaptive designs have been proposed in randomized clinical trials to achieve ethical and/or cost advantages by using sequential accrual information collected during the trial to dynamically update the probabilities of treatment assignments. In this context, urn models-where the probability to assign patients to treatments is interpreted as the proportion of balls of different colors available in a virtual urn-have been used as response-adaptive randomization rules. We propose the use of Randomly Reinforced Urn (RRU) models in a simulation study based on a published randomized clinical trial on the efficacy of home enteral nutrition in cancer patients after major gastrointestinal surgery. We compare results with the RRU design with those previously published with the non-adaptive approach. We also provide a code written with the R software to implement the RRU design in practice. In detail, we simulate 10,000 trials based on the RRU model in three set-ups of different total sample sizes. We report information on the number of patients allocated to the inferior treatment and on the empirical power of the t-test for the treatment coefficient in the ANOVA model. We carry out a sensitivity analysis to assess the effect of different urn compositions. For each sample size, in approximately 75% of the simulation runs, the number of patients allocated to the inferior treatment by the RRU design is lower, as compared to the non-adaptive design. The empirical power of the t-test for the treatment effect is similar in the two designs.

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Urn models for response-adaptive randomized designs: a simulation study based on a non-adaptive randomized trial

Ghiglietti

Scarale

Miceli

et al. 2018

Journal of Biopharmaceutical Statistics

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Central limit theorem for an adaptive randomly reinforced urn model

Ghiglietti¹,

Vidyashankar²,

Rosenberger³

2017

Ann. Appl. Probab.

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Abstract:The generalized Pólya urn (GPU) models and their variants have been investigated in several disciplines. However, typical assumptions made with respect to the GPU do not include urn models with diagonal replacement matrix, which arise in several applications, specifically in clinical trials. To facilitate mathematical analyses of models in these applications, we introduce an adaptive randomly reinforced urn model that uses accruing statistical information to adaptively skew the urn proportion toward specific targets. We study several probabilistic aspects that are important in implementing the urn model in practice. Specifically, we establish the law of large numbers and a central limit theorem for the number of sampled balls. To establish these results, we develop new techniques involving last exit times and crossing time analyses of the proportion of balls in the urn. To obtain precise estimates in these techniques, we establish results on the harmonic moments of the total number of balls in the urn. Finally, we describe our main results in the context an application to response-adaptive randomization in clinical trials. Our simulation experiments in this context demonstrate the ease and scope of our model.

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An urn model to construct an efficient test procedure for response adaptive designs

Cited by 2 publications

References 22 publications

Urn models for response-adaptive randomized designs: a simulation study based on a non-adaptive randomized trial

Urn models for response-adaptive randomized designs: a simulation study based on a non-adaptive randomized trial

Central limit theorem for an adaptive randomly reinforced urn model

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