Nonparametric covariate-adjusted response-adaptive design based on a functional urn model

In this paper we propose a general class of covariate-adjusted response-adaptive (CARA) designs based on a new functional urn model. We prove strong consistency concerning the functional urn proportion and the proportion of subjects assigned to the treatment groups, in the whole study and for each covariate profile, allowing the distribution of the responses conditioned on covariates to be estimated nonparametrically. In addition, we establish joint central limit theorems for the above quantities and the sufficient statistics of features of interest, which allow to construct procedures to make inference on the conditional response distributions. These results are then applied to typical situations concerning Gaussian and binary responses

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes.

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context

Central limit theorem for an adaptive randomly reinforced urn model

The generalized P\uf2lya 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 of an application to response-adaptive randomization in clinical trials. Our simulation experiments in this context demonstrate the ease and scope of our model

Analysis of time trends in adaptive designs with application to a neurophysiology experiment

10.1002/1097-0258(20000815)19:153.0.CO;2-LStatistics in Medicine19152067-2075SMED

Bootstrap methods for adaptive designs

10.1002/(SICI)1097-0258(19990730)18:143.0.CO;2-RStatistics in Medicine18141757-1767SMED

Optimality, Variability, Power: Evaluating Response-Adaptive Randomization Procedures for Treatment Comparisons

10.1198/016214503000000576Journal of the American Statistical Association98463671-67

Asymptotic properties of adaptive designs for clinical trials with delayed response

10.1214/aos/1015362187Annals of Statistics301122-13

Relevance weighted likelihood for dependent data

Metrika513223-24