A New Family of Covariate-Adjusted Response Adaptive Designs and their Asymptotic Properties

It is often important to incorporating covariate information in the design of clinical trials. In literature, there are many designs of using stratification and covariate-adaptive randomization to balance on certain known covariate. Recently Zhang, Hu, Cheung and Chan (2007) have proposed a family of covariate-adjusted response-adaptive (CARA) designs and studied their asymptotic properties. However, these CARA designs often have high variabilities. In this paper, we propose a new family of covariate-adjusted response-adaptive (CARA) designs. We show that the new designs have smaller variabilities and therefore more efficient

A simulation study for comparing testing statistics in response-adaptive randomization

<p>Abstract</p> <p>Background</p> <p>Response-adaptive randomizations are able to assign more patients in a comparative clinical trial to the tentatively better treatment. However, due to the adaptation in patient allocation, the samples to be compared are no longer independent. At large sample sizes, many asymptotic properties of test statistics derived for independent sample comparison are still applicable in adaptive randomization provided that the patient allocation ratio converges to an appropriate target asymptotically. However, the small sample properties of commonly used test statistics in response-adaptive randomization are not fully studied.</p> <p>Methods</p> <p>Simulations are systematically conducted to characterize the statistical properties of eight test statistics in six response-adaptive randomization methods at six allocation targets with sample sizes ranging from 20 to 200. Since adaptive randomization is usually not recommended for sample size less than 30, the present paper focuses on the case with a sample of 30 to give general recommendations with regard to test statistics for contingency tables in response-adaptive randomization at small sample sizes.</p> <p>Results</p> <p>Among all asymptotic test statistics, the Cook's correction to chi-square test (<it>T</it>_<it>MC</it>) is the best in attaining the nominal size of hypothesis test. The William's correction to log-likelihood ratio test (<it>T</it>_<it>ML</it>) gives slightly inflated type I error and higher power as compared with <it>T</it>_<it>MC</it>, but it is more robust against the unbalance in patient allocation. <it>T</it>_{<it>MC </it>}and <it>T</it>_{<it>ML </it>}are usually the two test statistics with the highest power in different simulation scenarios. When focusing on <it>T</it>_{<it>MC </it>}and <it>T</it>_<it>ML</it>, the generalized drop-the-loser urn (GDL) and sequential estimation-adjusted urn (SEU) have the best ability to attain the correct size of hypothesis test respectively. Among all sequential methods that can target different allocation ratios, GDL has the lowest variation and the highest overall power at all allocation ratios. The performance of different adaptive randomization methods and test statistics also depends on allocation targets. At the limiting allocation ratio of drop-the-loser (DL) and randomized play-the-winner (RPW) urn, DL outperforms all other methods including GDL. When comparing the power of test statistics in the same randomization method but at different allocation targets, the powers of log-likelihood-ratio, log-relative-risk, log-odds-ratio, Wald-type Z, and chi-square test statistics are maximized at their corresponding optimal allocation ratios for power. Except for the optimal allocation target for log-relative-risk, the other four optimal targets could assign more patients to the worse arm in some simulation scenarios. Another optimal allocation target, <it>R</it>_{<it>RSIHR</it>}, proposed by Rosenberger and Sriram (<it>Journal of Statistical Planning and Inference</it>, 1997) is aimed at minimizing the number of failures at fixed power using Wald-type Z test statistics. Among allocation ratios that always assign more patients to the better treatment, <it>R</it>_{<it>RSIHR </it>}usually has less variation in patient allocation, and the values of variation are consistent across all simulation scenarios. Additionally, the patient allocation at <it>R</it>_{<it>RSIHR </it>}is not too extreme. Therefore, <it>R</it>_{<it>RSIHR </it>}provides a good balance between assigning more patients to the better treatment and maintaining the overall power.</p> <p>Conclusion</p> <p>The Cook's correction to chi-square test and Williams' correction to log-likelihood-ratio test are generally recommended for hypothesis test in response-adaptive randomization, especially when sample sizes are small. The generalized drop-the-loser urn design is the recommended method for its good overall properties. Also recommended is the use of the <it>R</it>_{<it>RSIHR </it>}allocation target.</p

The Gaussian approximation for multi-color generalized Friedman's urn model

The Friedman's urn model is a popular urn model which is widely used in many disciplines. In particular, it is extensively used in treatment allocation schemes in clinical trials. In this paper, we prove that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a multi-color generalized Friedman's urn model with non-homogeneous generating matrices. The Gaussian process is a solution of a stochastic differential equation. This Gaussian approximation together with the properties of the Gaussian process is important for the understanding of the behavior of the urn process and is also useful for statistical inferences. As an application, we obtain the asymptotic properties including the asymptotic normality and the law of the iterated logarithm for a multi-color generalized Friedman's urn model as well as the randomized-play-the-winner rule as a special case

EEG power spectra response to a 4-h phase advance and gaboxadol treatment in 822 men and women.

To explore the effect of gaboxadol on NREM EEG in transient insomnia using power spectral analysis and evaluate the response between men and women

Covariate Adjusted Designs for Combining Efficiency, Ethics and Randomness in Normal Response Trials

This paper deals with the problem of allocating patients to two competing treatments in the presence of covariates in order to achieve a good trade-off between efficiency, ethical concern and randomization. We propose a compound criterion that combines inferential precision and ethical gain by flexible weights depending on the unknown treatment effects. In the absence of treatment-covariate interactions, this criterion leads to a locally optimal allocation which does not depend on the covariates and can be targeted by a suitable implementation of the doubly-adaptive biased coin design aimed at balancing the roles of randomization, ethics and information. Some properties of the suggested procedure are described

Response-adaptive randomization for survival trials: the parametric approach

Few references deal with response-adaptive randomization procedures for survival outcomes and those that do either dichotomize the outcomes or use a non-parametric approach. In this paper, the optimal allocation approach and a parametric response-adaptive randomization procedure are used under exponential and Weibull distributions. The optimal allocation proportions are derived for both distributions and the doubly adaptive biased coin design is applied to target the optimal allocations. The asymptotic variance of the procedure is obtained for the exponential distribution. The effect of intrinsic delay of survival outcomes is treated. These findings are based on rigorous theory but are also verified by simulation. It is shown that using a doubly adaptive biased coin design to target the optimal allocation proportion results in more patients being randomized to the better performing treatment without loss of power. We illustrate our procedure by redesigning a clinical trial. Copyright 2007 Royal Statistical Society.

Change in cartilage morphometry: a sample of the progression cohort of the osteoarthritis initiative,” Ann Rheum Dis

ABSTRACT Objective: The performance characteristics of hyaline articular cartilage measurement on magnetic resonance imaging (MRI) need to be accurately delineated before widespread application of this technology. Our objective was to assess the rate of natural disease progression of cartilage morphometry measures from baseline to 1 year in knees with osteoarthritis (OA) from a subset of participants from the Osteoarthritis Initiative (OAI). Methods: Subjects included for this exploratory analysis are a subset of the approximately 4700 participants in the OAI Study. Bilateral radiographs and 3T MRI (Siemans Trio) of the knees and clinical data were obtained at baseline and annually in all participants. 160 subjects from the OAI Progression subcohort all of whom had both frequent symptoms and, in the same knee, radiographic OA based on a screening reading done at the OAI clinics were eligible for this exploratory analysis. One knee from each subject was selected for analysis. 150 participants were included. Using sagittal 3D DESSwe (double echo, steady-state sequence with water excitation) MR images from the baseline and 12 follow-up month visit, a segmentation algorithm was applied to the cartilage plates of the index knee to compute the cartilage volume, normalised cartilage volume (volume normalised to bone surface interface area), and percentage denuded area (total cartilage bone interface area denuded of cartilage). Results: Summary statistics of the changes (absolute and percentage) from baseline at 1 year and the standardised response mean (SRM), ie, mean change divided by the SD change were calculated. On average the subjects were 60.9 years of age and obese, with a mean body mass index of 30.3 kg/m Osteoarthritis (OA) is a significant public health challenge, being ranked as the leading cause of disability in elderly people. 1 OA affects an estimated 21 million Americans. 2 Recent estimates suggest that symptomatic knee OA occurs in 6% of adults 30 years of age or older, 3 and in 13% of people age 60 and over.