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Covariate‐adaptive randomization (CAR) is widely used in clinical trials to balance treatment allocation over covariates. Over the past decade, significant progress has been made on the theoretical properties of covariate‐adaptive design and associated inference. However, most results are established under the assumption that the covariates are correctly measured. In practice, measurement error is inevitable, resulting in misclassification for discrete covariates. When covariate misclassification is present in a clinical trial conducted using CAR, the impact is twofold: it impairs the intended covariate balance, and raises concerns over the validity of test procedures. In this paper, we consider the impact of misclassification on covariate‐adaptive randomized trials from the perspectives of both design and inference. We derive the asymptotic normality, and thereby the convergence rate, of the imbalance of the true covariates for a general family of covariate‐adaptive randomization methods, and show that a superior covariate balance can still be attained compared to complete randomization. We also show that the two sample t‐test is conservative, with a reduced Type I error, but that this can be corrected using a bootstrap method. Moreover, if the misclassified covariates are adjusted in the model used for analysis, the test maintains its nominal Type I error, with an increased power. Our results support the use of covariate‐adaptive randomization in clinical trials, even when the covariates are subject to misclassification. [ABSTRACT FROM AUTHOR]

Response‐adaptive designs allow the randomization probabilities to change during the course of a trial based on cumulated response data so that a greater proportion of patients can be allocated to the better performing treatments. A major concern over the use of response‐adaptive designs in practice, particularly from a regulatory viewpoint, is controlling the type I error rate. In particular, we show that the naïve z‐test can have an inflated type I error rate even after applying a Bonferroni correction. Simulation studies have often been used to demonstrate error control but do not provide a guarantee. In this article, we present adaptive testing procedures for normally distributed outcomes that ensure strong familywise error control by iteratively applying the conditional invariance principle. Our approach can be used for fully sequential and block randomized trials and for a large class of adaptive randomization rules found in the literature. We show there is a high price to pay in terms of power to guarantee familywise error control for randomization schemes with extreme allocation probabilities. However, for proposed Bayesian adaptive randomization schemes in the literature, our adaptive tests maintain or increase the power of the trial compared to the z‐test. We illustrate our method using a three‐armed trial in primary hypercholesterolemia. [ABSTRACT FROM AUTHOR]

We propose a likelihood ratio test framework for testing normal mean vectors in high‐dimensional data under two common scenarios: the one‐sample test and the two‐sample test with equal covariance matrices. We derive the test statistics under the assumption that the covariance matrices follow a diagonal matrix structure. In comparison with the diagonal Hotelling's tests, our proposed test statistics display some interesting characteristics. In particular, they are a summation of the log‐transformed squared t‐statistics rather than a direct summation of those components. More importantly, to derive the asymptotic normality of our test statistics under the null and local alternative hypotheses, we do not need the requirement that the covariance matrices follow a diagonal matrix structure. As a consequence, our proposed test methods are very flexible and readily applicable in practice. Simulation studies and a real data analysis are also carried out to demonstrate the advantages of our likelihood ratio test methods. [ABSTRACT FROM AUTHOR]

Summary: In order for historical data to be considered for inclusion in the design and analysis of clinical trials, prospective rules are essential. Incorporation of historical data may be of particular interest in the case of small populations where available data is scarce and heterogeneity is not as well understood, and thus conventional methods for evidence synthesis might fall short. The concept of power priors can be particularly useful for borrowing evidence from a single historical study. Power priors employ a parameter γ ∈ [ 0 , 1 ] that quantifies the heterogeneity between the historical study and the new study. However, the possibility of borrowing data from a historical trial will usually be associated with an inflation of the type I error. We suggest a new, simple method of estimating the power parameter suitable for the case when only one historical dataset is available. The method is based on predictive distributions and parameterized in such a way that the type I error can be controlled by calibrating to the degree of similarity between the new and historical data. The method is demonstrated for normal responses in a one or two group setting. Generalization to other models is straightforward. [ABSTRACT FROM AUTHOR]

Some covariate-adaptive randomization methods have been used in clinical trials for a long time, but little theoretical work has been done about testing hypotheses under covariate-adaptive randomization until Shao et al. (2010) who provided a theory with detailed discussion for responses under linear models. In this article, we establish some asymptotic results for covariate-adaptive biased coin randomization under generalized linear models with possibly unknown link functions. We show that the simple t-test without using any covariate is conservative under covariate-adaptive biased coin randomization in terms of its Type I error rate, and that a valid test using the bootstrap can be constructed. This bootstrap test, utilizing covariates in the randomization scheme, is shown to be asymptotically as efficient as Wald's test correctly using covariates in the analysis. Thus, the efficiency loss due to not using covariates in the analysis can be recovered by utilizing covariates in covariate-adaptive biased coin randomization. Our theory is illustrated with two most popular types of discrete outcomes, binary responses and event counts under the Poisson model, and exponentially distributed continuous responses. We also show that an alternative simple test without using any covariate under the Poisson model has an inflated Type I error rate under simple randomization, but is valid under covariate-adaptive biased coin randomization. Effects on the validity of tests due to model misspecification is also discussed. Simulation studies about the Type I errors and powers of several tests are presented for both discrete and continuous responses. [ABSTRACT FROM AUTHOR]