Covariate-adaptive designs are often implemented to balance important covariates in clinical trials. However, the theoretical properties of conventional testing hypotheses are usually unknown under covariate-adaptive randomized clinical trials. In the literature, most studies are based on simulations. In this article, we provide theoretical foundation of hypothesis testing under covariate-adaptive designs based on linear models. We derive the asymptotic distributions of the test statistics of testing both treatment effects and the significance of covariates under null and alternative hypotheses. Under a large class of covariate-adaptive designs, (i) the hypothesis testing to compare treatment effects is usually conservative in terms of small Type I error; (ii) the hypothesis testing to compare treatment effects is usually more powerful than complete randomization; and (iii) the hypothesis testing for significance of covariates is still valid. The class includes most of the covariate-adaptive designs in the literature; for example, Pocock and Simon's marginal procedure, stratified permuted block design, etc. Numerical studies are also performed to assess their corresponding finite sample properties. Supplementary material for this article is available online.
Background The incidence of tuberculosis (TB) remains high worldwide. Current strategies will not eradicate TB by 2035; instead, by 2182 is more likely. Therefore, it is urgent that new risk factors be identified. Methods An ecological study was conducted in 340 prefectures in China from 2005 to 2015. The spatial distribution of TB incidence was shown by clustering and hotspot analysis. The relationship between the distribution patterns and six meteorological factors was evaluated by the geographically weighted regression (GWR) model. Results During the 11 years of the study period, TB incidence was persistently low in the east and high in the west. Local coefficients from the GWR model showed a positive correlation between TB incidence and yearly average rainfall (AR) but a negative correlation with other meteorological factors. Average relative humidity (ARH) was negatively correlated with the incidence of TB in all prefectures ( p < 0.05). Conclusion Meteorological factors may play an important role in the prevention and control of TB. Electronic supplementary material The online version of this article (10.1186/s12879-019-4008-1) contains supplementary material, which is available to authorized users.
Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or covariate-adaptive randomization is used. In this article, we investigate several of the most intuitive and commonly used regression models for estimating and inferring the treatment effect in randomized clinical trials. By allowing the regression model to be arbitrarily misspecified, we demonstrate that all these regression-based estimators robustly estimate the treatment effect, albeit with possibly different efficiency. We also propose consistent non-parametric variance estimators and compare their performances to those of the model-based variance estimators that are readily available in standard statistical software.Based on the results and taking into account both theoretical efficiency and practical feasibility, we make recommendations for the effective use of regression under various scenarios. For equal allocation, it suffices to use the regression adjustment for the stratum covariates and additional baseline covariates, if available, with the usual ordinary-least-squares variance estimator. For unequal allocation, regression with treatment-by-covariate interactions should be used, together with our proposed variance estimators. These recommendations apply to simple and stratified randomization, and minimization, among others. We hope this work helps to clarify and promote the usage of regression in randomized clinical trials.
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.
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