Statistical Issues of Unobserved Covariates in Covariate-Adaptive Randomized Trials
Open AccessIn clinical trials, causal inference, and other comparative studies, the goal of the experiment is to detect the treatment effect by comparing a new treatment with a control. In such studies, balancing covariates is often important to ensure the credibility of the trial. While complete randomization can be easily implemented to balance both the observed and unobserved covariates, the chance of imbalanced distributions of the covariates across the treatment arms may always exist. In clinical trials, covariate-adaptive randomization procedures are commonly implemented to improve the balance for the observed baseline covariates. However, their balance properties with respect to unobserved covariates are less understood. Therefore, the use of covariate-adaptive randomization is often controversial in the literature. While the balance of the covariates is of great importance, it is not a panacea for the valid statistical inference. If the response to a treatment interacts with some unobserved covariates, the conclusion drawn from a covariate-adaptive randomized trial can be affected and may thus be inconsistent with other evidence. Furthermore, the balance with respect to the unobserved covariates may have an impact on the subsequent hypothesis tests. These concerns are of clear relevance to the valid statistical inference with covariate-adaptive randomized trials, but they have been less rigorously studied. These two aforementioned statistical issues describe the fundamental challenges we faced in validating the design with covariate-adaptive randomization as well as the methodology used for statistical inference. In this dissertation, we try to tackle these issues by developing a framework to study the properties of covariate-adaptive randomization procedures. In Chapter 2, we provide a theoretical framework to study the balance properties of covariate-adaptive randomization with respect to the unobserved covariates. In particular, we introduce four measures of the unobserved covariates imbalance and derive general theorems for these imbalance measures. These results are used to derive and compare the balance properties for several randomization procedures. Our findings theoretically demonstrate the advantage of covariate-adaptive randomization over complete randomization on balancing unobserved covariates. More importantly, our results can provide practical guidelines for the clinical trial design to address the concern of unobserved covariates imbalance. In Chapter 3, we demonstrate the relationships between the unobserved covariates and the statistical inference for the treatment effect and the covariate effects. Asymptotic properties of the statistical methods are derived under a linear model framework with an interaction between the treatment and an unobserved covariate. We also derive sufficient conditions for the identifiability of the two effects. These results can theoretically explain the inconsistent estimations generated in a covariate-adaptive randomized trial, when the sufficient conditions are not met. Furthermore, when these sufficient conditions hold, we show that the model-based tests for the two effects can have reduced Type I errors under covariate-adaptive randomization procedures. A residual-based adjusted test is proposed to recover the correct Type I error, when the effects can be correctly estimated. Numerical studies are conducted to evaluate our theoretical findings as well as the performance of our proposed adjusted test.
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