Randomization Tests in Randomized Clinical Trials



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A clinical trial is a medical experiment using human volunteers. It is a highly controlled process required by the U.S. Food and Drug Administration in the research and development of medical innovations. From development to approval, an innovative therapy needs to go through up to four phases of clinical trial, which might take a considerable amount of human resources and investment. The key component of a phase III clinical trial is randomization, or the use of probability to assign treatments to patients. Randomization assists in mitigating certain biases and is the basis for valid statistical inference. In this dissertation, we examine the randomization test, an inferential approach which integrates and utilizes the experimental randomization in the evaluation of the treatment difference. Randomization-based inference was introduced as the method of analyzing randomized experiments since the formal introduction of the logic of experimentation, pioneered by Sir R. A. Fisher in the 1920s. The utility of the randomization test lies in the non-circumstantial statistical validity and the connection of statistical properties to the randomization. However, the computational limitations rendered the method infeasible in the early days, and statistical analysis was mostly formulated on the basis of the normal distribution and random sampling as a matter of approximation. Because it has been largely ignored in practice, other inferential methods which may not possess the same statistical properties have been mistaken for the randomization test, including the permutation test. Today, it has become a convention to present the study conclusions using statistical inference based on the invocation of a (parametric) population distribution function. We will develop (i) a theoretical framework of randomization tests in terms of the hypothesis, the random mechanism, the reference set, (ii) an exploration of the statistical properties including the statistical validity and the power of the test under various models of variability in the patient responses, and (iii) a solution to the computational complexity, particularly in the analysis of multi-armed clinical trials. Further, we will discuss the randomization-based interval estimation. We will contextualize the definition of a confidence interval for the treatment difference and examine efficient algorithms for computing an interval estimate. We conclude that randomization-based inference is adaptable to nearly any primary outcome analysis, and should be used as a matter of course.