Participants in clinical trials are often viewed as a unique, finite population. Yet, statistical analyses often assume that participants were randomly sampled from a larger population. Under Complete Randomization, Randomization-Based Inference (RBI; a finite population inference) and Analysis of Variance (ANOVA; a random sampling inference) provide asymptotically equivalent difference-in-means tests. However, sequentially-enrolling trials typically employ restricted randomization schemes, such as block or Maximum Tolerable Imbalance (MTI) designs, to reduce the chance of chronological treatment imbalances. The impact of these restrictions on RBI and ANOVA concordance is not well understood. With real-world frames of reference, such as rare and ultra-rare diseases, we review full versus random sampling of finite populations and empirically evaluate finite population Type I error when using ANOVA following randomization restrictions. Randomization restrictions strongly impacted ANOVA Type I error, even for trials with 1,000 participants. Properly adjusting for restrictions corrected Type I error. We corrected for block randomization, yet leave open how to correct for MTI designs. More directly, RBI accounts for randomization restrictions while ensuring correct finite population Type I error. Novel contributions are: 1) deepening the understanding and correction of RBI and ANOVA concordance under block and MTI restrictions and 2) using finite populations to estimate the convergence of Type I error to a nominal rate. We discuss the challenge of specifying an estimand's population and reconciling with sampled trial participants.

翻译：临床试验的参与者通常被视为一个独特的有限总体。然而，统计分析通常假设参与者是从一个更大的总体中随机抽取的。在完全随机化下，随机化推断（一种有限总体推断）与方差分析（一种随机抽样推断）提供了渐近等价的均值差异检验。然而，序贯入组试验通常采用限制性随机化方案，例如区组或最大可容忍不平衡设计，以减少时序性治疗不平衡的可能性。这些限制对随机化推断与方差分析一致性的影响尚未得到充分理解。我们结合现实世界的参考框架（如罕见病和超罕见病），回顾了有限总体的完全抽样与随机抽样，并实证评估了在随机化限制后使用方差分析时有限总体的第一类错误。随机化限制强烈影响了方差分析的第一类错误，即使在有1000名参与者的试验中也是如此。对限制进行适当调整可以校正第一类错误。我们校正了区组随机化，但对于如何校正最大可容忍不平衡设计仍保持开放。更直接地，随机化推断考虑了随机化限制，同时确保了正确的有限总体第一类错误。本文的新贡献在于：1）深化了对区组和最大可容忍不平衡限制下随机化推断与方差分析一致性的理解与校正；2）利用有限总体估计第一类错误收敛至名义水平的速率。我们讨论了指定估计目标总体并与抽样的试验参与者相协调的挑战。