Hybrid randomized controlled trials (hybrid RCTs) integrate external control data, such as historical or concurrent data, with data from randomized trials. While numerous frequentist and Bayesian methods, such as the test-then-pool and Meta-Analytic-Predictive prior, have been developed to account for potential disagreement between the external control and randomized data, they cannot ensure strict type I error rate control. However, these methods can reduce biases stemming from systematic differences between external controls and trial data. A critical yet underexplored issue in hybrid RCTs is the prespecification of external data to be used in analysis. The validity of statistical conclusions in hybrid RCTs depends on the assumption that external control selection is independent of historical trials outcomes. In practice, historical data may be accessible during the planning stage, potentially influencing important decisions, such as which historical datasets to include or the sample size of the prospective part of the hybrid trial, thus introducing bias. Such data-driven design choices can be an additional source of bias, which can occur even when historical and prospective controls are exchangeable. Through a simulation study, we quantify the biases introduced by outcome-dependent selection of historical controls in hybrid RCTs using both Bayesian and frequentist approaches, and discuss potential strategies to mitigate this bias. Our scenarios consider variability and time trends in the historical studies, distributional shifts between historical and prospective control groups, sample sizes and allocation ratios, as well as the number of studies included. The impact of different rules for selecting external controls is demonstrated using a clinical trial example.

翻译：混合随机对照试验（混合RCT）将外部对照数据（如历史或同期数据）与随机试验数据相结合。尽管已开发出多种频率学派和贝叶斯方法（如检验后合并法和元分析预测先验法）来处理外部对照与随机数据之间的潜在差异，但这些方法无法确保严格的I类错误率控制。然而，这些方法可以减少因外部对照与试验数据之间的系统差异而产生的偏倚。混合RCT中一个关键但尚未充分探讨的问题是在分析中使用的外部数据的预先设定。混合RCT中统计结论的有效性依赖于外部对照选择独立于历史试验结果的假设。在实践中，历史数据可能在规划阶段即可获取，这可能影响重要决策，例如纳入哪些历史数据集或混合试验前瞻性部分的样本量，从而引入偏倚。此类数据驱动的设计选择可能成为额外的偏倚来源，即使历史对照与前瞻性对照可互换时也可能发生。通过模拟研究，我们使用贝叶斯和频率学派方法量化了混合RCT中基于结果的历史对照选择所引入的偏倚，并讨论了减轻这种偏倚的潜在策略。我们的模拟场景考虑了历史研究中的变异性和时间趋势、历史对照组与前瞻性对照组之间的分布偏移、样本量和分配比例，以及纳入研究的数量。通过一个临床试验案例展示了不同外部对照选择规则的影响。