It has long been noticed that the efficacy observed in small early phase studies is generally better than that observed in later larger studies. Historically, the inflation of the efficacy results from early proof‐of‐concept studies is either ignored, or adjusted empirically using a frequentist or Bayesian approach. In this article, we systematically explained the underlying reason for the inflation of efficacy results in small early phase studies from the perspectives of measurement error models and selection bias. A systematic method was built to adjust the early phase study results from both frequentist and Bayesian perspectives. A hierarchical model was proposed to estimate the distribution of the efficacy for a portfolio of compounds, which can serve as the prior distribution for the Bayesian approach. We showed through theory that the systematic adjustment provides an unbiased estimator for the true mean efficacy for a portfolio of compounds. The adjustment was applied to paired data for the efficacy in early small and later larger studies for a set of compounds in diabetes and immunology. After the adjustment, the bias in the early phase small studies seems to be diminished.

中文翻译：

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从概念验证研究到更具确认性的研究，了解并调整选择偏向。

长期以来，人们一直注意到在小型早期研究中观察到的疗效通常好于在后期大型研究中观察到的功效。从历史上看，早期概念验证研究导致的功效膨胀要么被忽略，要么使用频率论者或贝叶斯方法进行经验调整。在本文中，我们从测量误差模型和选择偏差的角度系统地解释了小型早期研究中功效结果膨胀的根本原因。建立了一种系统的方法，从常客和贝叶斯的角度调整早期研究的结果。提出了一个层次模型来估计化合物组合的功效分布，该分布可以用作贝叶斯方法的先验分布。我们通过理论表明，系统调整为化合物组合的真实平均功效提供了一个无偏估计。这项调整应用于配对数据的早期和较小规模的大型和晚期研究中一组化合物在糖尿病和免疫学方面的功效。调整后，早期小型研究的偏见似乎已减少。