一个简单的模型表明经济合理的样本量选择驱动不可重复性
A simple model suggesting economically rational sample-size choice drives irreproducibility
摘要：
一些系统性研究表明，很大一部分已发表的研究是不可复制的。低重现性的一个可能原因是样本量不足，导致低功效和低阳性预测值。有人认为，样本量不足的选择是由科学竞争和“积极的出版偏见”的组合驱动的。在这里，我们将这种直觉形式化为一个简单的模型，在这个模型中，科学家选择经济上合理的样本量，平衡实验成本和出版收入。具体来说，假设一个科学家的收入只来自于“积极”的发现（积极的出版偏见），并且单个样本的成本是固定的，允许利用基本的统计公式进行经济最优性预测。我们发现，如果影响i）低的基本概率，ii）小的效果大小或iii）低赠款收入每次出版，那么合理的（经济上最优的）样本量是小的。此外，对于这些参数的合理分布，我们发现一个强大的双峰分布的出现所获得的统计功率和低的整体再现率，两者都匹配的实证研究结果。最后，我们探讨了条件等价性检验作为一种手段，使经济激励与足够的样本量。总体而言，该模型描述了一个简单的机制，解释了小样本的流行和持久性，是非常适合的实证验证。它提出经济理性或经济压力是不可复制性的主要驱动力，并提出了改变这种情况的策略。
英文摘要：
Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It has been suggested that insufficient sample-size choice is driven by a combination of scientific competition and 'positive publication bias'. Here we formalize this intuition in a simple model, in which scientists choose economically rational sample sizes, balancing the cost of experimentation with income from publication. Specifically, assuming that a scientist's income derives only from 'positive' findings (positive publication bias) and that individual samples cost a fixed amount, allows to leverage basic statistical formulas into an economic optimality prediction. We find that if effects have i) low base probability, ii) small effect size or iii) low grant income per publication, then the rational (economically optimal) sample size is small. Furthermore, for plausible distributions of these parameters we find a robust emergence of a bimodal distribution of obtained statistical power and low overall reproducibility rates, both matching empirical findings. Finally, we explore conditional equivalence testing as a means to align economic incentives with adequate sample sizes. Overall, the model describes a simple mechanism explaining both the prevalence and the persistence of small sample sizes, and is well suited for empirical validation. It proposes economic rationality, or economic pressures, as a principal driver of irreproducibility and suggests strategies to change this.
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