Department of Methodology and Statistics, Utrecht University, PO Box 80140, 3508 TC, Utrecht, The Netherlands.
Behav Res Methods. 2024 Sep;56(6):5849-5861. doi: 10.3758/s13428-023-02320-0. Epub 2023 Dec 29.
In many studies in the social and behavioral sciences, the data have a multilevel structure, with subjects nested within clusters. In the design phase of such a study, the number of clusters to achieve a desired power level has to be calculated. This requires a priori estimates of the effect size and intraclass correlation coefficient. If these estimates are incorrect, the study may be under- or overpowered. This may be overcome by using a group-sequential design, where interim tests are done at various points in time of the study. Based on interim test results, a decision is made to either include additional clusters or to reject the null hypothesis and conclude the study. This contribution introduces Bayesian sequential designs as an alternative to group-sequential designs. This approach compares various hypotheses based on the support in the data for each of them. If neither hypothesis receives a sufficient degree of support, additional clusters are included in the study and the Bayes factor is recalculated. This procedure continues until one of the hypotheses receives sufficient support. This paper explains how the Bayes factor is used as a measure of support for a hypothesis and how a Bayesian sequential design is conducted. A simulation study in the setting of a two-group comparison was conducted to study the effects of the minimum and maximum number of clusters per group and the desired degree of support. It is concluded that Bayesian sequential designs are a flexible alternative to the group sequential design.
在社会科学和行为科学的许多研究中，数据具有多层次结构，其中主体嵌套在聚类中。在这种研究的设计阶段，必须计算达到所需功率水平所需的聚类数量。这需要对效应大小和组内相关系数进行先验估计。如果这些估计不正确，研究可能会功率不足或过度。这可以通过使用群组序贯设计来克服，其中在研究的不同时间点进行中间测试。根据中间测试结果，决定是增加额外的聚类，还是拒绝零假设并结束研究。本贡献介绍了贝叶斯序贯设计作为群组序贯设计的替代方案。这种方法基于每个假设在数据中的支持程度来比较各种假设。如果没有一个假设得到足够的支持，则在研究中增加更多的聚类，并重新计算贝叶斯因子。此过程将一直持续到其中一个假设得到足够的支持。本文解释了如何将贝叶斯因子用作假设支持的度量标准，以及如何进行贝叶斯序贯设计。在两组比较的设置中进行了模拟研究，以研究每组的最小和最大聚类数量以及所需的支持程度的影响。结论是，贝叶斯序贯设计是群组序贯设计的灵活替代方案。
