Hendriks J C M, Teerenstra S, Punt-Van der Zalm J P E, Wetzels A M M, Westphal J R, Borm G F
Department of Epidemiology and Biostatistics, Radboud University Nijmegen Medical Centre, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands.
Stat Med. 2005 Dec 30;24(24):3757-72. doi: 10.1002/sim.2412.
Mouse embryo assays are recommended to test materials used for in vitro fertilization for toxicity. In such assays, a number of embryos is divided in a control group, which is exposed to a neutral medium, and a test group, which is exposed to a potentially toxic medium. Inferences on toxicity are based on observed differences in successful embryo development between the two groups. However, mouse embryo assays tend to lack power due to small group sizes. This paper focuses on the sample size calculations for one such assay, the Nijmegen mouse embryo assay (NMEA), in order to obtain an efficient and statistically validated design. The NMEA follows a stratified (mouse), randomized (embryo), balanced design (also known as a split-cluster design). We adopted a beta-binomial approach and obtained a closed sample size formula based on an estimator for the within-cluster variance. Our approach assumes that the average success rate of the mice and the variance thereof, which are breed characteristics that can be easily estimated from historical data, are known. To evaluate the performance of the sample size formula, a simulation study was undertaken which suggested that the predicted sample size was quite accurate. We confirmed that incorporating the a priori knowledge and exploiting the intra-cluster correlations enable a smaller sample size. Also, we explored some departures from the beta-binomial assumption. First, departures from the compound beta-binomial distribution to an arbitrary compound binomial distribution lead to the same formulas, as long as some general assumptions hold. Second, our sample size formula compares to the one derived from a linear mixed model for continuous outcomes in case the compound (beta-)binomial estimator is used for the within-cluster variance.
推荐使用小鼠胚胎试验来测试体外受精所用材料的毒性。在这类试验中，将一定数量的胚胎分为对照组和试验组，对照组暴露于中性培养基中，试验组暴露于潜在有毒的培养基中。关于毒性的推断是基于两组胚胎成功发育情况的观察差异。然而，由于样本量小，小鼠胚胎试验往往缺乏效力。本文聚焦于其中一种试验——奈梅亨小鼠胚胎试验（NMEA）的样本量计算，以获得一个高效且经统计学验证的设计。NMEA采用分层（小鼠）、随机（胚胎）、平衡设计（也称为裂区设计）。我们采用了贝塔二项式方法，并基于组内方差估计器获得了一个封闭的样本量公式。我们的方法假设小鼠的平均成功率及其方差是已知的，这两个参数作为品系特征，可从历史数据中轻松估计得出。为评估样本量公式的性能，我们进行了一项模拟研究，结果表明预测的样本量相当准确。我们证实，纳入先验知识并利用组内相关性能够减小样本量。此外，我们探讨了一些偏离贝塔二项式假设的情况。首先，只要一些一般假设成立，从复合贝塔二项分布偏离到任意复合二项分布会得到相同的公式。其次，如果将复合（贝塔 -）二项式估计器用于组内方差，我们的样本量公式与从连续结果的线性混合模型导出的公式相比。
