@entity19 embryo assays are recommended to test materials used for in vitro fertilization for @entity137 . 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 @entity137 are based on observed differences in successful embryo development between the two groups. However, @entity19 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 @entity19 embryo assay (NMEA), in order to obtain an efficient and statistically validated design. The NMEA follows a stratified ( @entity19 ), randomized (embryo), balanced design (also known as a split-cluster design). We adopted @entity15370 -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 @entity19 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.

Sample size calculations for a split-cluster, beta-binomial design in the assessment of XXXX .

@entity19 :: ('10090', 'Species') :: ['mice', 'Mouse', 'mouse'] @entity137 :: ('MESH:D064420', 'Disease') :: ['toxicity'] @entity15370 :: ('11820(Tax:10090)', 'Gene') :: ['a beta']
@entity137 :: (MESH:D064420,Disease) :: ['toxicity']
