title: Sample size calculations for a split-cluster, beta-binomial design in the assessment of toxicity.
abstract: 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.
authors.affiliation: Department of Epidemiology and Biostatistics, Radboud University Nijmegen Medical Centre, P.O. Box 9101, 6500 HB Nijmegen, The Netherlands. j.hendriks@epib.umcn.nl
authors.forename: J C M
authors.initials: JC
authors.lastname: Hendriks
authors.forename: S
authors.initials: S
authors.lastname: Teerenstra
authors.forename: J P E
authors.initials: JP
authors.lastname: Punt-Van der Zalm
authors.forename: A M M
authors.initials: AM
authors.lastname: Wetzels
authors.forename: J R
authors.initials: JR
authors.lastname: Westphal
authors.forename: G F
authors.initials: GF
authors.lastname: Borm
mesh_terms: D000818:Animals; D016010:Binomial Distribution; D016000:Cluster Analysis; D004622:Embryo, Mammalian; D005260:Female; D005285:Fermentation; D051379:Mice; D008808:Mice, Inbred CBA; D015233:Models, Statistical; D018401:Sample Size; D018675:Toxicity Tests / Q000706:statistics & numerical data*