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Journal Article 
Supplemental Data 
Dose-response modeling with summary data from developmental toxicity studies : Supplementary materials 
Fox, JR; Hogan, KA; Davis, A 
Risk Analysis
ISSN: 0272-4332
EISSN: 1539-6924 
is a supplement to 3392311 Dose-response modeling with summary data from developmental toxicity studies
Dose-response analysis of binary developmental data (e.g., implant loss, fetal abnormalities) is best done using individual fetus data (identified to litter) or litter-specific statistics such as number of offspring per litter and proportion abnormal. However, such data are not often available to risk assessors. Scientific articles usually present only dose-group summaries for the number or average proportion abnormal and the total number of fetuses. Without litter-specific data, it is not possible to estimate variances correctly (often characterized as a problem of overdispersion, intralitter correlation, or “litter effect”). However, it is possible to use group summary data when the design effect has been estimated for each dose group. Previous studies have demonstrated useful dose-response and trend test analyses based on design effect estimates using litter-specific data from the same study. This simplifies the analysis but does not help when litter-specific data are unavailable. In the present study, we show that summary data on fetal malformations can be adjusted satisfactorily using estimates of the design effect based on historical data. When adjusted data are then analyzed with models designed for binomial responses, the resulting benchmark doses are similar to those obtained from analyzing litter-level data with nested dichotomous models. 
Benchmark dose; design effect; developmental; dose response; fetal; intralitter correlation; overdispersion