Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis.
Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.
Slaton
T L
TL
Department of Pharmacy, University of South Carolina, Columbia 29208, USA.
Piegorsch
W W
WW
Durham
S D
SD
D000818:Animals; D001699:Biometry; D001888:Boric Acids / Q000008:administration & dosage / Q000633:toxicity; D004305:Dose-Response Relationship, Drug; D005260:Female; D005313:Fetal Death / Q000139:chemically induced; D016015:Logistic Models; D051379:Mice; D011247:Pregnancy
D001888:Boric Acids; C032688:boric acid