Jg. Morel et Nk. Neerchal, CLUSTERED BINARY LOGISTIC-REGRESSION IN TERATOLOGY DATA USING A FINITE MIXTURE DISTRIBUTION, Statistics in medicine, 16(24), 1997, pp. 2843-2853
The beta-binomial distribution introduced by Skellam has been applied
in many teratology problems for modelling the litter effect. Recently,
Morel and Nagaraj proposed a new distribution for modelling cluster m
ultinomial data when the clustering is believed to be caused by clumpe
d sampling. It turns out that the distribution is a mixture of two bin
omial distributions and accommodates the estimation of an additional p
arameter to account for intra-litter effect. The new distribution aris
es from a cluster mechanism in which some individuals within a cluster
exhibit the same behaviour while the remaining individuals from the c
luster react independently of each other. Such a mechanism is a natura
l model in teratology problems, where typically a genetic trait is pas
sed with a certain probability to the foetuses of the same litter. In
this article, we use the new distribution to model binary responses wi
th logistic regression. We analyse data from a teratology experiment t
o demonstrate that the new model provides a useful addition to current
methodology. The experiment investigates the synergistic effect of th
e anticonvulsant phenytoin and trichloropopene oxide on the prenatal d
evelopment of inbred mice. In a simulation study we investigate the ty
pe I error rate and the power of the maximum likelihood ratio test whe
n the data follow a finite mixture distribution. (C) 1997 by John Wile
y & Sons, Ltd.