Methods of incorporating litter size in the analysis of teratology data.

Abstract

Teratology studies examine the effect a substance has on the proportion of malformed fetuses. Factors which can influence the probability of an anomaly include genetic and environmental information shared by the fetuses as well as litter size, which is a random variable. Several methods to compare proportions have been developed which adjust for the variability from genetic and environmental factors, but the methods do not incorporate the contribution of the litter size. Three methods of testing the equality of the rate of malformations between treatment groups are developed in this thesis. Two statistics test this simple hypothesis. The first has a form similar to a chi-square goodness of fit statistic; its distribution is approximated by that of a chi-square. The second method uses estimators that are obtained by minimizing the mean squared error; its statistic has the form of a Behrens-Fisher two-sample t-test for unequal variances. The third method uses a quasi-likelihood to extend an approach of Williams (1975) and tests a compound hypothesis both that the rates of malformations are equal and that the litter sizes have the same distribution in two treatment groups. The approximate chi-square has conservative type I error rates for low incidence malformations and, in these situations, demonstrates the best power of the methods examined. For higher incidence rates the statistic produces type I error rates that make its use questionable. The approximate t-test produces conservative type I error rates for low incidence malformations and demonstrates moderate power. The extended Williams' statistic has conservative type I error and has superior power when differences exist between the dose groups in both the litter size distribution and in the proportion of affected fetuses.