Work has progressed in two major areas: (1) models for human fertility; and (2) statistical methods for studying genetic effects. In the first area, we have adapted our fertility model to take into account possible measurement errors in identifying the day of ovulation. This makes it possible to correct for both the artifactual lengthening such errors cause in the apparent fertile interval and the biases caused in estimation of fertility parameters. Case-control studies aimed at elucidating genetic contributors to the etiology of diseases are problematic because of the """"""""admixture"""""""" problem: If a particular variant allele is to be studied, there may be subpopulations that simultaneously have elevated prevalence of the variant and increased risk of the defect, for unrelated reasons. Such an admixture will produce biased estimation in a traditional population-based case-control study. Also, healthy members of the population may resist genotyping. The case-parents design avoids both these issues by only genotyping cases and their parents. Using the genetic """"""""triad"""""""" data from such a study, under assumed Mendelian inheritance, one can estimate relative risks for an allelic variant and can differentiate effects that depend on the prenatal effects of the maternal genotype from effects mediated by the (correlated) offspring's inherited genotype. The log-linear model we developed also allows for possible effects of parental imprinting. Simulations reveal that, for example, with such a design 100 case families yield a power in excess of 90% to detect a relative risk (dominance model) of 3.0.
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