Abstract
BackgroundThis article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls.ResultsFrequencies of genotypes in cases and controls can be estimated directly from retrospective case-control data. On the other hand, genetic susceptibility defined as the expected proportion of cases among individuals with a particular genotype depends on the population proportion of cases (prevalence). Given this design, prevalence is an external parameter and hence the susceptibility cannot be estimated based on only the observed data. Interval estimation of susceptibility that can incorporate uncertainty in prevalence values is explored from both classical and Bayesian perspective. Similarity between classical and Bayesian interval estimates in terms of frequentist coverage probabilities for this problem allows an appealing interpretation of classical intervals as bounds for genetic susceptibility. In addition, it is observed that both the asymptotic classical and Bayesian interval estimates have comparable average length. These interval estimates serve as a very good approximation to the "exact" (finite sample) Bayesian interval estimates. Extension from genotypic to allelic susceptibility intervals shows dependency on phenotype-induced deviations from Hardy-Weinberg equilibrium.ConclusionsThe suggested classical and Bayesian interval estimates appear to perform reasonably well. Generally, the use of exact Bayesian interval estimation method is recommended for genetic susceptibility, however the asymptotic classical and approximate Bayesian methods are adequate for sample sizes of at least 50 cases and controls.
Highlights
This article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls
Under a beta-binomial model there is a close connection between the two types of intervals for genetic susceptibility, which allows flexibility in the interpretation
Susceptibility intervals Association studies are often "retrospective" in the sense that samples of cases and controls are determined by recruitment ("fixed"), and the genetic variants, e.g. genotypes AA and AA at a genetic marker, are random
Summary
This article describes classical and Bayesian interval estimation of genetic susceptibility based on random samples with pre-specified numbers of unrelated cases and controls. Association mapping of complex phenotypes in case-control samples involves analysis of tables of genotype/allele counts collected at a large number of genetic loci. Relating single-locus genotype and allele frequencies to the outcome is a basic analysis step even if complex interactions among loci are expected. Biologically realistic models that involve multiple interacting polymorphisms may induce considerable "marginal effects" associated with individual loci. Often the numbers of cases and controls are fixed in advance by the experimental design, and the multiple markers are typed. Case/control proportions remain the same for all markers, whereas genotype and allele numbers in cases and controls are subject to the random sampling variation. The reverse is of greater interest: what is the genetic susceptibility, or the (page number not for citation purposes)
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