On the resolution and feasibility of genome scanning approaches.
Before contemplating a genome scan to identify the map position of disease-predisposing genes, an investigator should have prior evidence of the genes' existence. It is therefore logically consistent to evaluate a genome scan experiment as an estimation problem, rather than as a hypothesis-testing problem, since absent prior evidence of the existence of disease genes, it is probably unwise to conduct the experiment at all. Recombination in a single meiosis can be modeled as a point process along the chromosome, and linkage or linkage disequilibrium (LD) mapping statistics are a simple function of the superposition of the recombination processes occurring in all meioses under study. Thus, multipoint lod scores are shown to be step functions, in the absence of ambiguity about the inheritance of chromosomal segments. The ability to map a disease gene is a function of how well the ascertained phenotypes predict the underlying trait locus genotypes. This chapter presents a thorough investigation of the properties of the multipoint lod score and uses results from renewal theory to examine the effects of deviations from a deterministic phenotype-genotype relationship. The quality of estimated gene locations is assessed through computing the mean and variance of the length of the expected 3-lod-unit support interval around the maximum likelihood estimate. The more deterministic the model, the smaller this interval is. A more exact quantification of details of this effect is used to describe the statistical properties of such genome scanning experiments from the perspective of estimation, with appropriately little regard to hypothesis testing. Hypothesis testing, however, is discussed as an appropriate context to describe linkage and LD analysis in situations where candidate genes are being screened, since only there does one have definable null and alternative hypotheses that have not been rejected before the beginning of the experiment. By contrast, it is hoped that the null hypothesis "there is no gene affecting this phenotype" has been rejected by other means before an expensive genome scan is even contemplated (though that this is often not done is probably the main problem!).