| In this thesis, we discuss statistical issues related to the use of score statistics to map genes in humans under variance-component linkage models.; We first discuss quantitative-trait-loci mapping via ascertained sibships. We show that two different schemes of ascertainment correction are asymptotically equivalent under the normality assumption. We study the effects of misspecification of nuisance parameters and show that incorrect values of the trait correlation and mean can lead to a substantial loss of power, while incorrect values of the variance lead to negligible loss of power. We also show that larger sibships and more stringent ascertainment rules are more robust to misspecifications. We propose to use conditional maximum likelihood estimators under normality assumption and show that this estimate results in only a small loss of power compared to the case of known nuisance parameters even when the trait distribution is non-normal and/or the ascertainment criterion is ill defined. Statistics based on the multivariate t-distribution are proposed to increase the power when the normality assumption is violated. All calculations and analysis are under the framework of local alternatives.; We then examine the efficacy of multipoint methods to compensate for markers that are incompletely polymorphic. We found, when markers are reasonably informative and closely spaced, relatively little power is lost when founders are not genotyped, but when markers are only moderately informative knowledge of founder genotypes can add substantially to power. We also consider genotyping in two stages in order to gain efficiency in genotyping and find that the trait gene can be detected with no loss of power and many fewer genotypes, except when information content is very low. Effects of misspecification of allele frequencies and efficient methods to approximate p-values are also discussed.; In the last part, we study an extended model, which incorporates gene-covariate interaction. We derive score statistics and noncentrality parameters from this model and compare them to the statistics from a genome scan that ignores interaction. For affected sib pair mapping, a simpler statistic is proposed, which has similar performance to the score statistic, but which does not require the estimate of any nuisance parameter. |
