POOR PERFORMANCE OF BOOTSTRAP CONFIDENCE INTERVALS FOR THE LOCATION OF A QUANTITATIVE TRAIT LOUCS

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTLs) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTLs are particularly important for the design of further experiments to identify the gene or genes responsible for the effect. Likelihood support intervals are the most widely used method to obtain confidence intervals for QTL location, but the non-parametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals are poorly behaved and so should not be used in this context. The profile likelihood (or LOD curve) for QTL location has a tendency to peak at genetic markers, and so the distribution of the maximum likelihood estimate (MLE) of QTL location has the unusual feature of point masses at genetic markers; this contributes to the poor behavior of the bootstrap. Likelihood support intervals and approximate Bayes credible intervals, on the other hand, are shown to behave appropriately.

Sequential Quantitative Trait Locus Mapping in Experimental Crosses

The etiology of complex diseases is heterogeneous. The presence of risk alleles in one or more genetic loci affects the function of a variety of intermediate biological pathways, resulting in the overt expression of disease. Hence, there is an increasing focus on identifying the genetic basis of disease by sytematically studying phenotypic traits pertaining to the underlying biological functions. In this paper we focus on identifying genetic loci linked to quantitative phenotypic traits in experimental crosses. Such genetic mapping methods often use a one stage design by genotyping all the markers of interest on the available subjects. A genome scan based on single locus or multi-locus models is used to identify the putative loci. Since the number of quantitative trait loci (QTLs) is very likely to be small relative to the number of markers genotyped, a one-stage selective genotyping approach is commonly used to reduce the genotyping burden, whereby markers are genotyped solely on individuals with extreme trait values. This approach is powerful in the presence of a single quantitative trait locus (QTL) but may result in substantial loss of information in the presence of multiple QTLs. Here we investigate the efficiency of sequential two stage designs to identify QTLs in experimental populations. Our investigations for backcross and F2 crosses suggest that genotyping all the markers on 60% of the subjects in Stage 1 and genotyping the chromosomes significant at 20% level using additional subjects in Stage 2 and testing using all the subjects provides an efficient approach to identify the QTLs and utilizes only 70% of the genotyping burden relative to a one stage design, regardless of the heritability and genotyping density. Complex traits are a consequence of multiple QTLs conferring main effects as well as epistatic interactions. We propose a two-stage analytic approach where a single-locus genome scan is conducted in Stage 1 to identify promising chromosomes, and interactions are examined using the loci on these chromosomes in Stage 2. We examine settings under which the two-stage analytic approach provides sufficient power to detect the putative QTLs.

Power and Robustness of Linkage Tests for Quantitative Traits in General Pedigrees

There are numerous statistical methods for quantitative trait linkage analysis in human studies. An ideal such method would have high power to detect genetic loci contributing to the trait, would be robust to non-normality in the phenotype distribution, would be appropriate for general pedigrees, would allow the incorporation of environmental covariates, and would be appropriate in the presence of selective sampling. We recently described a general framework for quantitative trait linkage analysis, based on generalized estimating equations, for which many current methods are special cases. This procedure is appropriate for general pedigrees and easily accommodates environmental covariates. In this paper, we use computer simulations to investigate the power robustness of a variety of linkage test statistics built upon our general framework. We also propose two novel test statistics that take account of higher moments of the phenotype distribution, in order to accommodate non-normality. These new linkage tests are shown to have high power and to be robust to non-normality. While we have not yet examined the performance of our procedures in the context of selective sampling via computer simulations, the proposed tests satisfy all of the other qualities of an ideal quantitative trait linkage analysis method.

USE OF HIDDEN MARKOV MODELS FOR QTL MAPPING

An important aspect of the QTL mapping problem is the treatment of missing genotype data. If complete genotype data were available, QTL mapping would reduce to the problem of model selection in linear regression. However, in the consideration of loci in the intervals between the available genetic markers, genotype data is inherently missing. Even at the typed genetic markers, genotype data is seldom complete, as a result of failures in the genotyping assays or for the sake of economy (for example, in the case of selective genotyping, where only individuals with extreme phenotypes are genotyped). We discuss the use of algorithms developed for hidden Markov models (HMMs) to deal with the missing genotype data problem.