Academic journal article Genetics

Poor Performance of Bootstrap Confidence Intervals for the Location of a Quantitative Trait Locus

Academic journal article Genetics

Poor Performance of Bootstrap Confidence Intervals for the Location of a Quantitative Trait Locus

Article excerpt

ABSTRACT

The aim of many genetic studies is to locate the genomic regions (called quantitative trait loci, QTL) that contribute to variation in a quantitative trait (such as body weight). Confidence intervals for the locations of QTL 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 nonparametric bootstrap has also been recommended. Through extensive computer simulation, we show that bootstrap confidence intervals behave poorly 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.

THERE is much interest in mapping the genetic loci (called quantitative trait loci, QTL) that contribute to variation in a quantitative trait. Once such a QTL has been identified, interest turns to the calculation of a confidence interval for its location, as such an interval estimate can be a useful guide for the design of further experiments, such as the generation of congenic lines.

LOD support intervals are the most commonly used interval estimates for the location of a QTL. A LOD support interval is defined as the interval in which the LOD score is within some value of its maximum. As an illustration, Figure 1A displays the LOD curve for chromosome 4 for the data of SUGIYAMA et al. (2001), concerning salt-induced hypertension in 250 backcross mice. Assuming that there is a single QTL on this chromosome, the maximum-likelihood estimate (MLE) of the location of the QTL is the position at which the LOD curve achieves its maximum, in this case at marker D4Mit164 (at 30 cM). The 1.5-LOD support interval for the location of the QTL is the region in which the LOD score is within 1.5 of its maximum; here, the interval extends from 19 to 31 cM. (When the relevant region is disconnected, we generally take the conservative approach of forming the longest contiguous interval.)

LANDER and BOTSTEIN (1989) recommended the use of 1- and 2-LOD support intervals. DUPUIS and SIEGMUND (1999) found that 1.5-LOD support intervals provide ∼95% coverage in the case of a dense marker map. However, it has often been observed (see, e.g., MANGIN et al. 1994) that the coverage of LOD support intervals depends upon the effect of the QTL, and so they do not behave as true confidence intervals.

VISSCHER et al. (1996) recommended the use of a nonparametric bootstrap to derive a confidence interval for the location of a QTL. For experimental cross data on n individuals, one makes n draws, with replacement, from the observed individuals to form a new data set in which some individuals are omitted and some appear multiple times. An estimate of QTL location is calculated with these new data, and the process is repeated many times. An ∼95% confidence interval for the location of the QTL is obtained as the interval containing 95% of the estimated locations from the bootstrap replicates.

As an illustration, Figure 1B contains a histogram of the results of 10,000 bootstrap replicates using the chromosome 4 data of SUGIYAMA et al. (2001). The 95% bootstrap confidence interval extends from 14 to 32 cM. A striking feature of these results is that ∼79% of the bootstrap replicates gave an estimated QTL location precisely at one of the 20 genetic markers on the chromosome. (Note that the calculations were performed at the markers and at 1-cM steps along the chromosome.) This is due to an unusual feature of the MLE of QTL location (previously observed by WALLING et al. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.