Groupe d’études et de recherche en analyse des décisions

Bias Reduction of Locus-specific Effect Estimates via the Bootstrap in Linkage Scans for Quantitative Trait Loci

Shelley Bull

In genome-wide linkage analysis of quantitative trait loci (QTL), heritability estimates are biased when the original data are used to both detect the location(s) of the QTL and estimate locus-specific effects. Because the locus-specific test statistic and the heritability estimate are positively correlated, maximization of the test statistic over the genome leads to upward bias in the heritability. Moreover, the upward bias is increased by adoption of a stringent level of statistical significance to control genome-wide type I error. To reduce upward bias, Sun and Bull (2005) proposed three bootstrap estimators for genetic effect estimation at a single locus: the shrinkage, the out-of-sample, and the weighted estimator, based on repeated sample splitting in the original dataset. We extended their approach to multi-loci estimation and examined the performance of both single and multi-loci estimators of heritability in QTL linkage analysis. Under simulation schema involving nuclear families and 0-5 QTL, the bootstrap locus-specific QTL-heritability estimates had reduced bias and smaller mean squared error compared to the naïve estimate in the original sample. The shrinkage estimator performed best at false positive localizations, whereas the other estimators did better at true positive localizations. We applied the multi-loci estimators to a quantitative trait derived from longitudinal systolic blood pressure measurements in extended pedigrees from the Framingham Heart Study. The bootstrap procedure yielded estimates as much as 70% smaller than the naïve estimates. Effect estimation by resampling provides a rather general platform for various linkage methods and can be easily combined with existing linkage analysis software.

This is joint work with Long Yang Wu, Samuel Lunenfeld Research Institute of Mount Sinai Hospital, Toronto, and Lei Sun, Department of Public Health Sciences, University of Toronto and Hospital for Sick Children Research Institute, Toronto