Presentation at Math & Stats, York University, 23 February 2007
Genetic Effect Estimates via the Bootstrap
in Genome-wide Linkage Scans
Shelley B. Bull, Samuel Lunenfeld Research Institute of Mount Sinai Hospital and
Department of Public Health Sciences, University of Toronto
Abstract
In multiple testing of a very large number of genetic markers distributed across
the genome, parameter estimates are biased when the original data are used to both detect
the location(s) of a linked marker and estimate the locus-specific effect. Because the
locus-specific test statistic and the parameter estimate are positively correlated,
maximization of the test statistic over the genome leads to upward bias in the estimate.
Moreover, the upward bias is increased by adoption of a stringent level of statistical
significance to control genome-wide type I error. To reduce bias, we propose three
bootstrap estimators for genetic effect estimation at a single locus: the shrinkage, the outof-sample, and the weighted estimators, based on repeated sample splitting in the original
dataset. We then extend the approach to multi-loci estimation and examine the
performance of both single and multi-loci parameter estimators in quantitative trait locus
(QTL) linkage analysis. Under simulation schema involving nuclear families and 0-5
QTL, the bootstrap locus-specific QTL-heritability estimates have reduced bias and
smaller mean squared error compared to the naïve estimate in the original sample. The
shrinkage estimator performs best at false positive localizations, whereas the other
estimators do better at true positive localizations. We apply 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 yields
estimates as much as 70% smaller than the naïve estimates. In on-going work we are
attempting to develop corresponding bootstrap interval estimates. Effect estimation by
resampling provides a rather general platform for various genetic analysis methods and
can be easily combined with existing genetic analysis software.
This is joint work with Lei Sun, Department of Public Health Sciences, University of
Toronto and Long Yang Wu, Samuel Lunenfeld Research Institute (now at the University
of Waterloo).