Using Importance Sampling to Improve Simulation in Linkage Analysis
Lars Ängquist and Ola Hössjer
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003
ISSN 14039338

Abstract:

In this article we describe and discuss implementation of a weighted simulation
procedure, importance sampling, in the context of nonparametric linkage analysis.
The objective is to estimate genomewide pvalues, i.e. the probability that
the maximal linkage score exceeds a given threshold under the null hypothesis
of no linkage. In order to reduce variance of the pvalue estimate for large
thresholds, we simulate linkage scores under a distribution different from
the null with an artificial disease locus positioned somewhere along the
genome. To compensate for the fact that we simulate under the wrong distribution,
the simulated scores are reweighted using a certain likelihood ratio. If
design parameters of the sampling distribution are chosen correctly, the
variance of the final significance value estimate is reduced. This results
in more accurate genomewide pvalue estimates for large thresholds, based
on a substantially smaller number of simulations than is needed using traditional
unweighted simulation.


We illustrate the performance of the method for several pedigree examples,
discuss implementation including choice of sampling parameters and describe
some possible generalizations.



Key words:

Nonparametric linkage analysis, importance sampling, change of probability
measure, exponential tilting, marker information, genomewide significance
