TY - JOUR
T1 - Using importance sampling to improve simulation in linkage analysis
AU - Ängquist, Lars
AU - Hössjer, Ola
PY - 2004/1/1
Y1 - 2004/1/1
N2 - 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 genome-wide p-values, i.e. the probability that the maximal linkage score exceeds given thresholds under the null hypothesis of no linkage. In order to reduce variance of the 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 the sampling distribution are properly chosen the variance of the corresponding estimate is reduced. This results in accurate genome-wide p-value estimates for a wide range of large thresholds with a substantially smaller cost adjusted relative efficiency with respect to standard unweighted simulation. We illustrate the performance of the method for several pedigree examples, discuss implementation including the amount of variance reduction and describe some possible generalizations.
AB - 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 genome-wide p-values, i.e. the probability that the maximal linkage score exceeds given thresholds under the null hypothesis of no linkage. In order to reduce variance of the 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 the sampling distribution are properly chosen the variance of the corresponding estimate is reduced. This results in accurate genome-wide p-value estimates for a wide range of large thresholds with a substantially smaller cost adjusted relative efficiency with respect to standard unweighted simulation. We illustrate the performance of the method for several pedigree examples, discuss implementation including the amount of variance reduction and describe some possible generalizations.
KW - Change of probability measure
KW - Cost adjusted relative efficiency
KW - Exponential tilting
KW - Genome-wide significance
KW - Importance sampling
KW - Marker information
KW - Nonparametric linkage analysis
KW - Variance reduction
UR - http://www.scopus.com/inward/record.url?scp=18544367812&partnerID=8YFLogxK
U2 - 10.2202/1544-6115.1049
DO - 10.2202/1544-6115.1049
M3 - Journal article
AN - SCOPUS:18544367812
SN - 1544-6115
VL - 3
JO - Statistical Applications in Genetics and Molecular Biology
JF - Statistical Applications in Genetics and Molecular Biology
IS - 1
M1 - 5
ER -