The Research Of Statistical Methods Based On Entropy Theory For QTL Mapping In Human Beings

Mapping genes associated with various traits and diseases is one of the most important research areas in human genetics.A major effort in the gene-mapping process is the detection of loci that influence quantitative traits,which are referred to as "quantitative trait loci"(QTLs).QTL mapping can be accomplished through the method of selective genotyping,which is based on the differences of frequencies between an upper sample and a lower sample in population,but this method is not uniformly the most powerful.However,amplifying the differences in marker allele frequencies in extreme samples may increase the probability for QTL mapping.Shannon entropy,which is a nonlinear function of allele frequencies,can be used to amplify the differences in marker allele frequencies.In this paper,based on entropy theory,a two-stage procedure that uses extreme samples and high-density marker maps is suggested for high-resolution mapping of a QTL.At the first stage,an entropy-based statistic T_PEfor genomic association study for disease-susceptibility locus is directly extended to association study of a QTL for quantitative traits from extreme individuals in population.The statistic T_QPEfor QTL association study is to compare the entropy of the haplotype in the upper sample and the lower sample.The statistical properties of the statistic T_QPE(the distribution, the typeâ… error rate,and the power)were examined under a range of parameters and population-sampling strategies(e.g.,various genetic models,various heritabilities,and various sample-selection threshold values)by simulation studies.The typeâ… error rates are around the nominal levels(α=0.05)and the power is above 90%in mostly scenarios.The power increases with increasing sample size, the increasing heritability,and the stringency of the sample selection. Under the additive model,the power is higher than that under the dominant model and the recessive model.A simulation study based on the haplotype frequencies of 10 single nucleotide polymorphisms (SNPs)of angiotensin-â… converting enzyme(ACE)genes is conducted to evaluate the performance of the statistic T_QPEfor genetic association study.The excellent results indicate that the statistic T_QPEis robust and powerful.Based on the results of the first stage,when a large genomic region is obtained in genomic association study,the fine-scale mapping study,which is to narrow the large genomic region,should be next to consider.Thus,at the second stage,two entropy-based measures (lx₁ and lx₂)for fine-scale linkage disequilibrium(LD)gene mapping are presented using high-density marker maps in extreme samples for quantitative trait.The measure lx₁ compares the entropy of a marker in population and the conditional entropy of a marker in the upper sample or the lower sample.It is for use when marker allele frequencies in a study population are known.The measure lx₂ compares the entropy and conditional entropy in a marker in extreme samples of population.It is for use when marker allele frequencies in a study population are not known and are only known in the extreme samples. Both the measures lx₁ and lx₂ are the function of LD between the marker and the QTL,and does not depend on the marker allele frequencies across the loci under the following assumptions:(a)there is initial complete LD between the marker locus and the QTL,(b) there are no new mutations at both the marker locus and the QTL, and(c)the population under study is large.The mapping perfor- mances of the measures lx₁ and lx₂ are investigated in both analytic and simulation scenarios of a single QTL linked to a single marker, and also compared with the common measure.In addition,a simulation study is performed on the basis of the haplotype frequencies of 10 SNPs of ACE genes.