Journal of Genetics

, Volume 79, Issue 2, pp 47–53 | Cite as

An improved procedure of mapping a quantitative trait locus via the EM algorithm using posterior probabilities

  • Saurabh Ghosh
  • Partha P. Majumder


Mapping a locus controlling a quantitative genetic trait (e.g. blood pressure) to a specific genomic region is of considerable contemporary interest. Data on the quantitative trait under consideration and several codominant genetic markers with known genomic locations are collected from members of families and statistically analysed to estimate the recombination fraction, θ, between the putative quantitative trait locus and a genetic marker. One of the major complications in estimating θ for a quantitative trait in humans is the lack of haplotype information on members of families. We have devised a computationally simple two-stage method of estimation of θ in the absence of haplotypic information using the expectation-maximization (EM) algorithm. In the first stage, parameters of the quantitative trait locus (QTL) are estimated on the basis of data of a sample of unrelated individuals and a Bayes’s rule is used to classify each parent into a QTL genotypic class. In the second stage, we have proposed an EM algorithm for obtaining the maximum-likelihood estimate of θ based on data of informative families (which are identified upon inferring parental QTL genotypes performed in the first stage). The purpose of this paper is to investigate whether, instead of using genotypically ‘classified’ data of parents, the use of posterior probabilities of QT genotypes of parents at the second stage yields better estimators. We show, using simulated data, that the proposed procedure using posterior probabilities is statistically more efficient than our earlier classification procedure, although it is computationally heavier.


recombination fraction linkage maximum likelihood estimation 


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  1. Almasy L. and Blangero J. 1998 Multipoint quantitative trait linkage analysis in general pedigrees.Am. J. Hum. Genet. 62, 1198–1211.PubMedCrossRefGoogle Scholar
  2. Amos C. I. and Elston R. C. 1989 Robust methods for the detection of genetic linkage for quantitative data from pedigrees.Genet. Epidemiol. 6, 349–360.PubMedCrossRefGoogle Scholar
  3. Dempster A. P., Laird N. M. and Rubin D. B. 1977 Maximum likelihood from incomplete data via the EM algorithm.J. R. Stat. Soc. B39, 1–38.Google Scholar
  4. Fergusson T. S. 1967Mathematical statistics: a decision-theoretic approach. Academic Press, New York.Google Scholar
  5. Ghosh S. and Majumder P. P. 2000 Mapping quantitative trait loci via the EM algorithm and Bayesian classification.Genet. Epidemiol. 19, 97–126.PubMedCrossRefGoogle Scholar
  6. Goldgar D. E. 1990 Multipoint analysis of human quantitative genetic variation.Am. J. Hum. Genet. 47, 957–967.PubMedGoogle Scholar
  7. Haley C. S. and Knott S. A. 1992 A simple regression method for mapping quantitative trait loci in line crosses using flanking markers.Heredity 69, 315–324.PubMedGoogle Scholar
  8. Haseman J. K. and Elston R. C. 1972 The investigation of linkage between a quantitative trait and a marker locus.Behav. Genet. 2, 3–19.PubMedCrossRefGoogle Scholar
  9. Kruglyak L. and Lander E. S. 1995 A nonparametric approach for mapping quantitative trait loci.Genetics 139, 1421–1428.PubMedGoogle Scholar
  10. Lander E. S. and Botstein D. 1989 Mapping Mendelian factors underlying quantitative traits using RFLP linkage maps.Genetics 121, 185–199.PubMedGoogle Scholar
  11. Lincoln S. E., Daly M. J. and Lander E. S. 1993 MAPMAKER/ QTL version 1.1. Scholar
  12. McLachlan G. J. and Krishnan T. 1997The EM algorithm and extensions. Wiley, New York.Google Scholar
  13. Olson J. M. 1995 Robust multipoint linkage analysis: an extension of the Haseman-Elston method.Genet. Epidemiol. 12, 177–193.PubMedCrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2000

Authors and Affiliations

  1. 1.Anthropology and Human Genetics UnitIndian Statistical InstituteCalcuttaIndia

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