The Combinatorial Partitioning Method

  • Matthew R. Nelson
  • Sharon L. Kardia
  • Charles F. Sing
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1848)


Recent advances in genome technology have led to an exponential increase in the ability to identify and measure variation in a large number of genes in the human genome. However, statistical and computational methods to utilize this information on hundreds, and soon thousands, of variable DNA sites to investigate genotype-phenotype relationships have not kept pace. Because genotype-phenotype relationships are combinatoric and non-additive in nature, traditional methods, such as generalized linear models, are limited in their ability to search through the high-dimensional genotype space to identify genetic subgroups that are associated with phenotypic variation. We present here a combinatorial partitioning method (CPM) that identifies partitions of higher dimensional genotype spaces that predict variation in levels of a quantitative trait. We illustrate this method by applying it to the problem of genetically predicting interindividual variation in plasma triglyceride levels, a risk factor for atherosclerosis.


Cross Validation Interindividual Variation Locus Genotype Phenotype Relationship Trait Variability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Boerwinkle and C. F. Sing, The use of measured genotype information in the analysis of quantitative phenotypes in man. III. Simultaneous estimation of the frequencies and effects of the apolipoprotein E polymorphism and residual polygenetic effects on cholesterol, betalipoprotein and triglyceride levels, Ann Hum Genet 51 (1987), 211–26.CrossRefGoogle Scholar
  2. 2.
    L. Comtet, Advanced combinatorics: The art of infinite expansions, Reidel Pub. Co., Boston, MA, 1974.zbMATHGoogle Scholar
  3. 3.
    D. E. Goldberg, Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading, MA, 1989.zbMATHGoogle Scholar
  4. 4.
    D. L. Hartl and A. G. Clark, Principles of population genetics, third ed., Sinauer Associates, Sunderland, MA, 1997.Google Scholar
  5. 5.
    S. Kirkpatrick, C. D. Gelatt Jr., and M. P. Vecchi, Optimization by simulated annealing, Science 220 (1983), 671–680.CrossRefMathSciNetGoogle Scholar
  6. 6.
    R. Kohavi, A study of cross-validation and bootstrap for accuracy estimation and model selection, Proc Int Joint Conf Artificial Intel, 1995, pp. 1137–1143.Google Scholar
  7. 7.
    B.-H. Liu, Statistical genomics: Linkage, mapping, and QTL analysis, CRC Press, Boca Raton, 1998.Google Scholar
  8. 8.
    M. R. Nelson, A combinatorial partitioning method to identify multi-genic multilocus models that predict quantitative trait variablility., Ph.D. thesis, University of Michigan, Department of Human Genetics, 1999.Google Scholar
  9. 9.
    M. R. Nelson, S. L. R. Kardia, R. E. Ferrell, and C. F. Sing, A combinatorial partitioning method to identify multi-locus genotype partitions that predict quantitative trait variation., (Submitted).Google Scholar
  10. 10.
    D. A. Nickerson, S. L. Taylor, K. M. Weiss, A. G. Hutchinson, J. Stengard, V. Salomaa, E. Vartiainen, E. Boerwinkle, and C. F. Sing, DNA sequence diversity in a 9.7 kb region of the human lipoprotein lipase gene., Nat. Genet. 19 (1998), 233–240.CrossRefGoogle Scholar
  11. 11.
    C. F. Sing, M. B. Haviland, and S. L. Reilly, Genetic architecture of common multifactorial diseases., Ciba Found Symp 197 (1996), 211–229.Google Scholar
  12. 12.
    G. S. Stent, Genetics: An introductory narrative, W.H. Freeman, San Francisco, 1971.Google Scholar
  13. 13.
    M. Stone, Cross-validation: A review, Math Operationsforsch Statist, Ser Statistics 9 (1978), 127–139.zbMATHGoogle Scholar
  14. 14.
    S. T. Turner, W. H. Weidman, V. V. Michels, T. J. Reed, C. L. Ormson, T. Fuller, and C. F. Sing, Distribution of sodium-lithium countertransport and blood pressure in Caucasians five to eighty-nine years of age, Hypertension 13 (1989), 378–391.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Matthew R. Nelson
    • 1
  • Sharon L. Kardia
    • 2
  • Charles F. Sing
    • 3
  1. 1.Dept. of GenomicsEsperion Therapeutics, IncAnn ArborUSA
  2. 2.Dept. of EpidemiologyUniversity of MichiganAnn ArborUSA
  3. 3.Dept. of Human GeneticsUniversity of MichiganAnn ArborUSA

Personalised recommendations