Abstract.
In this paper we introduce two information criteria in linkage analysis. The setup is a sample of families with unusually high occurrence of a certain inheritable disease. Given phenotypes from all families, the two criteria measure the amount of information inherent in the sample for 1) testing existence of a disease locus harbouring a disease gene somewhere along a chromosome or 2) estimating the position of the disease locus.
Both criteria have natural interpretations in terms of effective number of meioses present in the sample. Thereby they generalize classical performance measures directly counting number of informative meioses.
Our approach is conditional on observed phenotypes and we assume perfect marker data. We analyze two extreme cases of complete and weak penetrance models in particular detail. Some consequences of our work for sampling of pedigrees are discussed. For instance, a large sibship family with extreme phenotypes is very informative for linkage for weak penetrance models, more informative than a number of small families of the same total size.
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References
Ängquist, L., Hössjer, O.: Improving the calculation of statistical significance in genome-wide scans. Report 2003:3, Mathematical Statistics, Stockholm University, To appear in Biostatistics (2003)
Commenges, D.: Robust genetic linkage analysis based on a score test of homogeneity: The weighted pairwise correlation statistic. Genet. Epidmiol. 11, 189–200 (1994)
Donnelly, P.: The probability that some related individuals share some section of the genome identical by descent. Theoret. Population Biol. 23, 34–64 (1983)
Dudoit, S., Speed, T.P.: A score test for linkage analysis of qualitative and quantitative traits based on identity by descent data from sib-pairs. Biostatist. 1, 1–26 (2000)
Feingold, E., O’Brown, P., Siegmund, D.: Gaussian models for genetic linkage analysis using complete high-resolution maps of identity by descent. Am. J. of Hum. Genet. 53, 234–251 (1993)
Fisher, R.: The correlation between relatives on the supposition of Mendelian inheritance. Proc. Roy. Soc. Edinburgh. 52, 399–433 (1918)
Haines, J.L., Paricak-Vance, M.A.: Approaches to Gene Mapping in Complex Human Diseases. New York: Wiley-Liss, (1998)
Hössjer, O.: Determining inheritance distributions via stochastic penetrances. J. Amer. Statist. Assoc. 98, 1035–1051 (2003e)
Hössjer, O.: Asymptotic estimation theory of multipoint linkage analysis under perfect marker information. Ann. Statist. 31, 1075–1109 (2003a)
Hössjer, O.: Assessing accuracy in linkage analysis by means of confidence regions. Genet. Epidemiol. 25, 59–72 (2003b)
Hössjer, O.: Conditional likelihood score functions in linkage analysis, 2003c. Report 2003:10, Mathematical Statistics, Stockholm University. To appear in Biostatistics
Hössjer, O.: Spectral decomposition of score functions in linkage analysis, 2003d. Report 2003:21, Mathematical Statistics, Stockholm University.
Kempthorne, O.: Genetic Statistics. New York: Wiley, (1955)
Kruglyak, L., Lander, E.S.: High-resolution gene mapping of complex traits. Am. J. Hum. Genet. 56, 1212–1223 (1995)
Kruglyak, L., Daly, M.J., Reeve-Daly, M.P., Lander, E.S.: Parametric and nonparametric linkage analysis: A unified multipoint approach. Am. J. Hum. Genet. 58, 1347–1363 (1996)
Kurbasic, A., Hössjer, O.: Computing p-values in parametric linkage analysis, 2003. Report 2003:18, Mathematical Statistics, Stockholm University. To appear in Human Heredity
Lynch, M., Walsh, B.: Genetics and Analysis of Quantitative Traits. Sinauer Associates Inc., (1998)
McPeek, M.S.: Optimal allele-sharing statistics for genetic mapping using affected relatives. Genet. Epid. 16, 225–249 (1999)
Ott, J.: Analysis of Human Genetic Linkage, third edn., John Hopkins Univ. Press, (1999)
Risch, N.: Linkage strategies for genetically complex traits I. Multilocus models. Am. J. Hum. Genet. 46, 222–228 (1990a)
Risch, N.: Linkage strategies for genetically complex traits II. The power of affected relative pairs. Am. J. Hum. Genet. 46, 229–241 (1990b)
Risch, N., Zhang, H.: Extreme discordant sib pairs for mapping quantitative trait loci in humans. Science 268, 1584–1589 (1995)
Siegmund, D.: Boundary crossing probabilities and statistical applications. Ann. Statist. 14, 361–404 (1986)
Sham, P.: Statistics in Human Genetics. Arnold Applications of Statistics, London, (1998)
Tang, H-K., Siegmund, D.: Mapping quantitative trait loci in oligogenic models. Biostatistics 2, 147–162 (2001)
Winter, R.M.: The estimation of phenotype distributions from pedigree data. Am. J. Med. Genet. 7, 537–542 (1980)
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Research sponsored by the Swedish Research Council, under contract nr. 626-2002-6286.
Acknowledgement The author wishes to thank two referees for helpful comments on an earlier version of the paper.
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Hössjer, O. Information and effective number of meioses in linkage analysis. J. Math. Biol. 50, 208–232 (2005). https://doi.org/10.1007/s00285-004-0289-z
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DOI: https://doi.org/10.1007/s00285-004-0289-z