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Hypothesis Testing and Categorical Data

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Mathematical and Statistical Methods for Genetic Analysis

Part of the book series: Statistics for Biology and Health ((SBH))

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Abstract

Most statistical geneticists are frequentists, and fairly traditional ones at that. In testing statistical hypotheses, they prefer pure significance tests or likelihood ratio tests based on large sample theory. Although one could easily dismiss this conservatism as undue reverence for Karl Pearson and R. A. Fisher, it is grounded in the humble reality of geneticists’ inability to describe precise alternative hypotheses and to impose convincing priors. In the first part of this chapter, we will review by way of example the large sample methods summarized so admirably by Cavalli-Sforza and Bodmer [6], Elandt-Johnson [11], and Weir [44]. Then we will move on to modern elaborations of frequentist tests for contingency tables. Part of the novelty here is in designing tests sensitive to certain types of departures from randomness. Permutation procedures permit approximation of the exact p-values for these tests and consequently relieve our anxieties about large sample approximations [28].

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References

  1. Agresti A (1992) A survey of exact inference for contingency tables. Stat Sci 7: 131–177

    Article  MathSciNet  MATH  Google Scholar 

  2. Allison DB, Heo M, Kaplan N, Martin ER (1999) Sibling-based tests of linkage and association for quantitative traits. Amer J Hum Genet 64: 1754–1763

    Article  Google Scholar 

  3. Badner JA, Chakravarti A, Wagener DK (1984) A test of nonrandom segregation. Genetic Epidemiology 1: 329–340

    Article  Google Scholar 

  4. Barbour AD, Holst L, Janson S (1992) Poisson Approximation. Oxford University Press, Oxford

    MATH  Google Scholar 

  5. Boehnke M, Langefeld CD (1998) Genetic association mapping based on discordant sib pairs: the discordant-alleles test. Amer J Hum Genet 62: 950–961

    Article  Google Scholar 

  6. Cavalli-Sforza LL, Bodmer WF (1971) The Genetics of Human Populations. Freeman, San Francisco

    Google Scholar 

  7. Clarke CA, Price Evans DA, McConnell RB, Sheppard PM (1959) Secretion of blood group antigens and peptic ulcers. Brit Med J1:603–607

    Article  Google Scholar 

  8. Clayton, D (1999). A generalization of the transmission/disequilibrium test for uncertain haplotype transmission. Amer J Hum Genet 65: 1170–1177

    Article  Google Scholar 

  9. De Braekeleer M, Smith B (1988) Two methods for measuring the non-randomness of chromosome abnormalities. Ann Hum Genet 52: 63–67

    Article  Google Scholar 

  10. de Vries RRP, Lai A, Fat RFM, Nijenhuis LE, van Rood JJ (1976) HLA-linked genetic control of host response to Mycobacterium leprae. Lancet 2: 1328–1330

    Article  Google Scholar 

  11. Elandt-Johnson RC (1971) Probability Models and Statistical Methods in Genetics. Wiley, New York

    MATH  Google Scholar 

  12. Ewens WJ, Griffiths RC, Ethier SN, Wilcox SA, Graves JAM (1992) Statistical analysis of in situ hybridization data: Derivation and use of the zmax test. Genomics 12: 675–682

    Article  Google Scholar 

  13. Falk CT, Rubinstein P (1987) Haplotype relative risks: an easy reliable way to construct a proper control sample for risk calculations. Annals Hum Genet 51: 227–233

    Article  Google Scholar 

  14. Ferguson TS (1996) A Course in Large Sample Theory. Chapman & Hall, London

    MATH  Google Scholar 

  15. Fuchs C, Kenett R (1980) A test for detecting outlying cells in the multinomial distribution and two-way contingency tables. J Amer Stat Assoc 75: 395–398

    Article  MathSciNet  MATH  Google Scholar 

  16. Guo S-W, Thompson E (1992) Performing the exact test of Hardy-Weinberg proportion for multiple alleles. Biometrics 48: 361–372.

    Article  MATH  Google Scholar 

  17. Hanash SM, Boehnke M, Chu EHY, Neel JV, Kuick RD (1988) Nonrandom distribution of structural mutants in ethylnitrosourea-treated cultured human lymphoblastoid cells. Proc Natl Acad Sci USA 85: 165–169

    Article  Google Scholar 

  18. Horvath S, Laird N (1998) A discordant sibship disequilibrium test for disequilibrium and linkage: No need for parental data. Amer J Hum Genet 63: 1886–1897

    Article  Google Scholar 

  19. Joag-Dev K, Proschan F (1983) Negative association of random variables with applications. Ann Stat 11: 286–295

    Article  MathSciNet  MATH  Google Scholar 

  20. Kaplan NL, Martin ER, Weir BS (1997) Power Studies for the transmission/disequilibrium tests with multiple alleles. Amer J Hum Genet 60: 691–702

    Google Scholar 

  21. Knapp M (1999) The transmission/disequilibrium test and parental-genotype reconstruction: The reconstruction-combined transmission/disequilibrium test. Amer J Hum Genet 64: 861–870

    Article  Google Scholar 

  22. Kolchin VF, Sevast’yanov BA, Chistyakov VP (1978) Random Allocations. Winston, Washington DC

    Google Scholar 

  23. Lange, K (1993) A stochastic model for genetic linkage equilibrium. Theor Pop Biol 44: 129–148

    Article  MATH  Google Scholar 

  24. Lazzeroni LC, Lange K (1997) Markov chains for Monte Carlo tests of genetic equilibrium in multidimensional contingency tables. Ann Stat 25: 138–168

    Article  MathSciNet  MATH  Google Scholar 

  25. Lazzeroni LC, Lange K (1998) A permutation framework for extending the transmission disequilibrium test. Human Hered48:67–81

    Article  Google Scholar 

  26. Lehmann EL (1998) Elements of Large-Sample Theory. Springer Verlag, New York

    Google Scholar 

  27. Mallows CL (1968). An inequality involving multinomial probabilities. Biometrika 55: 422–424

    Article  MATH  Google Scholar 

  28. Manly BFJ (1997) Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman & Hall, London

    MATH  Google Scholar 

  29. Nijenhuis A, Wilf HS (1978) Combinatorial Algorithms for Computers and Calculators, 2nd ed. Academic Press, New York

    MATH  Google Scholar 

  30. Rabinowitz D, Laird N (2000) A unified approach to adjusting association tests for population admixture with arbitrary pedigree structure and arbitrary missing marker information. Hum Hered 50: 227–233

    Article  Google Scholar 

  31. Rice JA (1995) Mathematical Statistics and Data Analysis, 2nd ed. Wadsworth, Belmont, CA

    MATH  Google Scholar 

  32. Sandell D (1991) Computing probabilities in a generalized birthday problem. Math Scientist 16: 78–82

    MathSciNet  MATH  Google Scholar 

  33. Schaid DJ (1996) General score tests for association of genetic markers with disease using cases and their parents. Genet Epidemiol 13: 423–449

    Article  Google Scholar 

  34. Schaid DJ, Rowland C (1998) Use of parents, sibs, and unrelated controls for detection of associations between genetic markers and disease. Amer J Hum Genet 63: 1492–1506

    Article  Google Scholar 

  35. Searle AG (1959) A study of variation in Singapore cats. J Genet 56:111–127

    Article  Google Scholar 

  36. Sen PK, Singer JM (1993) Large Sample Methods in Statistics: An Introduction with Applications. Chapman & Hall, New York

    MATH  Google Scholar 

  37. Sham PC, Curtis D (1995) An extended transmission/disequilibrium test (TDT) for multi-allele marker loci. Ann Hum Genet 59: 323–336

    Article  Google Scholar 

  38. Spielman RS, Ewens WJ (1998) A sibship test for linkage in the presence of association: the sib transmission/disequilibrium test. Amer J Hum Genet 62: 450–458

    Article  Google Scholar 

  39. Spielman RS, McGinnis RE, Ewens WJ (1993) Transmission test for linkage disequilibrium: The insulin gene region and Insulin-Dependent Diabetes Mellitus (IDDM). Amer J Hum Genet 52: 506–516

    Google Scholar 

  40. Teng J, Risch N (1999) The relative power of family-based and casecontrol designs for linkage disequilibrium studies of complex human diseases. II. Individual genotyping. Genome Res 9: 234–241

    Google Scholar 

  41. Terwilliger JD, Ott J (1992) A haplotype-based “haplotype relative risk” approach to detecting allelic associations. Hum Hered 42: 337–346

    Article  Google Scholar 

  42. Uhrhammer N, Lange E, Porras E, Naiem A, Chen X, Sheikhavandi S, Chiplunkar S, Yang L, Dandekar S, Liang T, Patel N, Teraoka S, Udar N, Calvo N, Concannon P, Lange K, Gatti RA (1995) Sublocalization of an ataxia-telangiectasia gene distal to D11S384 by ancestral haplotyping of Costa Rican families. Amer J Hum Genet 57: 103–111

    Google Scholar 

  43. Vogel F, Motulsky AG (1986) Human Genetics: Problems and Approaches, 2nd ed. Springer-Verlag, Berlin

    Google Scholar 

  44. Weir BS (1996) Genetic Data Analysis II. Sinauer, Sunderland, MA

    Google Scholar 

  45. Weir BS, Brooks LD (1986) Disequilibrium on human chromosome llp. Genet Epidemiology Suppl 1: 177–183.

    Article  Google Scholar 

  46. Zhao H (2000) Family-based association studies. Stat Methods Med Res 9: 563–587

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Departments of Biomathematics and Human Genetics, UCLA School of Medicine, 90095, Los Angeles, CA, USA

    Kenneth Lange

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  1. Kenneth Lange
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© 2002 Springer-Verlag New York, Inc.

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Lange, K. (2002). Hypothesis Testing and Categorical Data. In: Mathematical and Statistical Methods for Genetic Analysis. Statistics for Biology and Health. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21750-5_4

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  • DOI: https://doi.org/10.1007/978-0-387-21750-5_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4684-9556-0

  • Online ISBN: 978-0-387-21750-5

  • eBook Packages: Springer Book Archive

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