Statistics in Biosciences

, Volume 1, Issue 2, pp 181–198 | Cite as

A Variance-Component Framework for Pedigree Analysis of Continuous and Categorical Outcomes

  • Michael P. Epstein
  • Jessica E. Hunter
  • Emily G. Allen
  • Stephanie L. Sherman
  • Xihong Lin
  • Michael Boehnke
Article

Abstract

Variance-component methods are popular and flexible analytic tools for elucidating the genetic mechanisms of complex quantitative traits from pedigree data. However, variance-component methods typically assume that the trait of interest follows a multivariate normal distribution within a pedigree. Studies have shown that violation of this normality assumption can lead to biased parameter estimates and inflations in type-I error. This limits the application of variance-component methods to more general trait outcomes, whether continuous or categorical in nature. In this paper, we develop and apply a general variance-component framework for pedigree analysis of continuous and categorical outcomes. We develop appropriate models using generalized-linear mixed model theory and fit such models using approximate maximum-likelihood procedures. Using our proposed method, we demonstrate that one can perform variance-component pedigree analysis on outcomes that follow any exponential-family distribution. Additionally, we also show how one can modify the method to perform pedigree analysis of ordinal outcomes. We also discuss extensions of our variance-component framework to accommodate pedigrees ascertained based on trait outcome. We demonstrate the feasibility of our method using both simulated data and data from a genetic study of ovarian insufficiency.

Keywords

Variance component model Linkage analysis Generalized linear mixed model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abecasis GR, Cardon LR, Cookson WOC (2000) A general test of association for quantitative traits in nuclear families. Am J Hum Genet 66:279–292 CrossRefGoogle Scholar
  2. 2.
    Allen EG, Sullivan AK, Marcus M, Small C, Dominguez C, Epstein MP, Charen K, He W, Taylor KC, Sherman SL (2007) Examination of reproductive aging milestones among women who carry the FMR1 premutation. Hum Reprod 22:2142–2152 CrossRefGoogle Scholar
  3. 3.
    Allison DB, Neale MC, Zannolli R, Schork NJ, Amos CI, Blangero J (1999) Testing the robustness of the likelihood-ratio test in a variance-component quantitative-trait loci-mapping procedure. Am J Hum Genet 65:531–544 CrossRefGoogle Scholar
  4. 4.
    Almasy L, Blangero J (1998) Multipoint quantitative-trait linkage analysis in general pedigrees. Am J Hum Genet 62:1198–1211 CrossRefGoogle Scholar
  5. 5.
    Amos CI (1994) Robust variance-components approach for assessing genetic linkage in pedigrees. Am J Hum Genet 54:535–543 Google Scholar
  6. 6.
    Blangero J, Williams JT, Almasy L (2001) Variance component methods for detecting complex trait loci. In: Rao DC, Province MA (eds) Genetic dissection of complex traits. Academic Press, San Diego, pp 151–182 Google Scholar
  7. 7.
    Breslow NE, Clayton DG (1993) Approximate inference in generalized linear mixed models. J Am Stat Assoc 88:9–25 CrossRefMATHGoogle Scholar
  8. 8.
    Burton PR, Tiller KJ, Gurrin LC, Cookson WO, Musk AW, Palmer LJ (1999) Genetic variance components analysis for binary phenotypes using generalized linear mixed models (GLMMs) and Gibbs sampling. Genet Epidemiol 17:118–140 CrossRefGoogle Scholar
  9. 9.
    Burton PR, Palmer LJ, Jacobs K, Keen KJ, Olson JM, Elston RC (2000) Ascertainment adjustment: where does it take us? Am J Hum Genet 67:1505–1514 CrossRefGoogle Scholar
  10. 10.
    de Andrade M, Fridley B, Boerwinkle E, Turner S (2003) Diagnostic tools in linkage analysis of quantitative traits. Genet Epidemiol 24:302–308 CrossRefGoogle Scholar
  11. 11.
    de Andrade M, Gueguen R, Visvikis S, Sass C, Siest G, Amos CI (2002) Extension of variance components approach to incorporate temporal trends and longitudinal pedigree data analysis. Genet Epidemiol 22:221–232 CrossRefGoogle Scholar
  12. 12.
    Diao G, Lin DY (2005) A powerful and robust method for mapping quantitative trait loci in general pedigrees. Am J Hum Genet 77:97–111 CrossRefGoogle Scholar
  13. 13.
    Duggirala R, Blangero J, Almasy L, Dyer TD, Williams KL, Leach RJ, O’Connell P, Stern MP (1999) Linkage of type 2 diabetes mellitus and of age at onset to a genetic location on chromosome 10q in Mexican Americans. Am J Hum Genet 64:1127–1140 CrossRefGoogle Scholar
  14. 14.
    Duggirala R, Williams JT, Williams-Blangero S, Blangero J (1997) A variance component approach to dichotomous trait linkage analysis using a threshold model. Genet Epidemiol 14:987–992 CrossRefGoogle Scholar
  15. 15.
    Epstein MP (2002) Comment on “Ascertainment adjustment in complex diseases”. Genet Epidemiol 23:209–213 CrossRefGoogle Scholar
  16. 16.
    Epstein MP, Lin X, Boehnke M (2002) Ascertainment-adjusted parameter estimates revisited. Am J Hum Genet 70:886–895 CrossRefGoogle Scholar
  17. 17.
    Epstein MP, Lin X, Boehnke M (2003) A tobit variance-component method for linkage analysis of censored trait data. Am J Hum Genet 72:611–620 CrossRefGoogle Scholar
  18. 18.
    Fulker DW, Cherny SS, Cardon LR (1995) Multipoint interval mapping of quantitative trait loci using sib pairs. Am J Hum Genet 56:1224–1233 Google Scholar
  19. 19.
    Glidden DV, Liang K-Y (2002) Ascertainment adjustment in complex diseases. Genet Epidemiol 23:201–208 CrossRefGoogle Scholar
  20. 20.
    Haseman JK, Elston RC (1972) The investigation of linkage between a quantitative trait and a marker locus. Behav Genet 2:3–19 CrossRefGoogle Scholar
  21. 21.
    Hasstedt SJ (1993) Variance components/major locus likelihood approximation for quantitative, polychotomous, and multivariate data. Genet Epidemiol 10:145–158 CrossRefGoogle Scholar
  22. 22.
    Hopper JL, Mathews JD (1982) Extensions to multivariate normal models for pedigree analysis. Ann Hum Genet 46:373–383 CrossRefMATHGoogle Scholar
  23. 23.
    Hunter JE, Epstein MP, Tinker SW, Charen KW, Sherman SL (2008) Fragile X-associated primary ovarian insufficiency: evidence for additional genetic contributions to severity. Genet Epidemiol 32:553–559 CrossRefGoogle Scholar
  24. 24.
    Jacquard A (1974) The genetic structure of populations. Springer, New York MATHGoogle Scholar
  25. 25.
    Kruglyak L, Daly M, Reeve-Daly M, Lander E (1996) Parametric and nonparametric linkage analysis: a unified multipoint approach. Am J Hum Genet 58:1347–1363 Google Scholar
  26. 26.
    Kruglyak L, Lander ES (1995) Complete multipoint sib-pair analysis of qualitative and quantitative traits. Am J Hum Genet 57:439–454 Google Scholar
  27. 27.
    Lander ES, Green P (1987) Construction of multilocus genetic linkage maps in humans. Proc Natl Acad Sci USA 84:2363–2367 CrossRefGoogle Scholar
  28. 28.
    Lange K (1978) Central limit theorems for pedigrees. J Math Biol 6:59–66 CrossRefMathSciNetMATHGoogle Scholar
  29. 29.
    Lange K, Boehnke M (1983) Extensions to pedigree analysis. IV. Covariance components models for multivariate traits. Am J Med Genet 14:513–524 CrossRefGoogle Scholar
  30. 30.
    Lange K, Westlake J, Spence MA (1976) Extensions to pedigree analysis. III. Variance components by the scoring method. Ann Hum Genet 39:485–491 CrossRefGoogle Scholar
  31. 31.
    Lin X (1997) Variance component testing in generalised linear models with random effects. Biometrika 84:309–326 CrossRefMathSciNetMATHGoogle Scholar
  32. 32.
    McCullagh P (1980) Regression models for ordinal data. J R Stat Soc, Ser B 42:109–142 MathSciNetMATHGoogle Scholar
  33. 33.
    McCullagh P, Nelder JA (1983) Generalized linear models. Chapman and Hall, London MATHGoogle Scholar
  34. 34.
    McCulloch CE, Searle SR (2000) Generalized, linear, and mixed models. Wiley-Interscience, New York CrossRefGoogle Scholar
  35. 35.
    Mitchell BD, Ghosh S, Schneider JL, Birznieks G, Blangero J (1997) Power of variance component linkage analysis to detect epistasis. Genet Epidemiol 14:1017–1022 CrossRefGoogle Scholar
  36. 36.
    Murray A, Webb J, MacSwiney F, Shipley EL, Morton NE, Conway GS (1999) Serum concentrations of follicle stimulating hormone may predict premature ovarian failure in FRAXA premutation women. Hum Reprod 14:1217–1218 CrossRefGoogle Scholar
  37. 37.
    Pankratz VS, de Andrade M, Therneau TM (2005) Random effects Cox proportional hazards model: general variance components methods for time-to-event data. Genet Epidemiol 28:97–109 CrossRefGoogle Scholar
  38. 38.
    Pinheiro JC, Bates DM (1995) Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comput Graph Stat 4:12–35 CrossRefGoogle Scholar
  39. 39.
    SAS Institute (1999) SAS version 8, Cary, NC Google Scholar
  40. 40.
    Self SG, Liang K-Y (1987) Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non-standard conditions. J Am Stat Assoc 82:605–610 CrossRefMathSciNetMATHGoogle Scholar
  41. 41.
    Sham PC, Purcell S (2001) Equivalence between Haseman–Elston and variance-components linkage analyses for sib pairs. Am J Hum Genet 68:1527–1532 CrossRefGoogle Scholar
  42. 42.
    Sherman SL (2000) Premature ovarian failure in the fragile X syndrome. Am J Med Genet 97:189–194 CrossRefGoogle Scholar
  43. 43.
    Sherman S, Pletcher BA, Driscoll DA (2005) Fragile X syndrome: diagnostic and carrier testing. Genet Med 7:584–587 CrossRefGoogle Scholar
  44. 44.
    Solomon PJ, Cox DR (1992) Nonlinear component of variance models. Biometrika 79:1–11 CrossRefMathSciNetMATHGoogle Scholar
  45. 45.
    Spiegelhalter D, Thomas A, Best N (2000) WinBUGS version 1.3 user manual. MRC Biostatistics Unit, Cambridge, UK Google Scholar
  46. 46.
    Sullivan AK, Marcus M, Epstein MP, Allen EG, Anido AE, Paquin JJ, Yadav-Shah M, Sherman SL (2005) Association of FMR1 repeat size with ovarian dysfunction. Hum Reprod 20:402–412 CrossRefGoogle Scholar
  47. 47.
    Tierney L, Kadane JB (1986) Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc 81:82–86 CrossRefMathSciNetMATHGoogle Scholar
  48. 48.
    Williams JT, Blangero J (1999) Comparison of variance components and sibpair-based approaches to quantitative trait linkage analysis in unselected samples. Genet Epidemiol 16:113–134 CrossRefGoogle Scholar
  49. 49.
    Yu X, Knott SA, Visscher PM (2004) Theoretical and empirical power of regression and maximum-likelihood methods to map quantitative trait loci in general pedigrees. Am J Hum Genet 75:17–26 CrossRefGoogle Scholar
  50. 50.
    Zeger SL, Karim MR (1991) Generalized linear models with random effects: a Gibbs sampling approach. J Am Stat Assoc 86:79–86 CrossRefMathSciNetGoogle Scholar

Copyright information

© International Chinese Statistical Association 2009

Authors and Affiliations

  • Michael P. Epstein
    • 1
  • Jessica E. Hunter
    • 1
  • Emily G. Allen
    • 1
  • Stephanie L. Sherman
    • 1
  • Xihong Lin
    • 2
  • Michael Boehnke
    • 3
  1. 1.Department of Human GeneticsEmory UniversityAtlantaUSA
  2. 2.Department of BiostatisticsHarvard UniversityBostonUSA
  3. 3.Department of Biostatistics and Center for Statistical GeneticsUniversity of MichiganAnn ArborUSA

Personalised recommendations