Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Statistical Applications in Genetics and Molecular Biology

Editor-in-Chief: Sanguinetti, Guido

IMPACT FACTOR 2017: 0.812
5-year IMPACT FACTOR: 1.104

CiteScore 2017: 0.86

SCImago Journal Rank (SJR) 2017: 0.456
Source Normalized Impact per Paper (SNIP) 2017: 0.527

Mathematical Citation Quotient (MCQ) 2017: 0.04

See all formats and pricing
More options …
Volume 14, Issue 3


Volume 10 (2011)

Volume 9 (2010)

Volume 6 (2007)

Volume 5 (2006)

Volume 4 (2005)

Volume 2 (2003)

Volume 1 (2002)

Bayes factors based on robust TDT-type tests for family trio design

Min Yuan
  • Corresponding author
  • School of mathematics, University of Science and Technology of China, Hefei 230026, Anhui, P.R. China
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Xiaoqing Pan
  • Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, Anhui, P.R. China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Yaning Yang
  • Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, Anhui, P.R. China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2015-05-30 | DOI: https://doi.org/10.1515/sagmb-2014-0051


Adaptive transmission disequilibrium test (aTDT) and MAX3 test are two robust-efficient association tests for case-parent family trio data. Both tests incorporate information of common genetic models including recessive, additive and dominant models and are efficient in power and robust to genetic model specifications. The aTDT uses information of departure from Hardy-Weinberg disequilibrium to identify the potential genetic model underlying the data and then applies the corresponding TDT-type test, and the MAX3 test is defined as the maximum of the absolute value of three TDT-type tests under the three common genetic models. In this article, we propose three robust Bayes procedures, the aTDT based Bayes factor, MAX3 based Bayes factor and Bayes model averaging (BMA), for association analysis with case-parent trio design. The asymptotic distributions of aTDT under the null and alternative hypothesis are derived in order to calculate its Bayes factor. Extensive simulations show that the Bayes factors and the p-values of the corresponding tests are generally consistent and these Bayes factors are robust to genetic model specifications, especially so when the priors on the genetic models are equal. When equal priors are used for the underlying genetic models, the Bayes factor method based on aTDT is more powerful than those based on MAX3 and Bayes model averaging. When the prior placed a small (large) probability on the true model, the Bayes factor based on aTDT (BMA) is more powerful. Analysis of a simulation data about RA from GAW15 is presented to illustrate applications of the proposed methods.

Keywords: adaptive transmission disequilibrium test; asymptotic distributions; Bayes factor; Bayes model averaging; MAX3; robustness


  • Falk, C. T. and P. Rubinstein (1987): “Haplotype relative risk: an easy reliable way to construct a proper control sample for risk calculation,” Ann. Hum. Genet., 51, 227–233.Google Scholar

  • Field, L. L., C. Fothergill-Payne, J. Bertrams, and M. P. Baur (1986): “HLA-DR effects in a large German IDDM dataset,” Genet. Epidemiol. Suppl., 1, 323–328.Google Scholar

  • Jeffreys, H. (1961): Theory of probability, 3rd edition. Oxford, UK: Oxford University Press.Google Scholar

  • Johnson, V. E. (2005): “Bayes factors based on test statistics,” J Roy. Stat. Soc. B, 67, 689–701.Google Scholar

  • Johnson, V. E. (2008): “Properties of bayes factors based on test statistics,” Scand. J. Stat., 35, 354–368.Web of ScienceGoogle Scholar

  • Kass, R. and A. Raftery (1995): “Bayes factors,” J. Am. Stat. Assoc., 90, 773–795.Google Scholar

  • Miller, M. B., G. R. Lind, N. Li and S. Y. Jang (2007): “Genetic Analysis Workshop 15: simulation of a complex genetic model for rheumatoid arthritis in nuclear families including a dense SNP map with linkage disequilibrium between marker loci and trait loci,” BMC Proc., 1, S4.Google Scholar

  • Ott, J. (1989): “Statistical properties of the haplotype relative risk,” Genet. Epidemiol., 6, 127–130.PubMedGoogle Scholar

  • Rubinstein, P., M. Walker, C. Carpenter, C. Carrier, J. Krassner, C. Falk and F. Ginsberg (1981): “Genetics of HLA disease association: the use haplotype relative risk (HRR) and the ‘haplo-delta’ (Dh) estimates in juvenile diabetes from three racial groups,” Hum. Immunol., 3, 384.Google Scholar

  • Sawcer, S. (2010): “Bayes factors in complex genetics,” Eur. J. Hum. Genet., 18, 746–750.Google Scholar

  • Schaid, D. J. and S. S. Sommer (1993): “Genotype relative risks: methods for design and analysis of candidate-gene association studies,” Am. J. Hum. Genet., 53, 1114–1126.Google Scholar

  • Schaid, D. J. and S. S. Sommer (1994): “Comparison of statistics for candidate-gene association studies using cases and parents,” Am. J. Hum. Genet., 55, 402–409.Google Scholar

  • Serfling, R. J. (1980): Approximation theorems of mathematical statistics, New York: Wiley.Google Scholar

  • Spielman, R. S., R. E. McGinnis and W. J. Ewens (1993): “Transmission test for linkage diseqilibrium: the insulin gene region and inculin-dependent diabetes mellitus (IDDM),” Am. J. Hum. Genet., 52, 506–516.Google Scholar

  • Stephens, M. and D. J. Balding (2009): “Bayesian statistical methods for genetic association studies,” Nat. Rev. Genet., 10, 681–690.Web of SciencePubMedGoogle Scholar

  • Terwilliger, J. D. and J. Ott (1992): “A haplotype-based ‘haplotype relative risk ’ approach to detecting allelic association,” Hum. Hered., 42, 337–346.Google Scholar

  • The Wellcome Trust Case-Control Consortium (WTCCC) (2007): “Genome-wide association study of 14,000 cases of seven common diseases and 3000 shared controls,” Nature, 447, 661–683.Google Scholar

  • Thomson, G., W. P. Robinson, M. K. Kuhner and S. Joe (1989): “HLA, insulin gene, and Gm associations with IDDM,” Genet. Epidemiol., 6, 155–160.PubMedGoogle Scholar

  • Wakefield, J. (2007): “A Bayesian measure of the probability of false discovery in genetic epidemiology studies,” Am. J. Hum. Genet., 81, 208–227.Web of ScienceGoogle Scholar

  • Wakefield, J. (2009): “Bayes factors for genome-wide association studies: comparison with p-values,” Genet. Epidemiol., 33, 79–86.Google Scholar

  • Yuan, M., X. Tian, Y. Yang and G. Zheng (2009): “Adaptive transmission disequilibrium test for family trio design,” Stat. Appl. Genet. Mol. Biol., 8(1), 1–20.Web of ScienceGoogle Scholar

  • Zheng, G., J. Joo and Y. Yang (2009): “Pearsons test, trend test, and MAX are all trend tests with different types of scores,” Ann. Hum. Genet., 73, 133–140.Web of ScienceGoogle Scholar

  • Zheng, G., Q. Li and A. Yuan (2014): “Some statistical properties of efficiency robust tests with applications to genetic association studies,” Scand. J. Stat., 41(3), 762–774.CrossrefWeb of ScienceGoogle Scholar

About the article

Corresponding author: Min Yuan, School of mathematics, University of Science and Technology of China, Hefei 230026, Anhui, P.R. China, e-mail:

Published Online: 2015-05-30

Published in Print: 2015-06-01

Citation Information: Statistical Applications in Genetics and Molecular Biology, Volume 14, Issue 3, Pages 253–264, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.1515/sagmb-2014-0051.

Export Citation

©2015 by De Gruyter.Get Permission

Comments (0)

Please log in or register to comment.
Log in