Brazilian Journal of Probability and Statistics

Test, estimation and model comparison for the meiosis I nondisjunction fraction in trisomies

Vanessa L. Silva and Rosangela H. Loschi

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Abstract

Trisomies are numerical chromosomal anomalies (aneuploidies) which are common causes of mental retardation, pregnancy losses and fetal death. The determination of the meiosis I nondisjunction fraction plays an important role in the identification of possible factors which could generate such aneuploidies. In this article, more flexible misclassification models for the number of peaks in a polymorphic locus of trisomic individuals are considered. They are compared to some others proposed in the literature. Estimation and tests for the nondisjunction fraction in meiosis I and for the misclassification errors are introduced extending previous works. Using the Decision Theory approach, we also build a criterion for making decisions under Jeffreys and Pereira–Stern tests. We apply the results to Down Syndrome data that is the most prevalent trisomy in humans.

Article information

Source
Braz. J. Probab. Stat., Volume 26, Number 2 (2012), 123-148.

Dates
First available in Project Euclid: 23 January 2012

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1327328081

Digital Object Identifier
doi:10.1214/10-BJPS125

Mathematical Reviews number (MathSciNet)
MR2880902

Zentralblatt MATH identifier
1236.92033

Keywords
Aneuploidy Bayes estimator Bayes tests DIC meiosis misclassification

Citation

Silva, Vanessa L.; Loschi, Rosangela H. Test, estimation and model comparison for the meiosis I nondisjunction fraction in trisomies. Braz. J. Probab. Stat. 26 (2012), no. 2, 123--148. doi:10.1214/10-BJPS125. https://projecteuclid.org/euclid.bjps/1327328081


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References

  • Abramowitz, M. and Stegun, I. A. (1972). Handbool of Mathematical Functions: With Formulas, Graphs and Mathematical Tables, 2nd ed. New York: Dover.
  • Barros, P. A. and Franco, G. C. (2002). Testes bootstrap para a fração de não disjunção meiótica em pacientes com síndrome de Down (in portuguese). Technical Report RTP-01/2002. Departamento de of Estatística, Universidade Federal de Minas Gerais. Available at http://www.est.ufmg.br/rts/#pes02.
  • Blake, D., Tan, S. L. and Ao, A. (1999). Assessment of multiplex fluorescent PCR for screening single cells for trisomy 21 and single gene defects. Molecular Human Reproduction 5, 1166–1175.
  • Bernardo, J. M. and Smith, A. F. M. (1994). Bayesian Theory, 1st ed. Chichester: Wiley.
  • Dawid, A. P. (1979). Conditional independence in statistical theory (with discussion). Journal of the Royal Statistical Society B 41, 1–31.
  • Franco, G. C., Lucio, P. S., Parra, F. C. and Pena, S. D. J. (2003). A probability model for the meiosis I non-disjunction fraction in numerical chromosomal anomalies. Statistics in Medicine 22, 2015–2024.
  • Gelfand, A. G. and Sahu, S. K. (1999). Identifiability, improper priors, and Gibbs sampling for generalized linear models. Journal of the American Statistical Association 94, 247–253.
  • Griffin, D. K. (1996). The incidence, origin, and etiology of aneuploidy. International Review of Cytology 167, 64–70.
  • Hartl, D. L. and Clark, A. G. (1997). Principles of Population in Genetics, 3rd. ed. Sunderland: Sinauer Associates.
  • Hassold, T. J. and Hunt, P. (2001). To err (meiotically) is human: The genesis of human aneuploidy. Nature Reviews in Genetics 2, 280–291.
  • Hassold, T. J. and Jacobs, P. A. (1984). Trisomy in man. Annual Reviews in Genetics 18, 69–97.
  • Jeffreys, H. (1961). Theory of Probability. Oxford: Claredon Press.
  • Kadane, J. B. and Lasar, N. A. (2004). Methods and criteria for model selection. Journal of the American Statistical Association 99, 279–290.
  • Koehler, K. E., Hawley, R. S., Sherman, S. and Hassold, T. (1996). Recombination and nondisjunction in humans and flies. Human Molecular Genetics 5, 1495–1505.
  • Lavine, M. and Schervish, M. J. (1999). Bayes factors: What they are and what they are not. The American Statistician 53, 119–122.
  • Lindley, D. V. (1971). Bayesian Statistics, a Review. CBMS-NSF Regional Conference Series in Applied Mathematics. Philadelphia: SIAM.
  • Lorber, B. J., Grantham, M. and Peters, J. (1992). Nondisjunction of chromosome 21: Comparisons of cytogenetic and molecular studies of the meiotic stage and parent origin. American Journal of Human Genetics 51, 1265–1276.
  • Loschi, R. H., Monteiro, J. V. D., Rocha, G. H. M. A. and Mayrink, V. D. (2007). Testing and estimating the non-disjunction fraction in meiosis I using reference priors. Biometrical Journal 49, 824–839.
  • Loschi, R. H., Monteiro, J. V. D. and Souto, C. S. (2008). A misclassification model for the non-disjunction fraction in meiosis I. Biometrical Journal 50, 1–14.
  • Madruga, M. R., Esteves, L. G. and Wechsler, S. (2001). On the Bayesianity of Pereira–Stern tests. Test 10, 291–299.
  • Madruga, M. R., Pereira, C. A. B. and Stern, J. M. (2003). Bayesian evidency test for precise hypotheses. Journal of Statistical Planning and Inference 117, 185–198.
  • Migon, H. S. and Gamerman, D. (1999). Statistical Inference: An Integrated Approach. London: Arnold.
  • Nicolaidis, P. and Petersen, M. B. (1998). Origin and mechanisms of non-disjunction in human autosomal trisomies. Human Reproduction 13, 313–319.
  • Ogilvie, C. M., Donaghue, C., Fox, S. P., Docherty, Z. and Mann, K. (2005). Rapid prenatal diagnosis of aneuploidy using quantitative fluorescent-PCR (QF-PCR). Journal of Histochemistry and Cytochemistry 53(3), 285–288.
  • Paulino, C. D., Soares, P. and Neuhaus, J. (2003). Binomial regression with misclassification. Biometrics 59, 670–675.
  • Pena, S. D. J. (1998). Molecular Cytogenetics I: PCR-based diagnosis of human trisomies using computer-assisted laser densitometry. Genetic Molecules Biology 3, 371–322.
  • Pereira, C. A. B. and Stern, J. M. (1999). Evidence and credibility: Full Bayesian significance test for precise hypotheses. Entropy 1, 69–80.
  • Pereira, C. A. B. and Stern, J. M. (2001). Model selection: Full Bayesian approach. Envirometrics 12, 559–568.
  • Petersen, M. B., Schinzel, A. A., Binkert, F., Tranebjaerg, L., Mikkelsen, M., Collins, F. A., Economou, C. P. and Antonarakis, S. E. (1992). Comparative study of micosatellite and cytogenetic markers for detecting the origin of the nondisjoined chromosome 21 in Down syndrome. American Journal of Human Genetic 167, 263–296.
  • Pont-Kingdon, G. and Lyon, L. (2003). Rapid detection of aneuploidy (trisomy 21) by allele quantification combined with melting curves analysis of single-nucleotide polymorphism loci. Clinical Chemistry 49, 1087–1094.
  • Robert, C. P. (1993). A note on Jeffreys–Lindley paradox. Statistica Sinica 3, 601–608.
  • Savage, A. R., Petersen, M. B., Pettay, B., Taft, L., Allran, K., Freeman, S. B., Karadina, G., Avramopoulos, D., Tofs, C., Mikkelsen, M., Hassold, T. J. and Sherman, S. L. (1998). Elucidating the mechanisms of parental non-disjunction of chromosome 21 in humans. Human Molecular Genetics 7, 1221–1227.
  • Schmidt, W., Jenderny, J., Hecher, K., Hackelöer, B. J., Keber, S., Kochhan, L. and Held, K. (2000). Detection of aneuploidy in chromosomes X, Y, 13, 18 and 21 by QF-PCR in 662 selected pregnancies at risk. Molecular Human Reproduction 6, 855–860.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Van Der Linde, A. (2002). Bayesian measures of model complexity and fit (with discussion). Journal of the Royal Statistical Society 64, 583–639.
  • Swartz, T., Haitovsky, Y., Vexler, A. and Yang, T. (2004). Bayesian identifiability and misclassification in multinomial data. The Canadian Journal of Statistics 32, 1–18.
  • Tsao, C. A. (2006). A note on Lindley’s paradox. Test 15, 125–139.
  • Valero, R., Marfany, G., Gil-Benso, R., Ibáñez, M. A., López-Pajares, I. Prieto, F., Rul.Ian, G., Saret, E. and González-Duarte, R. (1999). Molecular characterization of partial chromosome 21 aneuploidies by fluorescent PCR. Journal of Medical Genetics 15, 125–139.
  • Viana, M. A. G. (1994). Bayesian small-sample estimation of misclassified multinomial data. Biometrics 50, 237–243.
  • Yoon, P. W., Freeman, S. B., Sherman, S. L., Taft, L. F., Gu, Y., Pettay, D., Flanders, W. D., Khoury, M. J. and Hassold, T. J. (1996). Advanced maternal age and the risk of Down syndrome characterized by the meiotic stage of the chromosomal error: A population based study. American Journal of Human Genetics 58, 628–633.
  • Zaragosa, M. V., Millie, E., Redline, R. W. and Hassold, T. J. (1994). Studies of non-disjunction in trisomies 2, 7, 15 and 22: Does the parental origin of trisomy influence placental morphology? Journal of Medical Genetics 35, 924–931.