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Bayesian Analysis for the Meiosis I Non‐disjunction Fraction in Numerical Chromosomal Anomalies
Author(s) -
Loschi Rosangela H.,
Franco Glaura C.
Publication year - 2006
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.200510171
Subject(s) - bayes' theorem , bayes factor , statistics , prior probability , estimator , bayesian probability , multinomial distribution , meiosis , mathematics , posterior probability , resampling , fraction (chemistry) , chromosome , biology , genetics , chemistry , organic chemistry , gene
The main causes of numerical chromosomal anomalies, including trisomies, arise from an error in the chromosomal segregation during the meiotic process, named a non‐disjunction. One of the most used techniques to analyze chromosomal anomalies nowadays is the polymerase chain reaction (PCR), which counts the number of peaks or alleles in a polymorphic microsatellite locus. It was shown in previous works that the number of peaks has a multinomial distribution whose probabilities depend on the non‐disjunction fraction F . In this work, we propose a Bayesian approach for estimating the meiosis I non‐disjunction fraction F in the absence of the parental information. Since samples of trisomic patients are, in general, small, the Bayesian approach can be a good alternative for solving this problem. We consider the sampling/importance resampling technique and the Simpson rule to extract information from the posterior distribution of F . Bayes and maximum likelihood estimators are compared through a Monte Carlo simulation, focusing on the influence of different sample sizes and prior specifications in the estimates. We apply the proposed method to estimate F for patients with trisomy of chromosome 21 providing a sensitivity analysis for the method. The results obtained show that Bayes estimators are better in almost all situations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)