Reference Analysis in a Misclassification Model for the Meiosis I Nondisjunction Fraction in Trisomies

The determination of the meiosis I nondisjunction fraction plays an important role in identifying the characteristics of affected individuals and their mothers, which can generate aneuploidies. The number of individuals with one, two, and three peaks pattern is used to obtain the information; however, the data are susceptible to misclassification. We review the misclassification model previously introduced in the literature which considers a common misclassification error. This paper aims to introduce a joint prior distribution for the meiosis I nondisjunction fraction and the misclassification error. We prove that the reference prior is a proper distribution. We analyze a Brazilian Down syndrome dataset and compare the results with those obtained through Bayes-Laplace and beta prior distributions. 1. Introduction In humans, aneuploidies are common causes of mental retardation, pregnancy losses, and fetal death. Although the causes of aneuploidies are unknown, it is known that the risk of having children with some kind of aneuploidy, such as trisomies 21 (Down syndrome), 18 (Edward’s syndrome), or 13 (Patau syndrome), increases with the mother’s age [1]. Trisomy 21 is the most prevalent human genetic disorder and occurs in approximately 1 out of 700 births. It is the most common cause of mental retardation of genetic origin. Down syndrome affects the cognitive abilities of the child and approximately half of them can also have congenital heart defects and problems with hearing and vision, and they are prone to develop pulmonary hypertension. The causes of Down syndrome are unknown, but there is evidence that in the trisomy of chromosome 21 the rate of nondisjunction increases with the age of the mother [2]. Women aged 35 or older have significantly higher risk of having a child with Down syndrome. In addition, the increase in the rate of non-disjunction in meiosis II is higher than in meiosis I, if the mother is between 35 and 39 years old. As a result, the determination of the fraction of non-disjunction in chromosomal segregation, taking place in meiosis I in each chromosome, plays an important role in understanding aneuploidies. It is useful to identify possible factors generating such abnormalities, for example: geography, nutrition, age, reproductive, practices. Prenatal diagnosis of aneuploidies is usually done by employing chromosome karyotype, fluorescent in situ hybridization (FISH), and polymerase chain reaction (PCR-) based approaches, see [1, 3–6] for further details. Methods to estimate considering information from the affected children and