A Bayesian approach for correlated binary data:
a longitudinal study oN the occurrence of menstruation in patients with polycystic
ovarian syndrome after treatment

Jorge Alberto ACHCAR[1]

Edson Zangiacomi MARTINEZ[2]

Eliza OMAI[3]

Adriana de Fátima LOURENÇON2

Gleici Castro PERDONÁ3

§     ABSTRACT: In this paper, we develop a Bayesian logistic regression analysis with random effects considering longitudinal correlated binary data. We illustrate the approach with an example in the field of clinical medicine involving the evaluation of the occurrence of menstruation in patients with polycystic ovarian syndrome after a treatment. This data set was obtained from a real study conducted at the Medical School of the University of São Paulo, Ribeirão Preto, Brazil (Penna et al., 2005, Human Reproduction. v.20, n.9, p.2396-401). The occurrence/no occurrence of menstruation was observed on each subject at three specific times over a given period. Consequently, a no-null correlation among the observations from a same subject is expected, and this effect is captured by adding a random effect in the model. We explore Bayesian approaches to modeling the data, assuming that the random effects are drawn from a normal distribution and also from a mixture of normal distributions. Inferences for the model parameters are based on MCMC methods. Model comparison is assessed via Deviance Information Criteria (DIC).

§     KEYWORD: Correlated binary data; logistic regression; Bayesian analysis; clinical trials.



[1]Departamento de EstatÍstica, Universidade Federal de São Carlos - UFSCar, CEP 13565-905, São Carlos, SP, Brasil. E-mail: jachcar@power.ufscar.br

[2]Centro de Métodos Quantitativos, Faculdade de Medicina de Ribeirão Preto, Universidade de São Paulo - CEMEQ/FMRP/USP, CEP 14049-900, Ribeirão Preto, SP, Brasil. E-mail: elizaomai@hotmail.com

[3]Departamento de Medicina Social, Faculdade de Medicina de Ribeirão Preto, Universidade de São Paulo - FAEPA/FMRP/USP, CEP 14049-900, Ribeirão Preto, SP, Brasil. E-mail: edson@fmrp.usp.br /  pgleici@fmrp.usp.br