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Bayesian Semiparametric Modeling for Matched Case–Control Studies with Multiple Disease States
Author(s) -
Sinha Samiran,
Mukherjee Bhramar,
Ghosh Malay
Publication year - 2004
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2004.00169.x
Subject(s) - statistics , markov chain monte carlo , logistic regression , econometrics , mathematics , bayesian probability , dirichlet distribution , dirichlet process , multinomial logistic regression , multinomial distribution , computer science , mathematical analysis , boundary value problem
Summary. We present a Bayesian approach to analyze matched “case–control” data with multiple disease states. The probability of disease development is described by a multinomial logistic regression model. The exposure distribution depends on the disease state and could vary across strata. In such a model, the number of stratum effect parameters grows in direct proportion to the sample size leading to inconsistent MLEs for the parameters of interest even when one uses a retrospective conditional likelihood. We adopt a semiparametric Bayesian framework instead, assuming a Dirichlet process prior with a mixing normal distribution on the distribution of the stratum effects. We also account for possible missingness in the exposure variable in our model. The actual estimation is carried out through a Markov chain Monte Carlo numerical integration scheme. The proposed methodology is illustrated through simulation and an example of a matched study on low birth weight of newborns (Hosmer, D. A. and Lemeshow, S., 2000, Applied Logistic Regression ) with two possible disease groups matched with a control group.