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A Bayesian approach to a logistic regression model with incomplete information.

Choi T, Schervish MJ, Schmitt KA, Small MJ

Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA. tchoi@math.umbc.edu

We consider a set of independent Bernoulli trials with possibly different success probabilities that depend on covariate values. However, the available data consist only of aggregate numbers of successes among subsets of the trials along with all of the covariate values. We still wish to estimate the parameters of a modeled relationship between the covariates and the success probabilities, e.g., a logistic regression model. In this article, estimation of the parameters is made from a Bayesian perspective by using a Markov chain Monte Carlo algorithm based only on the available data. The proposed methodology is applied to both simulation studies and real data from a dose-response study of a toxic chemical, perchlorate.

Published 16 May 2008 in Biometrics, 64(2): 424-30.
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