Abstract
Conditional inference methods are proposed for the odds ratio between binary exposure and disease variables when only the probability of exposure is known for each study subject. We develop a conditional likelihood approach that removes nuisance parameters and permits inferences to be made about important parameters in log odds ratio regression models. We also discuss a heuristic procedure based on estimating the (unknown) number of truly exposed individuals; this procedure provides a simple framework for interpreting our likelihood-based statistics, and leads to a Mantel-Haenszel-type estimator and a goodness-of-fit test. As an example of the use of this methodology, we present an analysis of some genetic data of Swift et al. (1976, Cancer Research 36, 209-215).
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