Model selection and the estimation of odds ratios in the presence of extraneous factors.

This paper deals with model selection and the estimation of odds ratios from cross-classified frequencies in the presence of extraneous factors. The odds ratio is estimated in different ways dependent on whether the extraneous factor is modelled as an effect modifier, a confounder, or neither. Routinely this choice is based on statistical tests of null hypotheses. By contrast, we propose selection of the model which is estimated to maximize the accuracy of the estimator of the odds ratio, on average. We demonstrate how a non-parametric bootstrap method can be used to carry out the selection, and illustrate the methodology using an example on use of oral contraceptives and myocardial infarction.