Exploring the order of odds ratios using the bootstrap

We show the use of the bootstrap resampling method to examine further the order of a series of odds ratios. Specifically, the bootstrap provides a method for estimating the probabilities that one would find in subsequent independent samples from the same population the observed odds ratio rankings. To illustrate this use of the bootstrap, we modelled the responses of 77 white male physicians to an ethical dilemma involving hypothetical patients. Would the physician report positive HIV status to the health department or would he maintain patient confidentiality? To see if a patient's sex, race, or sexual preference would influence the physicians' decisions, each physician received one of eight randomly selected descriptions of a hypothetical patient. To evaluate the initial order of the patient categories, we constructed 1000 bootstrap samples. Black heterosexual males ranked first or second in 92.2 per cent of the bootstrap samples; black homosexual males ranked first, second or third in 88.6 per cent; and white homosexual females ranked sixth or seventh in 82.9 per cent. Thus we would expect to observe these rankings of the categories in a high percentage of subsequent independent samples.