Hierarchical bayes analysis of the simplest case-crossover design
In the simplest form of a case-crossover design, the relative risk of an event (such as death) under two different 'exposures' is assessed. The exposure is observed only twice, once at the time of the event. The probability of exposure is required for each individual in the study. These probabilities are traditionally estimated using historical data. The traditional approach yields probabilities of 0, 1/2, and 1 only. A hierarchical Bayesian model is used to obtain more realistic estimates of these probabilities and consequently of the relative risk. Differences between the conventional and Bayes results are exhibited in specific examples.