Presenting the Uncertainties of Odds Ratios Using Empirical-Bayes Prediction Intervals

Quantifying exposure-disease associations is a central issue in epidemiology. Researchers of a study often present an odds ratio (or a logarithm of odds ratio, logOR) estimate together with its confidence interval (CI), for each exposure they examined. Here the authors advocate using the empirical-Bayes-based ‘prediction intervals’ (PIs) to bound the uncertainty of logORs. The PI approach is applicable to a panel of factors believed to be exchangeable (no extra information, other than the data itself, is available to distinguish some logORs from the others). The authors demonstrate its use in a genetic epidemiological study on age-related macular degeneration (AMD). The proposed PIs can enjoy straightforward probabilistic interpretations—a 95% PI has a probability of 0.95 to encompass the true value, and the expected number of true values that are being encompassed is for a total of 95% PIs. The PI approach is theoretically more efficient (producing shorter intervals) than the traditional CI approach. In the AMD data, the average efficiency gain is 51.2%. The PI approach is advocated to present the uncertainties of many logORs in a study, for its straightforward probabilistic interpretations and higher efficiency while maintaining the nominal coverage probability.