Empirical Bayes adjustments for multiple results in hypothesis-generating or surveillance studies

Abstract

Traditional methods of adjustment for multiple comparisons (e.g., Bonferroni adjustments) have fallen into disuse in epidemiological studies. However, alternative kinds of adjustment for data with multiple comparisons may sometimes be advisable. When a large number of comparisons are made, and when there is a high cost to investigating false positive leads, empirical or semi-Bayes adjustments may help in the selection of the most promising leads. Here we offer an example of such adjustments in a large surveillance data set of occupation and cancer in Nordic countries, in which we used empirical Bayes (EB) adjustments to evaluate standardized incidence ratios (SIRs) for cancer and occupation among craftsmen and laborers. For men, there were 642 SIRs, of which 138 (21%) had a P < 0.05 (13% positive with SIR > 1.0 and 8% negative with SIR < or = 1.0) when testing the null hypothesis of no cancer/occupation association; some of these were probably due to confounding by nonoccupational risk factors (e.g., smoking). After EB adjustments, there were 95 (15%) SIRs with P < 0.05 (10% positive and 5% negative). For women, there were 373 SIRs, of which 37 (10%) had P < 0.05 before adjustment (6% positive and 4% negative) and 13 (3%) had P < 0.05 after adjustment (2% positive and 1% negative). Several known associations were confirmed after EB adjustment (e.g., pleural cancer among plumbers, original SIR 3.2 (95% confidence interval, 2.5-4.1), adjusted SIR 2.0 (95% confidence interval, 1.6-2.4). EB can produce more accurate estimates of relative risk by shrinking imprecise outliers toward the mean, which may reduce the number of false positives otherwise flagged for further investigation. For example, liver cancer among chimney sweepers was reduced from an original SIR of 2.2 (range, 1.1-4.4) to an adjusted SIR of 1.1 (range, 0.9-1.4). A potentially important future application for EB is studies of gene-environment-disease interactions, in which hundreds of polymorphisms may be evaluated with dozens of environmental risk factors in large cohort studies, producing thousands of associations.