Sequential tests for gene–environment interactions in matched case–control studies

Abstract

The sample size necessary to detect a significant gene × environment interaction in an observational study can be large. For reasons of cost-effectiveness and efficient use of available biological samples we investigated the properties of sequential designs in matched case–control studies to test for both nonhierarchical and hierarchical interactions. We derived the test statistics Z and V and their characteristics when applied in a two-sided triangular test. Results of simulations show good agreement with theoretical values for V and the type I error. Power values were larger than their theoretical values for very large sample sizes. Median gain in effciency was about 27 per cent. For a ‘rare’ phenotype gain in efficiency was larger when the alternative hypothesis was true than under the null hypothesis. Sequential designs lead to substantial efficiency gains in tests for interaction in matched case–control studies.