Is the familywise error rate in genomics controlled by methods based on the effective number of independent tests?

In genome-wide association (GWA) studies the goal is to detect association between one or more genetic markers and a given phenotype. The number of genetic markers in a GWA study can be in the order hundreds of thousands and therefore multiple testing methods are needed. This paper presents a set of popular methods to be used to correct for multiple testing in GWA studies. All are based on the concept of estimating an effective number of independent tests. We compare these methods using simulated data and data from the TOP study, and show that the effective number of independent tests is not additive over blocks of independent genetic markers unless we assume a common value for the local significance level. We also show that the reviewed methods based on estimating the effective number of independent tests in general do not control the familywise error rate.
Comment: 20 pages, 3 figures