Internal validation analysis of the observed associations by a two-stage design

These days, the use of single nucleotide polymorphisms (SNP) is increasing for the genetic dissection of complex common diseases, and many studies have been conducted to identify SNPs associated with diseases. If the number of subjects with the objective disease is large enough, then we detect disease-associated SNPs with statistical tests by a two-stage replication study design. For the design, several ways to calculate a power of a test have been considered. They show that the well-constructed two-stage replication study designs maintain enough powers of the tests. However, we cannot handle a large quantity of data well for all diseases, and we perform statistical tests by a one-stage design for diseases with small sample sizes. In this paper, we propose a method to estimate the proportion of significant results of the tests for such diseases by using a similar method to calculate the power of statistical tests with the two-stage replication study design.