A two-stage design for multiple testing in large-scale association studies

Abstract

Modern association studies often involve a large number of markers and hence may encounter the problem of testing multiple hypotheses. Traditional procedures are usually over-conservative and with low power to detect mild genetic effects. From the design perspective, we propose a two-stage selection procedure to address this concern. Our main principle is to reduce the total number of tests by removing clearly unassociated markers in the first-stage test. Next, conditional on the findings of the first stage, which uses a less stringent nominal level, a more conservative test is conducted in the second stage using the augmented data and the data from the first stage. Previous studies have suggested using independent samples to avoid inflated errors. However, we found that, after accounting for the dependence between these two samples, the true discovery rate increases substantially. In addition, the cost of genotyping can be greatly reduced via this approach. Results from a study of hypertriglyceridemia and simulations suggest the two-stage method has a higher overall true positive rate (TPR) with a controlled overall false positive rate (FPR) when compared with singlestage approaches. We also report the analytical form of its overall FPR, which may be useful in guiding study design to achieve a high TPR while retaining the desired FPR.

A grid-search algorithm for optimal allocation of sample size in two-stage association studies

“…Different from Wen et al (2006), the optimization is related to limited resources and focuses on efficient allocation of subjects. To accomplish the purpose of maintaining good power when detecting truly relevant markers, we suggest a grid-search algorithm for optimal cost-efficient strategies.…”

“…We considered two indices, TPR (true-positive rate) and FPR, to evaluate the performance of the two-stage procedure. According to Wen et al (2006), both overall FPR and TPR are functions of sample sizes (N 1 , N 2 ), significance levels (a 1 , a 2 ), number of total markers M, and the irrelevant proportion w. In addition, the disease model parameters such as the allele frequency and effect size of tests also affect the FPR and TPR. Therefore, an optimal design must take these into account.…”

“…One advantage is the complete utilization of all information. Another is putting more emphasis on the power to detect associated markers than focusing simply on false-positive rate (Wen et al 2006). Kuchiba et al (2006) controlled the FDR with optimal sample size and reduced cost.…”

“…Wang et al (2006) considered various configurations of per-genotype cost ratio and significance levels in both stages to achieve the desired power with minimum cost. Wen et al (2006) recommended excluding mostly irrelevant markers while adopting a large significance level in the first stage, and controlling the overall false-positives with a downward significance level in the second stage. Different from Satagopan et al (2002Satagopan et al ( , 2004, they can choose the promising markers at a pre-specified significance level and control the false-positive rate (FPR) adequately.…”

Optimum two-stage designs in case–control association studies using false discovery rate

“…Previous proposed two-stage designs, for example, Satagopan and Elston (2003), have proposed controlling the overall a error of the twostage procedure. Also, Wen et al (2006) showed the overall a error and FDR when certain fixed design parameters were used, of which the only second-stage significance level was corrected by Bonferroni's method. Recently, controlling the FDR has been considered to be more relevant for eliminating false positives, especially in the exploratory studies.…”