Abstract Lately, several powerful two-stage strategies for

1. 2 Two-stage multiple testing method - Population case-control data  False Positive Rate (FPR)  True Positive Rate (TPR) Using N1 subjects H0H1 Observe M P-value X X X X X X X X 0 Remain R P-value X X X X X X X 0 0.05 1st stage Add N2 and combine N1 subjects R1R2 Promising markers New R P-value X X X X X X X X 2nd stage 0 Final K P-value X1X2 X X X X X 0.05/R 0 4 Simulation results: FPR and FDR Comparison with single stage methods The FPR or FDR of two-stage method was stable small under various combinations of N1 and N2. 5 Simulation results: TPR The TPR of the two-stage setting varied greatly and was often larger than that of single stage methods. FTGC FSS Note: (a)-(b) for FTGC; (c)-(d) for FSS Note: (a)-(b) for FTGC; (c)-(d) for FSS Optimal allocation of sample size in two-stage association studies : A grid-search algorithm S. H. Wen*Department of Public Health Tzu-Chi University, Taiwan C. K. Hsiao Department of Public Health and Institute of Epidemiology, National Taiwan University 1 Background Family-wise error rate (FWER) controlling methods may fail for being too conservative and single stage strategies, such as false discovery rate (FDR) controlling methods, are not cost-efficient under limited resources, especially when testing a large number of markers. Objective We propose a grid-search algorithm for an optimal design for sample size allocation under two-stage multiple testing procedures. Two different situations are considered (1) Fixed total genotyping cost (FTGC) (2) Fixed sample sizes (FSS) Mw M(1-w) Abstract Lately, several powerful two-stage strategies for multiple testing in genome-wide association studies have received great attention. We propose optimal designs for these two-stage procedures under two different situations, where one is fixed total genotyping cost (FTGC) and the other is fixed sample sizes (FSS). For FTGC, allocating at least 80% of the total cost in stage one provides maximum power. For limited total sample size, evaluating all the markers on 55% of subjects in the first stage provides the maximum power while the cost reduction is approximately 43%. 3 Grid-Search Algorithm  N1  k or   E(R)  FPR, TPR FTGC: cost=MN1+E(R)N2  Let N2=kN1 and k=(cost – MN1)/(N1E(R)) FSS: N=N1+N2  Let N1=N (e.g. N=1000) Note: cost/M=600, M=500, w=0.95, 6 7 Comparison with existing 2-stage methods  Overall Type I error The proposed optimal design produced less false positives than that of existing alternatives regardless of allelic odds ratio and the total number of markers.  Overall power The power of the optimal 2-stage design was consistently larger than that ofexisting methods.  Cost-effectiveness The superiority remains when compared in terms of total sample size or cost-efficiency. Conclusions  The proposed approach provides specific criteria in formal testing with pre-specified significance level for each stage.  The (N1, k) or (N1, π) can be determined analytically with optimal TPR, bearable FPR and satisfied cost.  Approximately 88% of total cost in earlier stage produces optimal power where 5000 markers are screened under fixed cost.  If the sample size is restricted, we recommend N1/N between 0.5 and 0.6 to get a higher overall power and substantial cost reduction. Y-axis: 1-2 M=5000, w=0.999; 3-4 M=100, w=0.95.