Abstract

1
Optimal allocation of sample size in two-stage
association studies A grid-search algorithm
S. H. WenDepartment of Public Health Tzu-Chi
University, Taiwan
C. K. Hsiao Department of Public Health and
Institute of Epidemiology, National Taiwan
University

• 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.

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)

• 3 Grid-Search Algorithm
• ? N1 ? k or ? ? E(R) ? FPR, TPR
• FTGC costMN1E(R)N2
• ? Let N2kN1 and k(cost MN1)/(N1E(R))
• FSS NN1N2
• ? Let N1?N (e.g. N1000)

Note cost/M600, M500, w0.95,
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 of existing
  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, p) 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 M5000, w0.999 3-4 M100, w0.95.