Table 5. Comparison of the median numbers of causal SNPs selected for different pre-specified odds ratios for the five simulation models using the FNR-based approach (given pre-specified power 80%) with traditional approaches.
| Odds ratios | |||||||||
|---|---|---|---|---|---|---|---|---|---|
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| Model (#of causal SNPs) | Approaches | Parameter values | 1.8 | 1.7 | 1.6 | 1.5 | 1.4 | 1.3 | 1.2 |
| Model 1 (5) | Bonferroni Correction | 0a/0b | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | |
| BH-FDR | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | ||
| Fixed p-value cutoff | p =10−5 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | |
| Fixed number cutoff | 10 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | |
| 20 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | ||
| 30 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 1/1 | 0/1 | ||
| FNR-based | λ = 10−5 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | |
| λ = 5 × 10−5 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | ||
| λ = 10−4 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 0/1 | 0/1 | ||
| λ = 10−3 | 0/0 | 0/0 | 1/1 | 1/1 | 1/1 | 1/1 | 0/1 | ||
| Model 2 (10) | Bonferroni Correction | 1/1 | 1/1 | 1/1 | 1/1 | 0/2 | 0/2 | 0/2 | |
| BH-FDR | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | ||
| Fixed p-value cutoff | p =10−5 | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | |
| Fixed number cutoff | 10 | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | |
| 20 | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | ||
| 30 | 1/1 | 1/1 | 1/1 | 1/1 | 2/2 | 1/2 | 0/2 | ||
| FNR-based | λ = 10−5 | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | |
| λ = 5 × 10−5 | 1/1 | 1/1 | 1/1 | 1/1 | 1/2 | 1/2 | 0/2 | ||
| λ = 10−4 | 1/1 | 1/1 | 1/1 | 1/1 | 2/2 | 1/2 | 0/2 | ||
| λ = 10−3 | 1/1 | 1/1 | 1/1 | 1/1 | 2/2 | 2/2 | 0/2 | ||
| Model 3 (15) | Bonferroni Correction | 1/2 | 2/2 | 2/2 | 1/2 | 1/2 | 0/2 | 0/3 | |
| BH-FDR | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | ||
| Fixed p-value cutoff | p =10−5 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | |
| Fixed number cutoff | 10 | 1/2 | 2/2 | 2/2 | 1/2 | 1/2 | 0/2 | 0/3 | |
| 20 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | ||
| 30 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | ||
| FNR-based | λ = 10−5 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | |
| λ = 5 × 10−5 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 0/2 | 0/3 | ||
| λ = 10−4 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 1/2 | 0/3 | ||
| λ = 10−3 | 2/2 | 2/2 | 2/2 | 2/2 | 2/2 | 1/2 | 0/3 | ||
| Model 4 (20) | Bonferroni Correction | 2/2 | 3/3 | 2/3 | 3/3 | 1/3 | 0/3 | 0/3 | |
| BH-FDR | 2/2 | 3/3 | 2/3 | 3/3 | 1/3 | 0/3 | 0/3 | ||
| Fixed p-value cutoff | p =10−5 | 2/2 | 3/3 | 2/3 | 3/3 | 2/3 | 0/3 | 0/3 | |
| Fixed number cutoff | 10 | 2/2 | 2/3 | 2/3 | 2/3 | 1/3 | 0/3 | 0/3 | |
| 20 | 2/2 | 3/3 | 2/3 | 3/3 | 1/3 | 0/3 | 0/3 | ||
| 30 | 2/2 | 3/3 | 2/3 | 3/3 | 1/3 | 0/3 | 0/3 | ||
| FNR-based | λ = 10−5 | 2/2 | 3/3 | 2/3 | 3/3 | 1/3 | 0/3 | 0/3 | |
| λ = 5 × 10−5 | 2/2 | 3/3 | 2/3 | 3/3 | 2/3 | 0/3 | 0/3 | ||
| λ = 10−4 | 2/2 | 3/3 | 2/3 | 3/3 | 2/3 | 0/3 | 0/3 | ||
| λ = 10−3 | 2/2 | 3/3 | 3/3 | 3/3 | 2/3 | 2/3 | 0/3 | ||
| Model 5 (25) | Bonferroni Correction | 3/3 | 2/3 | 1/3 | 2/4 | 0/4 | 0/4 | 0/4 | |
| BH-FDR | 3/3 | 2/3 | 2/3 | 3/4 | 0/4 | 0/4 | 0/4 | ||
| Fixed p-value cutoff | p =10−5 | 3/3 | 3/3 | 2/3 | 3/4 | 4/4 | 1/4 | 0/4 | |
| Fixed number cutoff | 10 | 3/3 | 2/3 | 1/3 | 1/4 | 0/4 | 0/4 | 0/4 | |
| 20 | 3/3 | 2/3 | 2/3 | 3/4 | 1/4 | 0/4 | 0/4 | ||
| 30 | 3/3 | 3/3 | 2/3 | 3/4 | 3/4 | 1/4 | 0/4 | ||
| FNR-based | λ = 10−5 | 3/3 | 3/3 | 2/3 | 3/4 | 2/4 | 1/4 | 0/4 | |
| λ = 5 × 10−5 | 3/3 | 3/3 | 3/3 | 3/4 | 4/4 | 1/4 | 0/4 | ||
| λ = 10−4 | 3/3 | 3/3 | 3/3 | 3/4 | 4/4 | 1/4 | 0/4 | ||
| λ = 10−3 | 3/3 | 3/3 | 3/3 | 4/4 | 4/4 | 2/4 | 0/4 | ||
a
Denotes how many causal SNPs were selected
b
Denotes how many causal SNPs in total in the models
p: p-value cutoff.
λ: parameter used for estimating number of null hypotheses.