Table 1.
Equivalent Detectable Odds Ratios
| Frequencies |
Overall Odds Ratio | Equivalent Detectable Odds Ratiosa |
|||||
|---|---|---|---|---|---|---|---|
| pb | Subtype A, % | Subtype B, % | Case Only | 2 Subtypes | 3 Subtypes | 4 Subtypes | |
| 0.10 | 20 | 80 | 1.20 | 1.51 (1.13) | 1.28 (1.18) | 1.32 (1.17) | 1.35 (1.16) |
| 0.10 | 20 | 80 | 1.50 | 2.37 (1.30) | 1.67 (1.46) | 1.75 (1.44) | 1.85 (1.42) |
| 0.10 | 20 | 80 | 2.00 | 4.05 (1.58) | 2.22 (1.95) | 2.31 (1.93) | 2.60 (1.87) |
| 0.10 | 50 | 50 | 1.20 | 1.35 (1.05) | 1.23 (1.17) | 1.26 (1.14) | 1.28 (1.13) |
| 0.10 | 50 | 50 | 1.50 | 1.91 (1.11) | 1.53 (1.46) | 1.64 (1.37) | 1.69 (1.32) |
| 0.10 | 50 | 50 | 2.00 | 2.93 (1.19) | 2.00 (1.99) | 2.24 (1.77) | 2.37 (1.66) |
| 0.10 | 80 | 20 | 1.20 | 1.28 (0.91) | 1.23 (1.09) | 1.24 (1.04) | 1.25 (1.01) |
| 0.10 | 80 | 20 | 1.50 | 1.71 (0.74) | 1.57 (1.22) | 1.61 (1.09) | 1.63 (1.01) |
| 0.10 | 80 | 20 | 2.00 | 2.52 (0.31) | 2.15 (1.44) | 2.24 (1.17) | 2.29 (1.00) |
| 0.25 | 20 | 80 | 1.20 | 1.53 (1.13) | 1.29 (1.18) | 1.33 (1.17) | 1.36 (1.16) |
| 0.25 | 20 | 80 | 1.50 | 2.52 (1.30) | 1.73 (1.45) | 1.84 (1.42) | 1.95 (1.40) |
| 0.25 | 20 | 80 | 2.00 | 5.01 (1.57) | 2.49 (1.89) | 2.72 (1.87) | 3.01 (1.84) |
| 0.25 | 50 | 50 | 1.20 | 1.36 (1.05) | 1.24 (1.16) | 1.26 (1.14) | 1.28 (1.12) |
| 0.25 | 50 | 50 | 1.50 | 1.95 (1.12) | 1.58 (1.41) | 1.66 (1.35) | 1.72 (1.30) |
| 0.25 | 50 | 50 | 2.00 | 3.14 (1.22) | 2.12 (1.89) | 2.37 (1.67) | 2.48 (1.65) |
| 0.25 | 80 | 20 | 1.20 | 1.28 (0.91) | 1.23 (1.09) | 1.24 (1.04) | 1.25 (1.02) |
| 0.25 | 80 | 20 | 1.50 | 1.72 (0.79) | 1.58 (1.21) | 1.62 (1.09) | 1.64 (1.02) |
| 0.25 | 80 | 20 | 2.00 | 2.53 (0.59) | 2.18 (1.39) | 2.27 (1.16) | 2.33 (1.03) |
| 0.50 | 20 | 80 | 1.20 | 1.56 (1.12) | 1.31 (1.17) | 1.35 (1.17) | 1.39 (1.16) |
| 0.50 | 20 | 80 | 1.50 | 2.86 (1.30) | 1.85 (1.43) | 2.01 (1.40) | 2.13 (1.39) |
| 0.50 | 20 | 80 | 2.00 | 10.91 (1.52) | 3.16 (1.80) | 3.76 (1.78) | 4.41 (1.77) |
| 0.50 | 50 | 50 | 1.20 | 1.37 (1.06) | 1.24 (1.16) | 1.27 (1.13) | 1.29 (1.12) |
| 0.50 | 50 | 50 | 1.50 | 2.03 (1.13) | 1.63 (1.39) | 1.71 (1.33) | 1.76 (1.28) |
| 0.50 | 50 | 50 | 2.00 | 3.56 (1.24) | 2.36 (1.71) | 2.57 (1.64) | 2.74 (1.50) |
| 0.50 | 80 | 20 | 1.20 | 1.28 (0.93) | 1.23 (1.08) | 1.24 (1.04) | 1.25 (1.01) |
| 0.50 | 80 | 20 | 1.50 | 1.74 (0.85) | 1.59 (1.20) | 1.63 (1.11) | 1.66 (1.03) |
| 0.50 | 80 | 20 | 2.00 | 2.63 (0.77) | 2.23 (1.34) | 2.33 (1.16) | 2.39 (1.20) |
a Minimum heterogeneity of relative risks for the subtypes required for a strategy of comparing the subtypes individually with the controls (or with each other in the case-only design) to achieve equivalent power to a test of the corresponding overall relative risk (i.e., comparing all cases vs. controls) at the 5% level. The numbers in parentheses are the corresponding relative risks for subtype B.
b Population prevalence of the risk factor.