Table 2. Mean values of different indirect effects, the total effect, and the percentages mediated for both standard regression and our approach.* .
| Matching | Genetic | Standard Approach | Our Approach | |||||||||||||||||
| Status | Δ | Model | IE1 | IE2 | IE3 | IEt | TE | PM1 | PM2 | PM3 | PMt | IE1 | IE2 | IE3 | IEt | TE | PM1 | PM2 | PM3 | PMt |
| Scenario I (true values): | 0.45 | 0.45 | 0.31 | 1.20 | 1.61 | 28% | 28% | 19% | 75% | 0.45 | 0.45 | 0.31 | 1.20 | 1.61 | 28% | 28% | 19% | 75% | ||
| Unmatched | − | DOM | 0.51 | 0.50 | 0.38 | 1.39 | 1.79 | 28% | 28% | 21% | 77% | 0.45 | 0.45 | 0.31 | 1.21 | 1.62 | 28% | 28% | 19% | 75% |
| − | ADD | 0.49 | 0.49 | 0.36 | 1.33 | 1.74 | 28% | 28% | 20% | 77% | 0.44 | 0.45 | 0.30 | 1.19 | 1.60 | 28% | 28% | 19% | 74% | |
| − | REC | 0.48 | 0.48 | 0.36 | 1.32 | 1.72 | 28% | 28% | 21% | 77% | 0.45 | 0.44 | 0.31 | 1.19 | 1.60 | 28% | 27% | 19% | 75% | |
| Matched on M1 | 0 | DOM | −0.05 | 0.50 | 0.15 | 0.60 | 1.00 | −5% | 49% | 15% | 59% | 0.43 | 0.44 | 0.29 | 1.17 | 1.57 | 27% | 28% | 19% | 74% |
| 0 | ADD | −0.06 | 0.48 | 0.14 | 0.57 | 0.97 | −6% | 50% | 15% | 58% | 0.43 | 0.44 | 0.29 | 1.16 | 1.56 | 27% | 28% | 19% | 74% | |
| 0 | REC | −0.04 | 0.48 | 0.14 | 0.58 | 0.99 | −4% | 49% | 14% | 59% | 0.42 | 0.44 | 0.29 | 1.15 | 1.56 | 27% | 28% | 19% | 74% | |
| −0.05 | DOM | 0.04 | 0.50 | 0.20 | 0.73 | 1.14 | 4% | 43% | 17% | 64% | 0.44 | 0.44 | 0.30 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| −0.05 | ADD | 0.02 | 0.49 | 0.19 | 0.70 | 1.11 | 2% | 44% | 17% | 63% | 0.44 | 0.44 | 0.30 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| −0.05 | REC | 0.04 | 0.48 | 0.19 | 0.72 | 1.12 | 4% | 43% | 17% | 64% | 0.43 | 0.44 | 0.30 | 1.17 | 1.58 | 27% | 28% | 19% | 74% | |
| 0.05 | DOM | −0.11 | 0.49 | 0.12 | 0.50 | 0.91 | −13% | 54% | 13% | 55% | 0.44 | 0.44 | 0.30 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| 0.05 | ADD | −0.12 | 0.49 | 0.11 | 0.48 | 0.88 | −14% | 55% | 13% | 54% | 0.44 | 0.45 | 0.30 | 1.18 | 1.58 | 28% | 28% | 19% | 75% | |
| 0.05 | REC | −0.10 | 0.48 | 0.11 | 0.49 | 0.90 | −12% | 54% | 13% | 55% | 0.43 | 0.44 | 0.30 | 1.17 | 1.58 | 27% | 28% | 19% | 74% | |
| −0.1 | DOM | 0.17 | 0.50 | 0.25 | 0.93 | 1.33 | 13% | 38% | 19% | 70% | 0.44 | 0.45 | 0.30 | 1.18 | 1.58 | 27% | 28% | 19% | 74% | |
| −0.1 | ADD | 0.14 | 0.49 | 0.24 | 0.87 | 1.28 | 11% | 38% | 19% | 68% | 0.44 | 0.45 | 0.29 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| −0.1 | REC | 0.17 | 0.48 | 0.25 | 0.90 | 1.31 | 13% | 37% | 19% | 69% | 0.43 | 0.44 | 0.30 | 1.17 | 1.58 | 27% | 28% | 19% | 74% | |
| 0.1 | DOM | −0.16 | 0.49 | 0.09 | 0.42 | 0.83 | −19% | 59% | 11% | 51% | 0.44 | 0.44 | 0.30 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| 0.1 | ADD | −0.16 | 0.49 | 0.09 | 0.41 | 0.82 | −20% | 59% | 11% | 50% | 0.44 | 0.44 | 0.30 | 1.18 | 1.59 | 28% | 28% | 19% | 74% | |
| 0.1 | REC | −0.15 | 0.48 | 0.09 | 0.42 | 0.83 | −18% | 58% | 11% | 51% | 0.44 | 0.44 | 0.31 | 1.19 | 1.60 | 27% | 28% | 19% | 74% | |
| Scenario II (true values): | 0.14 | 0.14 | 0.05 | 0.32 | 1.01 | 13% | 13% | 5% | 32% | 0.14 | 0.14 | 0.05 | 0.32 | 1.01 | 13% | 13% | 5% | 32% | ||
| Unmatched | − | DOM | 0.16 | 0.15 | 0.06 | 0.36 | 1.05 | 15% | 14% | 5% | 34% | 0.14 | 0.14 | 0.05 | 0.32 | 1.01 | 14% | 13% | 5% | 32% |
| − | ADD | 0.15 | 0.15 | 0.05 | 0.35 | 1.05 | 14% | 14% | 5% | 33% | 0.14 | 0.14 | 0.05 | 0.32 | 1.02 | 13% | 14% | 5% | 32% | |
| − | REC | 0.15 | 0.14 | 0.05 | 0.34 | 1.04 | 14% | 14% | 5% | 33% | 0.14 | 0.13 | 0.05 | 0.31 | 1.02 | 13% | 13% | 5% | 31% | |
| Matched on M1 | 0 | DOM | −0.02 | 0.15 | 0.04 | 0.17 | 0.86 | −3% | 18% | 4% | 19% | 0.13 | 0.14 | 0.05 | 0.32 | 1.01 | 13% | 13% | 5% | 31% |
| 0 | ADD | −0.04 | 0.15 | 0.03 | 0.15 | 0.84 | −4% | 18% | 4% | 18% | 0.13 | 0.14 | 0.04 | 0.32 | 1.01 | 13% | 14% | 4% | 31% | |
| 0 | REC | −0.02 | 0.15 | 0.03 | 0.16 | 0.86 | −2% | 17% | 4% | 19% | 0.13 | 0.14 | 0.04 | 0.31 | 1.01 | 13% | 14% | 4% | 31% | |
| −0.05 | DOM | 0.12 | 0.15 | 0.05 | 0.32 | 1.01 | 12% | 15% | 5% | 32% | 0.13 | 0.14 | 0.04 | 0.31 | 1.01 | 13% | 14% | 4% | 31% | |
| −0.05 | ADD | 0.09 | 0.15 | 0.05 | 0.29 | 0.98 | 9% | 15% | 5% | 29% | 0.13 | 0.14 | 0.04 | 0.32 | 1.01 | 13% | 14% | 4% | 31% | |
| −0.05 | REC | 0.12 | 0.15 | 0.05 | 0.32 | 1.02 | 12% | 14% | 5% | 31% | 0.13 | 0.14 | 0.04 | 0.31 | 1.01 | 13% | 13% | 4% | 31% | |
| 0.05 | DOM | −0.10 | 0.15 | 0.03 | 0.08 | 0.78 | −12% | 20% | 3% | 11% | 0.14 | 0.14 | 0.05 | 0.32 | 1.02 | 13% | 13% | 4% | 31% | |
| 0.05 | ADD | −0.10 | 0.15 | 0.02 | 0.07 | 0.76 | −13% | 19% | 3% | 9% | 0.13 | 0.14 | 0.04 | 0.31 | 1.00 | 13% | 14% | 4% | 31% | |
| 0.05 | REC | −0.09 | 0.15 | 0.03 | 0.09 | 0.78 | −11% | 19% | 3% | 11% | 0.13 | 0.14 | 0.05 | 0.32 | 1.01 | 13% | 14% | 5% | 31% | |
| −0.1 | DOM | 0.45 | 0.15 | 0.08 | 0.68 | 1.37 | 33% | 11% | 6% | 49% | 0.14 | 0.13 | 0.04 | 0.31 | 1.01 | 14% | 13% | 4% | 31% | |
| −0.1 | ADD | 0.36 | 0.15 | 0.07 | 0.57 | 1.27 | 29% | 12% | 5% | 45% | 0.14 | 0.13 | 0.04 | 0.31 | 1.01 | 14% | 13% | 4% | 31% | |
| −0.1 | REC | 0.44 | 0.15 | 0.07 | 0.66 | 1.35 | 32% | 11% | 5% | 49% | 0.13 | 0.14 | 0.04 | 0.31 | 1.01 | 13% | 14% | 4% | 31% | |
| 0.1 | DOM | −0.13 | 0.15 | 0.02 | 0.04 | 0.74 | −17% | 20% | 3% | 5% | 0.14 | 0.13 | 0.05 | 0.31 | 1.01 | 13% | 13% | 4% | 31% | |
| 0.1 | ADD | −0.13 | 0.15 | 0.02 | 0.04 | 0.73 | −18% | 20% | 2% | 5% | 0.13 | 0.14 | 0.04 | 0.31 | 1.01 | 13% | 14% | 4% | 31% | |
| 0.1 | REC | −0.12 | 0.14 | 0.02 | 0.04 | 0.74 | −16% | 19% | 2% | 6% | 0.14 | 0.13 | 0.05 | 0.31 | 1.01 | 13% | 13% | 5% | 31% | |
DOM: dominant genetic model; ADD: additive genetic model; REC: recessive genetic model
*
Includes the indirect effect through M1 (i.e., IE1 = a1b1), the indirect effect through M2 (i.e., IE2 = a2b2), the three-path indirect effect through M1 and M2 (i.e., IE3 = a1db2), the total indirect effect (i.e., IEt = IE1+IE2+IE3), the total effect (i.e., TE = IEt+c′), and the percentages of the SNP-disease association explained by different paths (i.e., PM1 = IE1/TE, PM2 = IE2/TE, PM3 = IE3/TE, and PMt = IEt/TE). All results are based on 1,000 replicates, each with 1,000 disease cases and 1,000 disease controls.