Table 1.
Type I Error Rates and Power for GWAS and Several GWIS Scenarios
| Simulated Effect | Sample | R2 | GWAS | GWIS | GWIS No Intercept | GWIS 50% Sample Overlap | GWIS 10% Sample Overlap | GWIS 0% Sample Overlap | GWIS Destandardized | GWIS Misspecified Height Mean | GWIS Second Order |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Type I Error | |||||||||||
| 0.00000 | 10,000 | 0.051 | 0.0509 | 0.0497 | 0.0523 | 0.0466 | 0.0461 | 0.0524 | 0.0512 | 0.0456 | |
| Power | |||||||||||
| 0.5477 | 1,000 | 0.00192 | 0.166 | 0.162 | 0.182 | 0.141 | 0.12 | 0.099 | 0.165 | 0.148 | 0.185 |
| 0.5477 | 2,000 | 0.00128 | 0.251 | 0.251 | 0.278 | 0.219 | 0.196 | 0.167 | 0.278 | 0.283 | 0.276 |
| 0.5477 | 3,000 | 0.00128 | 0.394 | 0.398 | 0.392 | 0.289 | 0.228 | 0.252 | 0.359 | 0.391 | 0.382 |
| 0.5477 | 4,000 | 0.00116 | 0.475 | 0.474 | 0.484 | 0.39 | 0.311 | 0.317 | 0.473 | 0.496 | 0.464 |
| 0.5477 | 5,000 | 0.00114 | 0.573 | 0.578 | 0.548 | 0.441 | 0.39 | 0.392 | 0.577 | 0.599 | 0.583 |
| 0.5477 | 6,000 | 0.00110 | 0.671 | 0.677 | 0.625 | 0.497 | 0.465 | 0.445 | 0.658 | 0.647 | 0.642 |
| 0.5477 | 7,000 | 0.00105 | 0.702 | 0.712 | 0.691 | 0.611 | 0.482 | 0.496 | 0.698 | 0.717 | 0.714 |
| 0.5477 | 8,000 | 0.00099 | 0.764 | 0.764 | 0.759 | 0.648 | 0.568 | 0.538 | 0.776 | 0.804 | 0.761 |
| 0.5477 | 9,000 | 0.00103 | 0.806 | 0.81 | 0.832 | 0.709 | 0.632 | 0.633 | 0.826 | 0.811 | 0.819 |
| 0.5477 | 10,000 | 0.00101 | 0.862 | 0.872 | 0.851 | 0.746 | 0.642 | 0.661 | 0.842 | 0.868 | 0.86 |
| 0.5477 | 11,000 | 0.00100 | 0.898 | 0.901 | 0.899 | 0.79 | 0.7 | 0.682 | 0.883 | 0.899 | 0.898 |
| 0.5477 | 12,000 | 0.00098 | 0.901 | 0.904 | 0.91 | 0.81 | 0.75 | 0.75 | 0.925 | 0.91 | 0.922 |
| 0.5477 | 13,000 | 0.00096 | 0.934 | 0.932 | 0.942 | 0.853 | 0.789 | 0.767 | 0.934 | 0.951 | 0.923 |
| 0.5477 | 14,000 | 0.00096 | 0.936 | 0.936 | 0.942 | 0.852 | 0.798 | 0.79 | 0.955 | 0.951 | 0.953 |
| 0.5477 | 15,000 | 0.00098 | 0.968 | 0.968 | 0.952 | 0.921 | 0.853 | 0.807 | 0.962 | 0.96 | 0.961 |
| 0.5477 | 17,000 | 0.00099 | 0.986 | 0.987 | 0.979 | 0.928 | 0.881 | 0.859 | 0.968 | 0.979 | 0.971 |
| 0.5477 | 19,000 | 0.00094 | 0.988 | 0.987 | 0.988 | 0.943 | 0.909 | 0.903 | 0.984 | 0.983 | 0.981 |
The table reports power estimates and type I error for simulated body mass index (BMI) genome-wide inferred statistics (GWIS) for several sample sizes and effect sizes, under several different circumstances. GWAS refers to a linear regression of BMI on the simulated genetic variant, GWIS is an approximation of the same linear regression based on the technique outlined in the paper. We reduce sample overlap between the height and weight sample that are used in GWIS and we explore the effect of substituting the regression intercept with the population mean and standardization of height and weight and subsequent destandardization in the GWIS. These results indicate that GWIS provides similar power to genome-wide association study (GWAS) when the intercepts and scaling of the original GWASs are known. In case the original samples have little to no overlap, the GWIS suffers from approximately 15%–20% power loss for moderate effect and sample sizes. On the other hand, a second-order approximation of BMI gives a similar or higher power to a GWAS of the original BMI GWAS.