Table 2. Simulation results for case-cohort studies with sampling fraction of 10% from 40,000 individuals for a SNP with RAF=0.10.
| Cox Regression (HR) | Logistic Regression (OR) | ||||||
|---|---|---|---|---|---|---|---|
| True HR | Mean(Bias) | Mean(SE) | Power | Mean(Bias) | Mean(SE) | Power | Diff in Power |
| Complete Follow-up, 5% Cumulative Disease Incidence | |||||||
| 1.1 | –0.0007 | 0.0635 | 0.3284 | 0.0021 | 0.0647 | 0.3318 | –0.0034 |
| 1.2 | –0.0002 | 0.0622 | 0.8308 | 0.0053 | 0.0634 | 0.8392 | –0.0084 |
| 1.5 | 0.0010 | 0.0596 | 1.0000 | 0.0143 | 0.0608 | 1.0000 | 0.0000 |
| 2 | 0.0007 | 0.0582 | 1.0000 | 0.0259 | 0.0588 | 1.0000 | 0.0000 |
| Complete Follow-up, 10% Cumulative Disease Incidence | |||||||
| 1.1 | 0.0001 | 0.0524 | 0.4480 | 0.0054 | 0.0542 | 0.4580 | –0.0100 |
| 1.2 | 0.0006 | 0.0517 | 0.9430 | 0.0119 | 0.0536 | 0.9522 | –0.0092 |
| 1.5 | –0.0001 | 0.0505 | 1.0000 | 0.0270 | 0.0524 | 1.0000 | 0.0000 |
| 2 | 0.0004 | 0.0503 | 1.0000 | 0.0531 | 0.0518 | 1.0000 | 0.0000 |
| Complete Follow-up, 15% Cumulative Disease Incidence | |||||||
| 1.1 | 0.0011 | 0.0484 | 0.5126 | 0.0098 | 0.0510 | 0.5402 | –0.0276 |
| 1.2 | –0.0008 | 0.0481 | 0.9674 | 0.0161 | 0.0507 | 0.9782 | –0.0108 |
| 1.5 | 0.0003 | 0.0475 | 1.0000 | 0.0418 | 0.0504 | 1.0000 | 0.0000 |
| 2 | 0.0022 | 0.0479 | 1.0000 | 0.0816 | 0.0507 | 1.0000 | 0.0000 |
| Survey Follow-up, 5% Cumulative Disease Incidence | |||||||
| 1.1 | 0.0002 | 0.0659 | 0.3120 | 0.0027 | 0.0643 | 0.3378 | –0.0258 |
| 1.2 | 0.0008 | 0.0647 | 0.8050 | 0.0049 | 0.0631 | 0.8402 | –0.0352 |
| 1.5 | –0.0002 | 0.0624 | 1.0000 | 0.0094 | 0.0607 | 1.0000 | 0.0000 |
| 2 | 0.0015 | 0.0612 | 1.0000 | 0.0195 | 0.0590 | 1.0000 | 0.0000 |
| Survey Follow-up, 10% Cumulative Disease Incidence | |||||||
| 1.1 | –0.0004 | 0.0569 | 0.3786 | 0.0026 | 0.0541 | 0.4350 | –0.0564 |
| 1.2 | 0.0009 | 0.0563 | 0.9038 | 0.0076 | 0.0536 | 0.9422 | –0.0384 |
| 1.5 | 0.0007 | 0.0553 | 1.0000 | 0.0171 | 0.0525 | 1.0000 | 0.0000 |
| 2 | 0.0024 | 0.0551 | 1.0000 | 0.0334 | 0.0519 | 1.0000 | 0.0000 |
| Survey Follow-up, 15% Cumulative Disease Incidence | |||||||
| 1.1 | 0.0019 | 0.0542 | 0.4332 | 0.0064 | 0.0510 | 0.5130 | –0.0798 |
| 1.2 | –0.0005 | 0.0538 | 0.9294 | 0.0089 | 0.0507 | 0.9682 | –0.0388 |
| 1.5 | 0.0016 | 0.0533 | 1.0000 | 0.0230 | 0.0504 | 1.0000 | 0.0000 |
| 2 | 0.0008 | 0.0535 | 1.0000 | 0.0424 | 0.0506 | 1.0000 | 0.0000 |
| Random Follow-up, 5% Cumulative Disease Incidence | |||||||
| 1.1 | –0.0007 | 0.0681 | 0.2864 | –0.0001 | 0.0645 | 0.3212 | –0.0348 |
| 1.2 | 0.0005 | 0.0670 | 0.7768 | 0.0030 | 0.0633 | 0.8334 | –0.0566 |
| 1.5 | –0.0005 | 0.0648 | 1.0000 | 0.0067 | 0.0609 | 1.0000 | 0.0000 |
| 2 | 0.0007 | 0.0639 | 1.0000 | 0.0143 | 0.0593 | 1.0000 | 0.0000 |
| Random Follow-up, 10% Cumulative Disease Incidence | |||||||
| 1.1 | 0.0006 | 0.0599 | 0.3536 | 0.0021 | 0.0543 | 0.4290 | –0.0754 |
| 1.2 | –0.0005 | 0.0593 | 0.8756 | 0.0037 | 0.0537 | 0.9398 | –0.0642 |
| 1.5 | 0.0004 | 0.0583 | 1.0000 | 0.0097 | 0.0526 | 1.0000 | 0.0000 |
| 2 | 0.0004 | 0.0583 | 1.0000 | 0.0192 | 0.0520 | 1.0000 | 0.0000 |
| Random Follow-up, 15% Cumulative Disease Incidence | |||||||
| 1.1 | –0.0002 | 0.0574 | 0.3740 | 0.0016 | 0.0509 | 0.4726 | –0.0986 |
| 1.2 | 0.0021 | 0.0571 | 0.9062 | 0.0055 | 0.0507 | 0.9578 | –0.0516 |
| 1.5 | 0.0004 | 0.0566 | 1.0000 | 0.0112 | 0.0503 | 1.0000 | 0.0000 |
| 2 | 0.0031 | 0.0571 | 1.0000 | 0.0199 | 0.0505 | 1.0000 | 0.0000 |
Abbreviations: Diff in Power, difference in power (Cox − logistic); HR, hazard ratio; OR, odds ratio; RAF, risk allele frequency; SE, standard error of the logarithm of hazard or odds ratio. Bias refers to either the estimated log(HR) or log(OR) minus the underlying log(HR). It is important to note that HRs and ORs are different measures of comparison and as such ORs are not 'biased' if different from the underlying HR. The Cox model was Prentice weighted and robust SEs were applied to account for the sampling process. This table is a subset of Supplementary Table S5.