Table 1.

Simulation results demonstrating bias and power loss caused by misclassification of OSA cases

$\pi$ Misclassification rate	Mean estimated ${\beta }_g$ (true OSA)	Mean estimated ${\beta }_g$ (observed OSA)	Bias of ${\beta }_g$ estimates (observed OSA)	Power (true OSA)	Power (observed OSA)
True OSA prevalence 19%
0.4	0.100	0.090	0.010	0.96	0.76
0.6	0.100	0.086	0.014	0.96	0.57
0.8	0.099	0.081	0.019	0.95	0.29
True OSA prevalence 28%
0.4	0.100	0.086	0.014	0.99	0.84
0.6	0.099	0.080	0.020	0.98	0.65
0.8	0.101	0.077	0.023	0.98	0.38
True OSA prevalence 39%
0.4	0.099	0.079	0.021	0.99	0.86
0.6	0.100	0.071	0.029	0.99	0.64
0.8	0.099	0.065	0.035	1.00	0.37

For each combination of parameters determining OSA prevalence and its rate of misclassification, the simulations compare the estimated effect size (log odds ratio) when using the real OSA status and when using the observed OSA status, that suffers from misclassification, as mean estimates across 1000 simulation repetitions. The power is computed as the proportion of simulations in which the p-value of the genetic variant effect estimate was <.05.