Table 1.

Proportional bias (%) of the uncorrected (naïve) and ascertainment-corrected MLEs of the allele frequency difference δ and odds ratio OR. Results are presented only for δ > 0.

p	N	power	δ	$\frac{{\widehat{\delta }}_{\mathit{\text{un}}}-\delta }{\delta }$	$$\frac{{\widehat{\delta }}_{\mathit{\text{as}}}-\delta }{\delta }$$	OR	$\frac{\stackrel{‵}{O}{R}_{\mathit{\text{un}}}-\mathit{\text{OR}}}{\mathit{\text{OR}}}$	$\frac{\stackrel{‵}{O}{R}_{\mathit{\text{as}}}-\mathit{\text{OR}}}{\mathit{\text{OR}}}$
		.01	.0376	101.9	-4.3	1.436	53.3	-1.8
		.10	.0541	47.9	-12.4	1.640	27.9	-5.7
	500	.30	.0665	26.2	-16.1	1.798	17.6	-7.2
		.50	.0752	16.2	-14.2	1.913	11.9	-6.5
		.80	.0898	6.0	-8.2	2.108	5.55	-1.7
.1
		.01	.0258	103.1	-7.0	1.295	31.2	-1.9
		.10	.0370	48.1	-15.7	1.429	19.2	-4.2
	1000	.30	.0453	26.5	-18.3	1.530	12.3	-7.1
		.50	.0512	16.0	-16.2	1.603	8.36	-6.3
		.80	.0609	6.1	-9.3	1.726	3.77	-4.1
		.01	.0576	103.0	-9.0	1.260	27.2	-2.1
		.10	.0806	48.3	-16.8	1.384	17.3	-5.3
	500	.30	.0972	26.3	-18.3	1.483	11.2	-6.3
		.50	.1086	16.2	-14.3	1.555	7.72	-5.8
		.80	.1270	6.1	-9.2	1.681	3.51	-3.6
.5
		.01	.0405	104.0	-13.1	1.176	18.5	-2.0
		.10	.0571	48.3	-18.6	1.258	11.8	-4.2
	1000	.30	.0690	26.4	-18.3	1.320	7.7	-4.9
		.50	.0772	16.2	-15.0	1.365	5.4	-4.5
		.80	.0903	6.1	-10.4	1.441	2.4	-3.1

un: uncorrected; as: ascertainment-corrected

p: disease allele frequency in controls; N: sample size (number of cases and of controls)

Assume testing at significance level α = 10^-6