Table 4. Power (%) of each test under the alternative hypothesis of interaction effect, $\gamma =0.2$.

		Power $\left(\text{\%}\right)$
		Probit			Logit			Log penetrance
Tests	d.f.	$p=10\text{\%}$	$p=1\text{\%}$	$p=0.1\text{\%}$	$p=10\text{\%}$	$p=1\text{\%}$	$p=0.1\text{\%}$	$p=10\text{\%}$	$p=1\text{\%}$	$p=0.1\text{\%}$
A. ${\beta }_1={\beta }_2=0$
SI	4	43.94	83.49	96.46	54.29	68.75	69.86	71.03	69.31	69.55
ImAP	4	35.20	87.53	99.31	47.71	66.90	68.65	68.71	68.02	69.22
$\mathrm{ImA}{\mathrm{P}}_2$	4	20.45	55.13	80.91	27.15	38.39	40.17	39.90	39.37	39.66
$\mathrm{ImA}{\mathrm{P}}_3$	4	88.76	99.89	100.00	95.39	99.06	99.05	99.12	99.17	99.24
$\mathrm{CLRP}{\mathrm{C}}_1$	4	33.32	70.24	89.30	41.58	54.65	55.88	56.04	55.88	56.24
SC	1	65.84	95.04	99.50	75.65	87.13	87.63	88.08	87.67	87.69
$\mathrm{CLRP}{\mathrm{C}}_2$	1	52.74	87.64	97.25	62.82	76.15	76.59	77.46	76.29	77.31
TC	1	69.70	97.16	99.87	79.67	90.23	90.71	91.21	90.97	90.81
B. ${\beta }_1={\beta }_2=0.2$
SI	4	13.77	27.50	43.71	34.79	62.81	66.54	67.22	67.67	67.56
ImAP	4	15.52	52.95	89.41	83.43	99.50	99.70	99.74	99.77	99.65
$\mathrm{ImA}{\mathrm{P}}_2$	4	6.10	12.71	20.90	16.72	35.99	38.62	40.02	40.18	40.42
$\mathrm{ImA}{\mathrm{P}}_3$	4	83.47	99.83	100.00	100.00	100.00	100.00	100.00	100.00	100.00
$\mathrm{CLRP}{\mathrm{C}}_1$	4	11.73	21.84	33.07	26.71	49.92	51.99	53.24	53.77	53.41
SC	1	23.14	47.00	65.28	53.61	82.69	85.60	86.04	85.50	85.58
$\mathrm{CLRP}{\mathrm{C}}_2$	1	18.28	36.36	52.98	42.39	71.19	73.90	74.92	74.95	74.57
TC	1	26.74	57.45	81.22	70.72	94.66	96.09	96.16	96.22	96.22

Results are based on 10,000 simulated data sets. p, disease prevalence in the population.