Table 2:

Empirical size and power (%) of testing ${\Delta }_{\mathbf{S}\to G\to Y}.Q_1$: model with only main effects; $Q_2$: model with main effects and microRNA-by-expression interaction; $Q_3$: model with main effects and two-way interactions; $Q_4$: model with main effects, two-way and three-way interactions; Omnibus: the omnibus test for $Q_1\text{-}{Q}_4$; Score test: the classic score test for $\beta ’\mathrm{s}$. The tuning parameter $\lambda$ was chosen using GCV.

	Null			Alternative
${\beta }_S$	0	0.2	0	0	0.2	0.2	0.2	0.1	0.1	0	0
${\beta }_M$	0	0	0.2	0	0.2	0.2	0.2	0.1	0.1	0	0
${\beta }_G$	0	0	0	0.3	0.2	0.3	0.4	0.1	0.1	0	0
${\beta }_{MG}$	0	0	0	0	0	0	0	0.3	0.5	0	0
${\beta }_{SM}$	0	0	0	0	0	0	0	0.3	0.5	0	0
${\beta }_{SG}$	0	0	0	0	0	0	0	0.3	0.5	0	0
${\beta }_{SMG}$	0	0	0	0	0	0	0	0	0	0.5	0.8
$Q_1$	4.70	4.40	4.65	90.2	56.2	88.5	98.8	6.30	3.35	7.55	11.3
$Q_2$	5.85	4.95	4.90	82.5	44.3	81.1	97.0	9.60	8.45	9.60	13.4
$Q_3$	5.00	5.20	5.00	73.5	36.8	72.8	94.1	60.5	93.5	10.9	20.7
$Q_4$	5.10	4.90	4.60	66.9	31.6	66.7	91.5	53.3	88.7	63.8	88.7
Omnibus	5.35	4.70	4.80	84.1	47.2	82.8	97.6	45.8	85.1	45.2	78.5
Score test	45.3	45.0	48.3