Table 2.

Performance of selecting causal omics variables under different B shapes for different methods, including tensor regression evaluated at true rank (TR.true), at AIC determined rank (TR.AIC) and at BIC determined rank (TR.BIC), as well as linear regression model (LM) and LASSO on vectorized omics variables, based on 200 replications

	B shape = Flat					B shape = I					B shape = T					B shape = Random
	TR.	TR.	TR.	LM	LASSO	TR.	TR.	TR.	LM	LASSO	TR.	TR.	TR.	LM	LASSO	TR.	TR.	TR.	LM	LASSO
	true	AIC	BIC			true	AIC	BIC			true	AIC	BIC			true	AIC	BIC
$d=$ 0.125
TPR	0.371	0.370	0.371	0.274	0.683	0.695	0.698	0.695	0.214	0.664	0.736	0.744	0.981	0.669	0.832	0.626	0.849	0.892	0.396	0.796
FDR	0.044	0.047	0.044	0.257	0.275	0.222	0.146	0.222	0.331	0.429	0.127	0.094	0.442	0.076	0.317	0.043	0.032	0.027	0.053	0.184
F-measure	0.530	0.529	0.530	0.398	0.702	0.731	0.756	0.731	0.321	0.613	0.797	0.813	0.711	0.776	0.750	0.756	0.899	0.929	0.557	0.806
$d=$ 0.25
TPR	0.649	0.649	0.649	0.564	0.753	0.795	0.870	0.873	0.554	0.855	0.868	0.899	0.973	0.809	0.939	0.860	0.872	0.969	0.709	0.914
FDR	0.033	0.033	0.033	0.141	0.320	0.235	0.118	0.116	0.158	0.423	0.141	0.057	0.288	0.061	0.332	0.032	0.034	0.044	0.030	0.189
F-measure	0.773	0.773	0.773	0.679	0.714	0.779	0.875	0.877	0.666	0.688	0.863	0.919	0.807	0.869	0.780	0.911	0.915	0.962	0.819	0.860
$d=$ 1
TPR	0.954	0.954	0.954	0.932	0.965	0.815	0.914	0.914	0.895	0.957	0.967	0.979	0.980	0.971	0.990	0.961	0.960	0.961	0.936	0.967
FDR	0.036	0.037	0.036	0.093	0.412	0.238	0.107	0.106	0.103	0.475	0.081	0.055	0.053	0.055	0.350	0.025	0.026	0.025	0.025	0.231
F-measure	0.954	0.954	0.954	0.919	0.730	0.785	0.902	0.903	0.895	0.677	0.942	0.962	0.963	0.957	0.784	0.968	0.967	0.968	0.955	0.856

Note: TPR = true positive rate; FDR = false discovery rate; d indicates the effect strength of causal omics variables. For TR and LM, a variable is selected as important if P-value < 0.05. The best performed methods among TR.AIC, LM and LASSO, judged by F-measures, are shown in shaded cells.