Table 2.

Selection performance of biomarker-treatment interactions and main effects corresponding to the selected interactions

			AL(LRT)	AL(SW)	AL(ridge)	SGL	cMCP	gel
Scenario 1 $q_{\mathit{Pe}}=0$ $q_{\mathit{Po}}=0$	Interactions	$n_{\mathit{Pe}}$	9.96	13.02	1.95	0.00	0.68	0.44
		FP	9.96	13.02	1.95	0.00	0.68	0.44
		FDR	0.95	0.97	0.95	-	0.24	0.20
	Main effects	$n_{\mathit{Po}}$ $(n_{\mathit{Po}}/n_{\mathit{Pe}})$	3.96 (40%)	5.68 (44%)	0.24 (12%)	0.00	0.01 (1%)	0.01 (2%)
		FP	3.96	5.68	0.24	0.00	0.01	0.01
		FDR	0.85	0.88	0.17	-	0.01	0.01
Scenario 2 $q_{\mathit{Pe}}=1$ $q_{\mathit{Po}}=0$	Interactions	$n_{\mathit{Pe}}$	8.89	6.71	4.31	1.37	2.28	1.54
		TP / FP	1.00/7.89	1.00/5.71	1.00/3.31	1.00/0.37	1.00/1.28	1.00/0.54
		FDR / FNR	0.72/0.00	0.44/0.00	0.53/0.00	0.15/0.00	0.26/0.00	0.15/0.00
	Main effects	$n_{\mathit{Po}}$ $(n_{\mathit{Po}}/n_{\mathit{Pe}})$	4.79 (54%)	3.67 (55%)	0.48 (11%)	0.11 (8%)	0.05 (2%)	0.34 (52%)
		TP / FP	0.87/3.93	0.73/2.94	0.07/0.41	0.05/0.06	0.03/0.02	0.33/0.01
		FDR / FNR	0.63/0.13	0.37/0.27	0.24/0.93	0.06/0.95	0.02/0.97	0.01/0.67
Scenario 3 $q_{\mathit{Pe}}=10$ $q_{\mathit{Po}}=0$	Interactions	$n_{\mathit{Pe}}$	15.51	15.18	22.40	20.20	13.68	10.48
		TP / FP	10.00/5.51	10.00/5.18	10.00/12.40	10.00/10.20	10.00/3.68	10.00/0.48
		FDR / FNR	0.33/0.00	0.32/0.00	0.51/0.00	0.48/0.00	0.24/0.00	0.04/0.00
	Main effects	$n_{\mathit{Po}}$ $(n_{\mathit{Po}}/n_{\mathit{Pe}})$	9.54 (61%)	9.15 (60%)	2.28 (1%)	4.09 (20%)	1.02 (7%)	5.73 (55%)
		TP / FP	6.74/2.80	6.61/2.54	0.93/1.35	1.69/2.40	0.96/0.07	5.72/0.01
		FDR / FNR	0.27/0.33	0.26/0.34	0.43/0.91	0.55/0.83	0.04/0.90	0.00/0.43
Scenario 4 $q_{\mathit{Pe}}=10$ $q_{\mathit{Po}}=10$	Interactions	$n_{\mathit{Pe}}$	15.15	70.88	19.93	26.27	14.57	19.67
		TP / FP	9.97/5.18	9.99/60.89	10.00/9.93	10.00/16.27	10.00/4.57	9.99/9.69
		FDR / FNR	0.32/0.00	0.85/0.00	0.46/0.00	0.60/0.00	0.29/0.00	0.49/0.00
	Main effects	$n_{\mathit{Po}}$ $(n_{\mathit{Po}}/n_{\mathit{Pe}})$	8.43 (56%)	52.40 (74%)	2.04 (10%)	6.88 (26%)	2.73 (19%)	15.56 (78%)
		TP / FP	5.80/2.63	8.99/43.41	0.91/1.13	2.07/4.82	1.11/1.62	6.05/9.51
		FDR / FNR	0.29/0.42	0.82/0.10	0.42/0.91	0.68/0.79	0.56/0.89	0.62/0.39

$q_{\mathit{Pe}}$ number of predictive biomarkers, $q_{\mathit{Po}}$ number of prognostic biomarkers, $n_{\mathit{Pe}}$ number of selected interactions, $n_{\mathit{Po}}$ number of selected main effects corresponding to the selected interactions, FP false positives, TP true positives, FDR false discovery rate, FNR false negative rate, AL adaptive lasso, LRT likelihood ratio test, SW single Wald