BMC Bioinformatics

Table 2 Resulting discriminatory power of C-index boosting in combination with stability selection for different values of q and π _thr compared to the competing Cox lasso approach

From: Boosting the discriminatory power of sparse survival models via optimization of the concordance index and stability selection

					C-index boosting						Cox
p	p _inf	n	PH-viol	q	π _thr = 0.5	π _thr = 0.6	π _thr = 0.7	π _thr = 0.8	π _thr = 0.9	without π _thr	lasso
1000	4	200	false	100	0.8150	0.8286	0.8358	0.8393	0.8396	0.7889	0.8148
				50	0.8343	0.8365	0.8381	0.8357	0.8253
				20	0.8324	0.8252	0.7829	0.7662	0.7394
				15	0.8309	0.7813	0.7694	0.7519	0.7340
				10	0.7799	0.7683	0.7519	0.7426	0.6202
				5	0.7497	0.7426	0.7323	0.6176	0.5993
500	4	200	false	100	0.7998	0.8179	0.8305	0.8361	0.8391	0.7735	0.8161
				50	0.8268	0.8332	0.8375	0.8388	0.8340
				20	0.8358	0.8351	0.8309	0.7744	0.7607
				15	0.8346	0.8314	0.7835	0.7672	0.7521
				10	0.8279	0.7801	0.7672	0.7587	0.7400
				5	0.7627	0.7587	0.7444	0.7347	0.6154
500	4	200	true	100	0.8304	0.8481	0.8612	0.8656	0.8671	0.7886	0.8345
				50	0.8555	0.8635	0.8664	0.8668	0.8664
				20	0.8657	0.8654	0.8626	0.8477	0.7662
				15	0.8654	0.8626	0.8554	0.7743	0.7573
				10	0.8598	0.8442	0.7757	0.7614	0.7360
				5	0.7660	0.7573	0.7391	0.7275	0.6219
50	4	200	false	20	0.8183	0.8248	0.8303	0.8333	0.8358	0.7939	0.8256
				15	0.8268	0.8298	0.8329	0.8353	0.8370
				10	0.8314	0.8348	0.8366	0.8370	0.8366
				5	0.8373	0.8353	0.8324	0.8247	0.7662
500	12	200	false	100	0.9109	0.9218	0.8996	0.8639	0.8081	0.8852	0.8834
				50	0.7991	0.7880	0.7451	0.7089	0.6482
				20	0.6954	0.6609	0.6239	0.5698	–
				15	0.6664	0.6274	0.5830	0.5549	–
				10	0.6275	0.5848	0.5610	–	–
500	40	200	false	200	0.6416	0.6269	0.6088	0.5755	0.5344	0.6983	0.5782
				100	0.6373	0.6245	0.6028	0.5706	0.5308
				50	0.5907	0.5703	0.5407	0.5129	–
				25	0.5411	0.5269	–	–	–

In case of C-index boosting, the final models were fitted with fixed m _stop=1000. Numbers represent the median \(\hat {C}_{\text {Uno}}\) on test samples from 100 simulation runs. PH-viol: settings were the proportional hazards assumption was violated. In cases where no variables at all are identified as stable, no discriminatory power can be computed (denoted as –). C-index boosting without stability selection (without π _thr) was fitted on all p predictors with a fixed large m _stop; in case of the Cox lasso the shrinkage parameter was optimized via 10-fold cross-validation

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