Table 5

Assessment of the added predictive value of the molecular variables by dataset. The second and seventh column show the best performing learners for the respective dataset and measure, the ‘cindex’ and ‘ibrier’ columns the performances of these learners. In the cases where the clinical only model is outperformed, the ‘Ref.’ columns show the corresponding cindex and ibrier values of the reference Cox model only using clinical variables. The “ci” columns show the 95% confidence intervals for the respective performance values based on quantiles of the t-distribution; observations are the learners’ CV iteration values. Note that these intervals are intended to give a notion of the stability of the mean values, but are—in contrast to Table 4—not valid confidence intervals, since the CV iterations are no independent observations [55, 56]. Bold letters indicate datasets for which there is a method using the group structure and outperforming the Cox model for both measures.

DataLearneribrierciRef.ciLearnercindexciRef.ci
BLCACoxBoost favoring0.190[0.181, 0.199]0.192[0.183, 0.201]CoxBoost favoring0.640[0.612, 0.668]0.633[0.607, 0.659]
BRCAblockForest0.141[0.134, 0.149]0.147[0.137, 0.158]CoxBoost favoring0.643[0.618, 0.669]0.637[0.608, 0.666]
COADblockForest0.087[0.075, 0.099]0.101[0.088, 0.115]blockForest0.656[0.586, 0.725]0.541[0.475, 0.608]
ESCAipflasso0.209[0.198, 0.221]0.214[0.199, 0.228]Clinical only0.574[0.536, 0.612]
HNSCglmboost0.202[0.193, 0.211]0.210[0.201, 0.220]blockForest0.582[0.554, 0.610]0.554[0.519, 0.588]
KIRCipflasso0.144[0.138, 0.149]0.146[0.140, 0.152]Clinical only0.761[0.734, 0.789]
KIRPranger0.118[0.106, 0.131]0.140[0.117, 0.163]grridge0.629[0.566, 0.692]0.572[0.502, 0.641]
LAMLranger0.182[0.165, 0.199]0.231[0.200, 0.263]ranger0.709[0.651, 0.766]0.596[0.534, 0.657]
LGGLasso*0.145[0.132, 0.157]0.168[0.154, 0.181]glmboost0.749[0.719, 0.779]0.652[0.618, 0.685]
LIHCranger0.146[0.135, 0.157]0.169[0.158, 0.180]grridge0.602[0.560, 0.645]0.586[0.542, 0.630]
LUADCoxBoost favoring*0.172[0.160, 0.183]0.172[0.161, 0.183]prioritylasso0.665[0.640, 0.690]0.663[0.631, 0.695]
LUSCgrridge0.210[0.203, 0.217]0.216[0.205, 0.227]prioritylasso favoring0.537[0.502, 0.572]0.531[0.502, 0.561]
OVipflasso*0.169[0.163, 0.174]0.173[0.167, 0.179]prioritylasso0.600[0.582, 0.618]0.598[0.580, 0.617]
PAADClinical only*0.190[0.178, 0.202]prioritylasso favoring0.686[0.658, 0.714]0.683[0.655, 0.712]
SARCglmboost*0.179[0.167, 0.190]0.202[0.188, 0.217]blockForest0.685[0.651, 0.720]0.673[0.637, 0.709]
SKCMClinical only0.191[0.185, 0.198]0.191[0.185, 0.198]blockForest0.597[0.556, 0.639]0.581[0.540, 0.623]
STADClinical only0.192[0.182, 0.202]Clinical only0.598[0.555, 0.641]
UCECipflasso0.091[0.079, 0.102]0.092[0.080, 0.105]Clinical only0.686[0.581, 0.791]
DataLearneribrierciRef.ciLearnercindexciRef.ci
BLCACoxBoost favoring0.190[0.181, 0.199]0.192[0.183, 0.201]CoxBoost favoring0.640[0.612, 0.668]0.633[0.607, 0.659]
BRCAblockForest0.141[0.134, 0.149]0.147[0.137, 0.158]CoxBoost favoring0.643[0.618, 0.669]0.637[0.608, 0.666]
COADblockForest0.087[0.075, 0.099]0.101[0.088, 0.115]blockForest0.656[0.586, 0.725]0.541[0.475, 0.608]
ESCAipflasso0.209[0.198, 0.221]0.214[0.199, 0.228]Clinical only0.574[0.536, 0.612]
HNSCglmboost0.202[0.193, 0.211]0.210[0.201, 0.220]blockForest0.582[0.554, 0.610]0.554[0.519, 0.588]
KIRCipflasso0.144[0.138, 0.149]0.146[0.140, 0.152]Clinical only0.761[0.734, 0.789]
KIRPranger0.118[0.106, 0.131]0.140[0.117, 0.163]grridge0.629[0.566, 0.692]0.572[0.502, 0.641]
LAMLranger0.182[0.165, 0.199]0.231[0.200, 0.263]ranger0.709[0.651, 0.766]0.596[0.534, 0.657]
LGGLasso*0.145[0.132, 0.157]0.168[0.154, 0.181]glmboost0.749[0.719, 0.779]0.652[0.618, 0.685]
LIHCranger0.146[0.135, 0.157]0.169[0.158, 0.180]grridge0.602[0.560, 0.645]0.586[0.542, 0.630]
LUADCoxBoost favoring*0.172[0.160, 0.183]0.172[0.161, 0.183]prioritylasso0.665[0.640, 0.690]0.663[0.631, 0.695]
LUSCgrridge0.210[0.203, 0.217]0.216[0.205, 0.227]prioritylasso favoring0.537[0.502, 0.572]0.531[0.502, 0.561]
OVipflasso*0.169[0.163, 0.174]0.173[0.167, 0.179]prioritylasso0.600[0.582, 0.618]0.598[0.580, 0.617]
PAADClinical only*0.190[0.178, 0.202]prioritylasso favoring0.686[0.658, 0.714]0.683[0.655, 0.712]
SARCglmboost*0.179[0.167, 0.190]0.202[0.188, 0.217]blockForest0.685[0.651, 0.720]0.673[0.637, 0.709]
SKCMClinical only0.191[0.185, 0.198]0.191[0.185, 0.198]blockForest0.597[0.556, 0.639]0.581[0.540, 0.623]
STADClinical only0.192[0.182, 0.202]Clinical only0.598[0.555, 0.641]
UCECipflasso0.091[0.079, 0.102]0.092[0.080, 0.105]Clinical only0.686[0.581, 0.791]

*indicates that there is a method with equal performance.

Table 5

Assessment of the added predictive value of the molecular variables by dataset. The second and seventh column show the best performing learners for the respective dataset and measure, the ‘cindex’ and ‘ibrier’ columns the performances of these learners. In the cases where the clinical only model is outperformed, the ‘Ref.’ columns show the corresponding cindex and ibrier values of the reference Cox model only using clinical variables. The “ci” columns show the 95% confidence intervals for the respective performance values based on quantiles of the t-distribution; observations are the learners’ CV iteration values. Note that these intervals are intended to give a notion of the stability of the mean values, but are—in contrast to Table 4—not valid confidence intervals, since the CV iterations are no independent observations [55, 56]. Bold letters indicate datasets for which there is a method using the group structure and outperforming the Cox model for both measures.

DataLearneribrierciRef.ciLearnercindexciRef.ci
BLCACoxBoost favoring0.190[0.181, 0.199]0.192[0.183, 0.201]CoxBoost favoring0.640[0.612, 0.668]0.633[0.607, 0.659]
BRCAblockForest0.141[0.134, 0.149]0.147[0.137, 0.158]CoxBoost favoring0.643[0.618, 0.669]0.637[0.608, 0.666]
COADblockForest0.087[0.075, 0.099]0.101[0.088, 0.115]blockForest0.656[0.586, 0.725]0.541[0.475, 0.608]
ESCAipflasso0.209[0.198, 0.221]0.214[0.199, 0.228]Clinical only0.574[0.536, 0.612]
HNSCglmboost0.202[0.193, 0.211]0.210[0.201, 0.220]blockForest0.582[0.554, 0.610]0.554[0.519, 0.588]
KIRCipflasso0.144[0.138, 0.149]0.146[0.140, 0.152]Clinical only0.761[0.734, 0.789]
KIRPranger0.118[0.106, 0.131]0.140[0.117, 0.163]grridge0.629[0.566, 0.692]0.572[0.502, 0.641]
LAMLranger0.182[0.165, 0.199]0.231[0.200, 0.263]ranger0.709[0.651, 0.766]0.596[0.534, 0.657]
LGGLasso*0.145[0.132, 0.157]0.168[0.154, 0.181]glmboost0.749[0.719, 0.779]0.652[0.618, 0.685]
LIHCranger0.146[0.135, 0.157]0.169[0.158, 0.180]grridge0.602[0.560, 0.645]0.586[0.542, 0.630]
LUADCoxBoost favoring*0.172[0.160, 0.183]0.172[0.161, 0.183]prioritylasso0.665[0.640, 0.690]0.663[0.631, 0.695]
LUSCgrridge0.210[0.203, 0.217]0.216[0.205, 0.227]prioritylasso favoring0.537[0.502, 0.572]0.531[0.502, 0.561]
OVipflasso*0.169[0.163, 0.174]0.173[0.167, 0.179]prioritylasso0.600[0.582, 0.618]0.598[0.580, 0.617]
PAADClinical only*0.190[0.178, 0.202]prioritylasso favoring0.686[0.658, 0.714]0.683[0.655, 0.712]
SARCglmboost*0.179[0.167, 0.190]0.202[0.188, 0.217]blockForest0.685[0.651, 0.720]0.673[0.637, 0.709]
SKCMClinical only0.191[0.185, 0.198]0.191[0.185, 0.198]blockForest0.597[0.556, 0.639]0.581[0.540, 0.623]
STADClinical only0.192[0.182, 0.202]Clinical only0.598[0.555, 0.641]
UCECipflasso0.091[0.079, 0.102]0.092[0.080, 0.105]Clinical only0.686[0.581, 0.791]
DataLearneribrierciRef.ciLearnercindexciRef.ci
BLCACoxBoost favoring0.190[0.181, 0.199]0.192[0.183, 0.201]CoxBoost favoring0.640[0.612, 0.668]0.633[0.607, 0.659]
BRCAblockForest0.141[0.134, 0.149]0.147[0.137, 0.158]CoxBoost favoring0.643[0.618, 0.669]0.637[0.608, 0.666]
COADblockForest0.087[0.075, 0.099]0.101[0.088, 0.115]blockForest0.656[0.586, 0.725]0.541[0.475, 0.608]
ESCAipflasso0.209[0.198, 0.221]0.214[0.199, 0.228]Clinical only0.574[0.536, 0.612]
HNSCglmboost0.202[0.193, 0.211]0.210[0.201, 0.220]blockForest0.582[0.554, 0.610]0.554[0.519, 0.588]
KIRCipflasso0.144[0.138, 0.149]0.146[0.140, 0.152]Clinical only0.761[0.734, 0.789]
KIRPranger0.118[0.106, 0.131]0.140[0.117, 0.163]grridge0.629[0.566, 0.692]0.572[0.502, 0.641]
LAMLranger0.182[0.165, 0.199]0.231[0.200, 0.263]ranger0.709[0.651, 0.766]0.596[0.534, 0.657]
LGGLasso*0.145[0.132, 0.157]0.168[0.154, 0.181]glmboost0.749[0.719, 0.779]0.652[0.618, 0.685]
LIHCranger0.146[0.135, 0.157]0.169[0.158, 0.180]grridge0.602[0.560, 0.645]0.586[0.542, 0.630]
LUADCoxBoost favoring*0.172[0.160, 0.183]0.172[0.161, 0.183]prioritylasso0.665[0.640, 0.690]0.663[0.631, 0.695]
LUSCgrridge0.210[0.203, 0.217]0.216[0.205, 0.227]prioritylasso favoring0.537[0.502, 0.572]0.531[0.502, 0.561]
OVipflasso*0.169[0.163, 0.174]0.173[0.167, 0.179]prioritylasso0.600[0.582, 0.618]0.598[0.580, 0.617]
PAADClinical only*0.190[0.178, 0.202]prioritylasso favoring0.686[0.658, 0.714]0.683[0.655, 0.712]
SARCglmboost*0.179[0.167, 0.190]0.202[0.188, 0.217]blockForest0.685[0.651, 0.720]0.673[0.637, 0.709]
SKCMClinical only0.191[0.185, 0.198]0.191[0.185, 0.198]blockForest0.597[0.556, 0.639]0.581[0.540, 0.623]
STADClinical only0.192[0.182, 0.202]Clinical only0.598[0.555, 0.641]
UCECipflasso0.091[0.079, 0.102]0.092[0.080, 0.105]Clinical only0.686[0.581, 0.791]

*indicates that there is a method with equal performance.

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