Inflammation-lipid metabolism biomarker-based machine learning models for predicting postoperative pulmonary metastasis in colorectal cancer

Table 1 Layer 4 (full-feature model): Internal validation performance comparison across 14 algorithms

Algorithm	AUC	AUC_95CI	AUPRC	Brier	ABscore	Accuracy	Sensitivity	Specificity	F1	PPV	NPV	Opt_Threshold
LightGBM	0.7507	0.6872-0.8157	0.5592	0.1856	1.0	0.7191	0.7907	0.6851	0.6445	0.544	0.8732	0.3144
RotF	0.7454	0.6783-0.8091	0.5333	0.1875	0.9583	0.7266	0.7326	0.7238	0.6332	0.5575	0.8506	0.3459
GBDT	0.7367	0.6723-0.7967	0.5439	0.1876	0.9113	0.6704	0.7791	0.6188	0.6036	0.4926	0.855	0.2922
RF	0.7252	0.6620-0.7862	0.5171	0.1935	0.8075	0.6779	0.8023	0.6188	0.6161	0.5	0.8682	0.3333
SVM	0.7222	0.6581-0.7879	0.5327	0.1938	0.7892	0.6779	0.7093	0.663	0.5865	0.5	0.8276	0.294
AdaBoost	0.7172	0.6472-0.7794	0.509	0.1976	0.7349	0.6479	0.8023	0.5746	0.5948	0.4726	0.8595	0.3209
ExtraTrees	0.7169	0.6519-0.7812	0.5125	0.1988	0.7248	0.6966	0.686	0.7017	0.593	0.5221	0.8247	0.3487
KNN	0.7162	0.6553-0.7778	0.4889	0.1977	0.7287	0.6517	0.7326	0.6133	0.5753	0.4737	0.8284	0.4286
MLP	0.7132	0.6436-0.7778	0.522	0.2539	0.3016	0.6667	0.7442	0.6298	0.5899	0.4885	0.8382	0.0523
DT	0.7096	0.6463-0.7688	0.4685	0.1951	0.7131	0.6667	0.7442	0.6298	0.5899	0.4885	0.8382	0.4217
XGBoost	0.6956	0.6276-0.7603	0.4896	0.1971	0.6243	0.633	0.7791	0.5635	0.5776	0.4589	0.843	0.2972
GAM	0.6848	0.6158-0.7573	0.4956	0.1997	0.5487	0.6554	0.6395	0.663	0.5446	0.4741	0.7947	0.3507
LR	0.6689	0.5988-0.7375	0.4832	0.2022	0.446	0.6667	0.5581	0.7182	0.5189	0.4848	0.7738	0.3677
NB	0.656	0.5881-0.7276	0.4897	0.2376	0.1198	0.6592	0.593	0.6906	0.5285	0.4766	0.7812	0.3976

AUC: Area under the curve; AUPRC: Area under the precision-recall curve; PPV: Positive predictive value; NPV: Negative predictive value; RotF: Rotation Forest; GBDT: Gradient Boosting Decision Tree; RF: Random Forest; SVM: Support Vector Machine; NB: Naive Bayes; KNN: K-Nearest Neighbors; MLP: Multi-Layer Perceptron; DT: Decision Tree; LR: Logistic regression; GAM: Generalized Additive Model.

Table 2 Internal validation performance comparison of ensemble models

Algorithm	Type	AUC	AUC_95CI	AUPRC	Brier	ABscore	Accuracy	Sensitivity	Specificity	F1	PPV	NPV	Opt_Threshold
WeightedVoting	Ensemble	0.7513	0.6884-0.8149	0.5508	0.1862	0.9632	0.7303	0.7093	0.7403	0.6289	0.5648	0.8428	0.3507
SoftVoting	Ensemble	0.7513	0.6882-0.8149	0.5506	0.1862	0.9600	0.7303	0.7093	0.7403	0.6289	0.5648	0.8428	0.3512
LightGBM	Single	0.7507	0.6872-0.8157	0.5592	0.1856	0.9889	0.7191	0.7907	0.6851	0.6445	0.544	0.8732	0.3144
RotF	Single	0.7454	0.6783-0.8091	0.5333	0.1875	0.769	0.7266	0.7326	0.7238	0.6332	0.5575	0.8506	0.3459
GBDT	Single	0.7367	0.6723-0.7967	0.5439	0.1876	0.5944	0.6704	0.7791	0.6188	0.6036	0.4926	0.855	0.2922
Stacking	Ensemble	0.7321	0.6701-0.7964	0.5317	0.1897	0.3698	0.6929	0.7093	0.6851	0.598	0.5169	0.8322	0.3221
RF	Single	0.7252	0.6620-0.7862	0.5171	0.1935	0	0.6779	0.8023	0.6188	0.6161	0.5	0.8682	0.3333

AUC: Area under the curve; AUPRC: Area under the precision-recall curve; PPV: Positive predictive value; NPV: Negative predictive value; RotF: Rotation Forest; GBDT: Gradient Boosting Decision Tree; RF: Random Forest.

Table 3 External validation (Gansu Provincial Cancer Hospital, Center B): Performance comparison across models

Algorithm	Type	Ext_AUC	Ext_AUC_95CI	Int_AUC	AUPRC	Brier	ABscore	Accuracy	Sensitivity	Specificity	F1	PPV	NPV	Threshold (from internal validation)
Stacking	Ensemble	0.7127	0.6533-0.7722	0.732	0.4476	0.1857	0.8881	0.6955	0.6796	0.702	0.5622	0.4795	0.8443	0.3221
Weighted Voting	Ensemble	0.7112	0.6498-0.7702	0.7498	0.439	0.185	0.9734	0.7039	0.699	0.7059	0.576	0.4898	0.8531	0.3507
Soft Voting	Ensemble	0.7111	0.6495-0.7699	0.7499	0.4389	0.185	0.9712	0.7067	0.699	0.7098	0.5783	0.4932	0.8538	0.3512
LightGBM	Single	0.7087	0.6492-0.7664	0.7507	0.4331	0.1863	0.725	0.676	0.7087	0.6627	0.5573	0.4591	0.8492	0.3144
GBDT	Single	0.7075	0.6473-0.7699	0.7367	0.4452	0.1874	0.528	0.648	0.7476	0.6078	0.55	0.435	0.8564	0.2922
RF	Single	0.6961	0.6352-0.7541	0.7252	0.4168	0.1882	0.204	0.6369	0.7476	0.5922	0.5423	0.4254	0.8531	0.3333
RotF	Single	0.6848	0.6228-0.7436	0.7454	0.4384	0.188	0.037	0.6732	0.6893	0.6667	0.5483	0.4551	0.8416	0.3459

AUC: Area under the curve; AUPRC: Area under the precision-recall curve; PPV: Positive predictive value; NPV: Negative predictive value; RotF: Rotation Forest; GBDT: Gradient Boosting Decision Tree; RF: Random Forest.