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Background Neoadjuvant systemic treatment elicits a pathologic complete response (pCR) in about 35% of women with breast cancer. In such cases, breast surgery may be considered overtreatment. We evaluated multivariate algorithms using patient, tumor, and vacuum-assisted biopsy (VAB) variables to identify patients with breast pCR. Methods We developed and tested four multivariate algorithms: a logistic regression with elastic net penalty, an Extreme Gradient Boosting (XGBoost) tree, Support Vector Machines (SVM), and neural network. We used data from 457 women, randomly partitioned into training and test set (2:1), enrolled in three trials with stage 1–3 breast cancer, undergoing VAB before surgery. False-negative rate (FNR) and specificity were the main outcome measures. The best performing algorithm was validated in an independent fourth trial. Results In the test set (n = 152), the logistic regression with elastic net penalty, XGboost tree, SVM, and neural network revealed an FNR of 1.2% (1 of 85 patients with missed residual cancer). Specificity of the logistic regression with elastic net penalty was 52.2% (35 of 67 women with surgically confirmed breast pCR identified), of the XGBoost tree 55.2% (37 of 67), of SVM 62.7% (42 of 67), and of the neural network 67.2% (45 of 67). External validation (n = 50) of the neural network showed an FNR of 0% (0 of 27) and a specificity of 65.2% (15 of 23). Area under the ROC curve for the neural network was 0.97 (95% CI, 0.94–1.00). Conclusion A multivariate algorithm can accurately select breast cancer patients without residual cancer after neoadjuvant treatment.