Figure 3

Flow chart of receiver operating characteristic (ROC) analysis. \(S_{{\nu_{bm} }}^{D}\) and \(S_{{\nu_{bm} }}^{0}\) are the SERS signals at the Raman shift of the biomarker peak,\(\nu_{{{\text{bm}}}}\), with and without antibiotic treatment, respectively. \(\nu_{{{\text{bm}}}}\) is 730 cm⁻¹ for S. aureus and is 724 cm⁻¹ for E. coli. \(r_{{\nu_{{{\text{bm}}}} }}\) is the ratio between \(S_{{\nu_{{{\text{bm}}}} }}^{{\text{D}}}\) and \(S_{{\nu_{{{\text{bm}}}} }}^{0}\). D1 indicates the lowest drug concentration, D2 indicates the second lowest drug concentration, and so on. \(r_{{\nu_{{{\text{bm}}}} }}^{*}\) is the cutoff signal ratio. \(r_{\nu_{{\text{bm}}}, {\text{Dj}}}\) is the signal ratio at \(\nu_{{{\text{bm}}}}\) of the bacterial sample treated with the antibiotic of concentration Dj. E. c. and S. a. are the abbreviations of E. coli and S. aureus, respectively. \(n_{{{\text{TP}}}}\), \(n_{{{\text{FP}}}}\), \(n_{{{\text{TN}}}}\) and \(n_{{{\text{FN}}}}\) are the numbers of true positive, false positive, true negative and false negative cases, respectively. M is the total number of samples. \(\max \left( {r_{{\nu_{{{\text{bm}}}} }} } \right)\) is the maximal measured \(r_{{\nu_{{{\text{bm}}}} }}\) obtained from the M samples.