3.3.1. Mahalanobis Distance (DM) between 1D Spectra

The 1D 1H NMR spectra of Rituxan® and Reditux® were used to calculate Mahalanobis distance [47]. The procedure was described previously [27]. Briefly, principal component analysis (PCA) was performed on the spectra of 7 lots of Rituxan® and 3 lots of Reditux®. The spectral regions corresponding to peaks of excipient and solvent were excluded, including regions of 0–0.2 ppm, 0.85–0.95 ppm, 1.15–1.45 ppm, 1.55–1.65 ppm, 1.9–2.1 ppm, 2.2–2.9 ppm, 3.3–6 ppm and 8.45–8.47. The rest of the spectra were binned at 0.01 ppm resolution, resulting in a total of 370 bins with summed spectral intensities within each bin. The summed intensities were subject to integrity checks, sum normalization and Pareto scaling before PCA using MestReNova 14.1 (Mestrelab Research S.L.).

The Mahalanobis distances (*DM*) between the two rituximab DPs were calculated using PC1-3 scores. PCA scores from all the lots of each brand were tabulated as sample matrices of *<sup>A</sup>*m×<sup>p</sup> and *<sup>B</sup>*n×<sup>p</sup> for Rituxan® and Reditux®, respectively, with m or n representing the number of lots and *p* representing the number of principal components used toward *DM* calculation. In the present study, m was 7 for Rituxan®, n was 3 for Reditux® and *p* was 3. The mean vector *<sup>A</sup>*1×*<sup>p</sup>* and covariance matrix *<sup>S</sup>*A,p×<sup>p</sup> was calculated using Rituxan® sample matrix *A*m×p. In parallel, the mean vector *B*1×<sup>p</sup> and covariance matrix *S*B,p×<sup>p</sup> was calculated using Reditux® sample matrix *<sup>B</sup>*n×p. The covariance matrices of the two were averaged per Equation (1) before calculating *DM* using Equation (2). The calculations were performed using MATLAB 9.0 (The MathWorks Inc.) and the code can be found in the Supplementary Materials.

$$S = (\mathbf{m}S\_A + \mathbf{n}S\_B)/(\mathbf{m} + \mathbf{n})\tag{1}$$

$$D\_M = \sqrt{(\overline{A} - \overline{B})S^{-1}(\overline{A} - \overline{B})'} \tag{2}$$

3.3.2. Chemical Shift Difference (Δδ) between 2D Spectra

The 2D 1H-13C NMR spectra of Lantus® and Basaglar® were used to calculate the chemical shift difference (Δδ). A total of 48 methyl peaks were identified with a signal to noise (*s*/*n*) ratio over 10. The peaks were approximately assigned to amino acid residue types of Ala, Thr, Ile, Leu and Val. Within each amino acid residue type, the peaks were labeled with alphabetic letters. The 1H and 13C chemical shift of each brand were averaged from the spectra of the 5 lots, representing the mean chemical shift of the peak in each brand. Chemical shift difference (Δδ) was the difference between the mean values of Basaglar® and Lantus®.
