Influence of sample size, content range, and sample removal on slope and bias correction in Fourier-transform mid-infrared spectroscopy for milk fatty acids.

This study examined how calibration sample size, fatty acid (FA) content range, and sample removal threshold influence the performance of slope and bias correction (SBC) during calibration transfer for Fourier-transform mid-infrared (FT-MIR) prediction of milk FA. A total of 143 producer milk samples, consisting of 92 individual cow milk samples and 51 bulk tank milk samples, were analyzed using FT-MIR spectroscopy and gas chromatography reference analysis. Prediction accuracy was first evaluated for de novo, mixed, and preformed FA using all 143 samples before and after SBC. De novo and mixed FA showed high prediction accuracy before SBC, with relative root mean square error (relRMSE) values of 4.46% and 7.85%, respectively, and only marginal improvements after SBC. In contrast, preformed FA showed lower initial prediction accuracy, with relRMSE decreasing from 17.6% before SBC to 5.81% after SBC. Therefore, subsequent numerical simulations focused on preformed FA. Calibration subsets of 3 to 30 samples were generated by 100,000 random samplings for each subset size, and SBC performance was evaluated with and without sample removal based on relative difference thresholds of 20 to 90%. The proportion of iterations achieving acceptable prediction accuracy (relRMSE ≤10%) generally increased with calibration subset size and was improved by moderate sample removal thresholds. At n = 7, moderate removal thresholds yielded acceptable accuracy in approximately 95% of iterations, suggesting that n = 7 may be a minimum practical candidate. More stable performance was observed at n ≥ 10, and n ≥ 15 achieved acceptable accuracy in almost all iterations under most conditions. Although wider FA content ranges were generally obtained as calibration subset size increased, subsets with the widest content range did not necessarily show the highest prediction accuracy, indicating that content range alone does not determine SBC performance. These findings indicate that effective SBC requires calibration subsets that represent not only FA content range but also the prediction error structure of the target population. The results provide practical guidance for constructing efficient calibration subsets for routine FT-MIR milk FA analysis.