## 5 Conclusions  
In this study, we used the Beer-Lambert law to estimate \(HbA1c\) noninvasively from the fingertip by considering only two wavelengths. In our previous work [14], three wavelengths were used, which made the system relatively complex. Obtaining nearly the same performance, as seen from Table 4, while reducing complexity was the main contribution of this study. To this end, two ratio calibrations were used to obtain results comparable to those of the previous study. In the ratio calibrations, two XGBoost models were used: one for \(SpO_{2}\) and the other for \(HbA1c\). The Pearson's r values for the estimated \(HbA1c\) values were 0.896 and 0.905 considering the ratio calibrations with the blood vessel and whole finger models, respectively. When value (\(HbA1c\)) calibrations were applied in addition to ratio calibrations, we could further improve the performance, and the Pearson's r values of the estimated \(HbA1c\) levels were 0.929 and 0.930 for the blood vessel and whole finger models, respectively. Further, as in the previous study, the whole finger model performed slightly better than the blood vessel model, as shown in Table 4. We also showed that the RCF score of \(SpO_{2}\) estimated in this study was nearly the same as that of the previous study (whole finger model). We expect that further studies using larger datasets and deep learning techniques can improve these results. The performance can also be improved by calibration in a more controlled manner, paying more attention to factors such as light scattering, finger-width variability, and data filtering. We also note that there is considerable potential for further research on the noninvasive estimation of \(HbA1c\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**MethodMetric** & **MSE** & **ME** & **MAD** & **RMSE** & **RCF** \\ \hline Previous (blood vessel) [14] & 4.038 & 0.178 & 1.676 & 2.010 & 0.983 \\ Previous (whole finger) [14] & 2.924 & \(-\)0.246 & 1.395 & 1.710 & 0.986 \\ Proposed & 2.831 & \(-\)0.089 & 1.392 & 1.683 & 0.986 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(SpO_{2}\) estimation performance comparison between this study and the previous study. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Metric** & **Bias** & **Limit of Agreement** & **Data Points Out of** \\ \multicolumn{4}{c}{} \\ Previous (blood vessel) [14] & \(-\)0.178 \(\pm\) 2.002 & \(-\)3.74 to 4.10 & 0 \\ Previous (whole finger) [14] & \(-\)0.246 \(\pm\) 1.690 & \(-\)3.56 to 3.07 & 0 \\ Proposed & \(-\)0.0894 \(\pm\) 3.293 & \(-\)3.38 to 3.20 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Bland-Altman-analysis-based comparison between this study and the previous study for estimating \(SpO_{2}\). **Author Contributions:** M.S.T. : conceptualization, methodology, software, and writing--original draft; T.-H.K. : formal analysis; H.K. : resources and validation; K.-D.K. : validation, supervision, project administration, and funding acquisition. All authors have read and agreed to the published version of the manuscript. **Funding:** This work was supported by the National Research Foundation (NRF) of Korea, funded by the Ministry of Science and ICT (2022R1A5A7000765), and it was also supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea, funded by the Ministry of Education (NRF-2022R1A2C2010298). This research was also supported through the Korea Industrial Technology Association (KODTA), funded by the Ministry of Science and ICT (MSIT). **Institutional Review Board Statement:** All protocols and procedures in this study were approved by the Institutional Review Board (IRB) of Kookmin University, Seoul, Republic of Korea (approval date: 17 July 2020). The procedures followed the Helsinki Declaration of 1975, as revised in 2008. All human participants agreed in advance to participate and share their data for academic research purposes. The IRB protocol number is: KMU-202006-HR-237.