## 4 Discussion  
To the best of our knowledge, this is the first study to examine age estimation methods based on brain MR images using deep learning over a wide age range from young people, including infants, to elderly individuals. Therefore, we were concerned that the age estimation would be affected by the difference in the head standard due to the age range of the target population, but we did not observe any decrease in accuracy even after data augmentation by scaling down/equalizing the images. In fact, the accuracy of age estimation improved as the number of data increased with the implementation of data augmentation, and we expect further improvement in accuracy by adding more data, including data in age ranges where data are lacking, and increasing the number of data through further implementation of data augmentation methods. A further increase in the number of data is expected to improve the accuracy. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**ALL\_Model**} & \multicolumn{2}{c}{**Male\_Model**} & \multicolumn{2}{c}{**Female\_Model**} \\ \cline{2-7}  & **With CC** & **Without CC** & **With CC** & **Without CC** & **With CC** & **Without CC** \\ \hline MAE & 5.2508 & 7.7777 & 6.3234 & 8.0344 & 5.7555 & 8.4124 \\ RMSE & 6.4215 & 9.2961 & 7.7338 & 9.6469 & 7.0057 & 10.201 \\ Radius2 & 0.96425 & 0.93054 & 0.94582 & 0.91073 & 0.93945 & 0.91764 \\ Radius2 & 0.92986 & 0.86602 & 0.89513 & 0.82725 & 0.88257 & 0.84228 \\ Slope & 0.78307 & 0.62174 & 0.75018 & 0.63040 & 0.75067 & 0.63020 \\ Intercept & 4.7428 & 11.520 & 4.9793 & 11.436 & 6.0545 & 9.3505 \\ \hline CC: corpus callosum. & & & & & & \\ \end{tabular}
\end{table} 
Table 6: Change in accuracy before and after deletion of the corpus callosum region. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Female\_Model**} \\ \cline{2-5}  & **Model\_A** & **Model\_B** & **Model\_C** & **Model\_D** & **Model\_E** \\ \hline \multirow{4}{*}{Male\_Model} & Model\_A & \(p=0.0007\) & \(p=0.6734\) & \(p=0.7517\) & \(p=0.9815\) & \(p=0.0037\) \\  & Model\_B & \(p=0.0817\) & \(p=0.0328\) & \(p=0.1345\) & \(p=0.0808\) & \(p=0.2647\) \\ \cline{1-1}  & Model\_C & \(p<0.0001\) & \(p=0.5071\) & \(p=0.1957\) & \(p=0.2895\) & \(p=0.0001\) \\ \cline{1-1}  & Model\_D & \(p=0.0537\) & \(p=0.0513\) & \(p=0.1949\) & \(p=0.1147\) & \(p=0.1889\) \\ \cline{1-1}  & Model\_E & \(p=0.1766\) & \(p=0.0017\) & \(p=0.0201\) & \(p=0.0068\) & \(p=0.3877\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Wilcoxon rank sum test. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **ALL\_Model** & **Male\_Model** & **Female\_Model** \\ \cline{2-5}  & _p Value_ & _p Value_ & _p Value_ \\ \hline Model\_A & \textless{}0.0001 & 0.0001 & 0.2523 \\ Model\_B & \textless{}0.0001 & 0.0825 & \textless{}0.0001 \\ Model\_C & \textless{}0.0001 & \textless{}0.0001 & \textless{}0.0001 \\ Model\_D & \textless{}0.0001 & 0.0025 & \textless{}0.0001 \\ Model\_E & \textless{}0.0001 & 0.0048 & 0.0046 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the Wilcoxon rank sum test. Compared with previous studies, the results of MAE are inferior to those of the previous studies, whereas the results of correlation coefficients are comparable to those of previous studies. [PERSON] et al. [32] reported the results of age estimation using 2D images segmented into gray matter and white matter in the axial, sagittal, and coronal sections. The results show that the best estimation accuracy is obtained for the combination of sagittal and GM, recording 3.57 years, which exceeds the MAE of 5.25 years in the present study. [PERSON] et al. [31] also reported an age estimation method for 10,691 subjects, which is 10 times larger than the present study, although using 3D brain MR images. In this report, the MAE was 3.21 years, which is approximately two years less than that of the present study.