## 3 Results
### Classification Performance with Time Gap Variation  
In this section, we reveal the time gap variation \(T_{TP}\) results. We studied the time gap from AKI onset to 48 h \(T_{TP}=[0,48]\) before onset using a feature window size of 24 h \(T_{FW}=24\). This is critical for identifying the most important point of time between slight AKI signs and emerging AKI oscillation. We compared the accuracy, AUROC, and NRI performance of \(V_{entropy}\), \(V_{mean}\), \(V_{variance}\), and \(V_{merge}\). The Model performance results are shown in Figure 5. It was shown in AUROC that the \(V_{merge}\), \(V_{mean}\) and \(V_{variance}\), performed steadily with different time gap variation. \(V_{entropy}\) performed better when time gap is longer.  
Figure 6 shows the F value from F test of AUROC along with the time gap. The F value on AUROC showed that the peak in F value was at 30 h; namely 30 h was the point that contributed the most information and was the turning point from slight AKI signs to emerging AKI oscillation. Therefore, clinicians may consider the patient has higher risk of having AKI onset. The overall model performance increased drastically, when starting at this point in time. The trend was most obvious in NRI for both \(V_{entropy}\) and \(V_{merge}\). As the NRI seeks to quantify whether a new marker provides clinically relevant improvements in model prediction, this result indicates that when passing the critical point of 30 h, the shorter the time gap and the more information available, the better the models performed.  
Figure 5: Visualization plot for time gap variance on AUROC, Accuracy and NRI performance.  
As 30 h was the critical point of time between slight AKI signs and rapid AKI oscillation, as shown in in Tables 9 and 10, we conducted a comparison between using a time gap of less than 30 h (after critical point, rapid AKI oscillation) and a time gap of more than 30 h (before critical point, slight AKI signs). Statistically significant differences (\(p<0.01\)) were observed in and \(V_{entropy}\) in AUROC; \(V_{entropy}\) and \(V_{merge}\) inaccuracy, NRI and precision. \(V_{entropy}\) and \(V_{mean}\) in Recall  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Feature Types** & \multicolumn{3}{c}{**AUROC Mean (STD)**} & \multicolumn{3}{c}{**Accuracy(\%) Mean (STD)**} \\ \hline \multirow{2}{*}{**Time Gap**} & **Before** & **After** & \multirow{2}{*}{\(p\)**Value**} & **Before** & **After** & \multirow{2}{*}{**\(p\)Value**} \\  & **Critical** & **Critical** & & & & **Critical** & \\  & **Point** & & & & **Point** & & **Point** \\ \hline Shannon & 55.74 & 53.88 & \(p<0.01\) ** & 60.57 & 58.42 & \(p<0.01\)** \\ entropy & (0.89) & (1.44) & (1.04) & (1.44) & & \\ Mean & 60.82 & 59.49 & \(p<0.05\) * & 59.98 & 59.51 & 0.19 \\  & (1.37) & (0.99) & & (0.46) & (0.69) & \\ Variance & 55.72 & 55.1 & 0.25 & 58.31 & 58.45 & 0.65 \\  & (1.24) & (0.94) & & (0.35) & (0.82) & \\  & (66.76 & 66.33 & 0.4 & 64.7 & 64.18 & \\  & (0.67) & (0.99) & & (0.44) & (0.58) & \\ \hline \hline \end{tabular}  
*: \(p<0.05\); **: \(p<0.01\).  
\end{table}
Table 10: Comparison between using a time gap of less than 30 h (rapid AKI oscillation) and a time gap greater than 30 h (slight AKI signs) on Recall, and Precision.  
Figure 6: Visualization plot for time gap variance F value from F test on AUROC.