## 3 Results and Discussions  
### Results Summary  
We analyzed 15,359 RR-intervals timeseries of 5 min in this study. Table 2 shows the descriptive statistic of the HRV features extracted from all users in the dataset. In particular, the users shows an average heart rate of about 75 \(\pm\) 14 beats per minute.  
Table 3 shows that the on-time approach (i.e., interpolation on the timestamp of heartbeats) produces more reliable HRV feature estimations compared to the on-duration approach (i.e., interpolation on interval duration between two consecutive heartbeats). In this table we provide the results of the best interpolation approach for each HRV feature and for all the percentages of missing values. The RE and RMSE values provided in this table refer to the error induced by missing values when we compare HRV features obtained from the real RR-intervals timeseries versus the ones obtained from interpolated timeseries. The best interpolation methods provided in Table 3 refer to the ones with lower RE. For all of the HRV features, the highest was the percentage of missing RR-intervals, and also the parameters estimation errors. This was due to the fact that the power spectrum of the RR-intervals signal changes with the number of missing values. The choice of the interpolation method also added different types of noise to the signal. As shown in Table 1, the interpolation on time, or not interpolation at all, produces more reliable HRV features compared to interpolating on duration.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**HRV Features** & **Mean** & **95\% CI** \\ \hline IBI (s) & 0.78 & [0.54, 1.11] \\ PNN50 (n) & 8 & [4, 16] \\ RMSSD (s) & 0.039 & [0.017, 0.36] \\ SD1 (s) & 0.027 & [0.012, 0.26] \\ SD2 (s) & 0.077 & [0.040, 0.25] \\ SDNN (s) & 0.059 & [0.017, 0.25] \\ VLF (s\({}^{2}\)) & 0.87 & [0.22, 4.15] \\ LF (s\({}^{2}\)) & 0.477 & [0.12, 5.57] \\ HF (s\({}^{2}\)) & 0.28 & [0.050, 3.024] \\ total power (s\({}^{2}\)) & 1.91 & [0.53, 21.44] \\ LF/HF (s\({}^{2}\)) & 2.9 & [1.2, 10.2] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Descriptive statistic of hart rate variability (HRV) features. Mean and 95% coefficient intervals (CI) are provided for all the feature.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Missing Values (\%)**} & \multicolumn{3}{c}{**Interpolation**} & \\  & **HRV** & **How** & **Method** & **RE (\%)** & **RMSE** \\ \hline \multirow{8}{*}{30} & RMSSD (s) & No-interpolation & 14.65 & 0.38 \\  & SDNN (s) & Time & quadratic & 9.42 & 0.34 \\  & PNN50 (n) & No-interpolation & 24.37 & 1.51 \\  & SD1 (s) & No-interpolation & 14.68 & 0.27 \\  & SD2 (s) & Time & quadratic & 8.57 & 0.47 \\  & VLF (s\({}^{2}\)) & Time & quadratic & 14.50 & 0.82 \\  & LF (s\({}^{2}\)) & Time & quadratic & 26.87 & 2.01 \\  & HF (s\({}^{2}\)) & Time & quadratic & 32.18 & 4.48 \\  & LF/HF (s\({}^{2}\)) & Time & cubic & 41.39 & 1.73 \\  & total power (s\({}^{2}\)) & Time & quadratic & 17.16 & 6.26 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Best performing interpolation approach (i.e., with low RE) for each HRV feature in each percentage of missing values evaluated. The error in estimating HRV features is reported using RE and root mean squared error (RMSE).  
The lowest errors on HRV features estimation with missing RR-intervals are obtained using the no-interpolation or the interpolation on time approaches, while the interpolation on duration approach consistently yields the worst results (Table 3). Even if low timeseries difference were detected in simulated linear interpolation on time (Figure 4 and Table 1), Table 3 suggests that the best interpolation method depends of the HRV features that we want to assess. Moreover, this table also shows that, as suspected, the higher is the percentage of missing values, the higher is also the HRV feature estimation error (i.e., RE and RMSE).