## 5 Results and Analysis
### Correlation Analyses
#### 5.4.1 Daily Correlation Analysis  
In order to evaluate the correlation between the daily features extracted from sensor data and clinical data, both need to be available in a daily format. The clinical data were collected on a biweekly basis; however, for the purposes of this analysis, they were repeated for every day of the two-week period. For example, if the SIS score collected on week 2 is 25, this score is applied to every day included in the first two weeks of data collection. These metrics were all saved in a csv file. The resulting file containing the daily sensor and clinical features consisted of 90 columns (53 features (5 position features, 5 motion features, 4 heart rate features, 11 sleep features, 5 step features, 23 acceleration features), 9 SIS measurements, 13 Oxford Hip Scores, 13 Oxford Knee Scores, and 2 physical tests features). Next, the correlation analysis was performed following the steps below:  
1. Four different daily-feature csv files were created for each type of clinical data, since the types of data missing for each clinical data were different. For example, in the daily feature file with respect to TUG, the days where TUG was missing were removed. The four resulting daily feature files consisted of the following: (1) daily features with respect to SIS, (2) daily features with respect to TUG, (3) daily features with respect to 30 s chair stand, (4) daily features with respect to Oxford Hip Score and Oxford Knee Score. 2. Using Python programming language and the Visual Studio Code IDE, the Spearman's correlation was calculated for every column of the daily features. In this step, any correlations with a \(p\) value less than 0.05 (statistically significant) were kept, and the rest were marked as \"0\" in the correlation matrix. 3. For each resulting correlation matrix generated in step 2, a second round of analysis was conducted in order to remove redundant features. In this step, every two features with an absolute correlation value higher than 0.90 were deemed as \"redundant\", and one of the two features was removed from the correlation matrix. The resulting daily correlation values after removing the redundancies are presented in this section. The Oxford Hip Score, the Oxford Knee Score, and the two physical tests (TUG and 30 s chair stand) represent the level of functional recovery in this population. The results of the strong correlations in Table 6 indicate that the various items of the Oxford Knee Score and Oxford Hip score, which assess functional physical recovery, had a strong positive correlations with average heart rate during sleep and total motion events. In contrast, only one item on the SIS exhibited a strong correlation with sensor data; however, several moderate correlations between SIS and sensor data were found and are presented in Table 7. The strong positive correlations between the various items of the Oxford scores mean that the higher the participant's score was on the questions on the Oxford Hip Score (Question 11) and Oxford Knee Score (Question 4, 5, 9, 10, and 11), the higher their average heart rate during sleep and the higher their motion count during the day. Conversely, the strong negative correlations between the various items of the Oxford scores mean that the higher the participant's score was on the questions on the Oxford Hip Score (Question 1, 4, and 11), the lower their motion ratio and total motion events were. There also existed a strong negative correlation between the TUG and the total sleep duration, indicating that the longer it takes the participants to complete the TUG test, the shorter their sleep duration is that day/night. The results of moderate correlations between SI and the sensor data are listed in Table 7. Various individual questions of the SIS are moderately positively correlated with average heart rate during the day and during sleep. Notably, the SIS questions related to the number of interactions are positively correlated with average heart rate during sleep and negatively correlated with total sleep duration.