Since we needed to respectively detect steps on the acceleration signals collected by wearable devices and mobile phones, we chose to use the step detection algorithm [43], which was based on mobile phones (Figure 1). Given a segment of 3-axis acceleration signals (x_i, y_i, z_i), the magnitude of the acceleration of the segment of acceleration signals was calculated to combine 3D signals to a single series, r_i, where . The magnitude of the acceleration signals does not depend on the orientation and tilt of the mobile phone during walking [43]. Subsequently, r_i was filtered by a weighted moving-average filter to remove noise (Equation 1, w=150 milliseconds). Next, the filtered r_i was subtracted by the mean of r̄_i to make r̄_i symmetric to the x-axis. We calculated two new series, B1_i and B2_i, based on two thresholds to detect the walking swing phase and stance phase, respectively (see Equations 2 and 3). If a swing phase ends and a stance phase starts, we can identify a step that occurred. The formal detection rule of a step S_i at sample i is that the following two conditions must be satisfied: (1) a change from –0.5 to 0 in B1 (B1_i=0 and B1_i–1=0.5); (2) there is at least one detection of B2=–0.5 in a window of size w=150 milliseconds in sample i (Min(B2_i:i+w)=–0.5).

Then, the gait cycle series could be derived by calculating time intervals between consecutive steps, which was denoted as Cycles. During each gait cycle, the amplitude from the peak to the valley of the magnitude of the acceleration signals was used to reflect the gait force of each step. The force of all steps in the given acceleration signal was denoted as the series Force.

For the LTMM data set, Spearman coefficients [50] were calculated to assess associations between the GDS-15 score and gait features (3 laboratory gait features and 12 long-term gait features). As the data in the RADAR-MDD-KCL data set are longitudinal (repeated PHQ-8 measurements for each participant), a series of pairwise linear mixed-effects regression models [51] with random participant intercepts were performed to explore the association between the PHQ-8 score and each of the 12 long-term gait features (no laboratory tests were included in the RADAR-MDD-KCL data set). Age, gender, and the number of comorbidities (see Table S1 in Multimedia Appendix 1) were considered as covariates. The Benjamini-Hochberg method was used for multiple-comparison corrections in both data sets [52].

To test whether long-term gait features could explain additional data variance in depression scores relative to laboratory gait features, we built two nested multivariate linear regression models without and with long-term gait features for the GDS-15 score (denoted as Model A and Model B; Equations 4 and 5) in the LTMM data set. Specifically, predictors of Model A are age, gender, and the 3 laboratory gait features, while predictors of Model B are age, gender, the 3 laboratory gait features, and the 12 long-term gait features. The coefficient of determination (R²) was calculated for both models to estimate how much data variance was explained by predictors. Then, the likelihood ratio test [53] was used to test whether Model B fit the GDS-15 score better than Model A. Since the laboratory walking test was not included in the RADAR-MDD-KCL data set, the likelihood ratio test was only performed in the LTMM data set.

The 71 participants in the LTMM data set have a mean age of 78.36 (SD 4.71) years with 18 (25%) participants having potential depressive disorders (GDS-15≥5) and 69.82 (SD 9.65) hours of acceleration signals per participant. The RADAR-MDD-KCL data set, according to the data inclusion criteria, contains 659 PHQ-8 records collected from 215 participants and corresponding 99,445 hours (average 463 hours per participant). The cohort in the RADAR-MDD-KCL data set has a mean age of 43.36 (SD 15.12) years with the majority being women (75%), and half of the PHQ-8 records indicated potential depression symptoms (PHQ-8≥10). The average missing rate of acceleration signals collected by phones in the RADAR-MDD-KCL data set (70.60%) was significantly higher than that of the acceleration signals collected by the wearable device in the LTMM data set (3.03%). A summary of the demographics, and distributions of depression scores and available acceleration signals for participants in the LTMM and the RADAR-MDD-KCL data sets is shown in Table 2. The heatmaps of correlations between the 12 long-term gait features of the LTMM and RADAR-MDD-KCL data sets are presented in Figure 3.

The Spearman correlations between the GDS-15 score and gait features (both laboratory and long-term gait features) in the LTMM data set are shown in Table 3. We found that a higher GDS-15 score was significantly correlated with a larger median of gait cycles, lower peak frequency, and smaller median gait force in the 1-minute laboratory walking test. For the long-term period, a higher GDS-15 score was significantly correlated with lower variance of gait force and slower cadence of high-performance walking and 75th percentile of peak frequency during 3-day activities.

The pairwise linear mixed-effects models performed in the RADAR-MDD-KCL data set revealed a significant and negative link between the PHQ-8 score and the gait cadence of high-performance walking during the 14 days before submitting PHQ-8 records. Specifically, the 25th percentile of median cycle was positively associated with the PHQ-8 score; that is, for every increase of 0.1 seconds in the median gait cycle of high-performance walking, the PHQ-8 score increased by 0.606 points. Likewise, the 75th percentile of peak frequency was negatively associated with the PHQ-8 score, indicating that a reduction of 0.1 Hz in the peak frequency of high-performance walking was associated with an increase of 0.26 PHQ-8 points. Other long-term gait features were not found to be significantly associated with the PHQ-8 score in the RADAR-MDD-KCL data set. A summary of all 12 linear mixed-effects regression models is provided in Table 4.

The regression model with long-term gait features (Model B) achieved better performance (R²=0.30) than the model without long-term gait features (Model A) (R²=0.06). We found that the 12 long-term gait features extracted from 3-day activities could explain an extra 24% data variance (an increase of 0.24 in R²) of GDS-15 scores relative to the laboratory gait features and participants’ demographics. The likelihood ratio test showed that Model B fitted GDS-15 scores significantly better than Model A (χ²=32.91>χ²_0.05(12), P=.001). The detailed results of the two nested regression models are shown in Table S2 of Multimedia Appendix 1.

This study retrospectively used two ambulatory data sets for exploring the associations between depression symptom severity and daily-life gait characteristics. We extracted 12 long-term gait features to describe the distribution and variance of gait cadence and force over a long-term period and link daily-life gait patterns with a self-reported depression score. The main findings of this study are (1) higher depression symptom severity is significantly associated with lower gait cadence of high-performance walking (faster walking in all continuous walking segments) over a long-term period; (2) long-term daily-life walking has the potential to provide additional information for predicting depression symptom severity relative to laboratory gait characteristics and demographics; and (3) wearable devices and mobile phones both have potential to capture the associations between daily gait and depression.

The results of Spearman correlations between laboratory gait features and the GDS-15 score in the LTMM data set are consistent with previous studies [17-25]; that is, the participants with more severe depression symptoms were more likely to have slower gait cadence (longer median of gait cycles and lower gait frequency) and smaller gait force in laboratory walking tests.

For daily-life walking, this study used the faster walking (75th percentile of peak frequency and 25th percentile of median cycle) in all detected continuous walking segments to represent high-performance walking during a feature window (3 days for LTMM and 14 days for RADAR-MDD-KCL). Only gait cadence of high-performance walking was found to be significantly and negatively associated with depression symptom severity, whereas gait patterns under medium/low-performance walking were not significantly associated with the depression score. This finding was consistent in both the LTMM and RADAR-MDD-KCL data sets. A potential reason is that the walking performance in real-world scenarios may be affected by multiple factors (such as walking during the day or at night, walking under fatigue or walking after rest, and walking to a destination or navigating a crowded supermarket) [29]; therefore, the lower walking performance may not fully reflect the participant’s physical or mental conditions. Therefore, from the main finding of this study, we speculated that faster steps over a long-term period could represent the high performance of participants’ walking, which could be closely associated with their depression status.

In the LTMM data set, we found that the variance of gait force (SD of median force) in 3-day activities was significantly and negatively associated with the depression symptom severity, indicating that participants with higher depression symptom severity were likely to have relatively monotonous walking over 3 days. However, the feature was not significantly associated with the PHQ-8 score in the RADAR-MDD-KCL data set. One reason is that the magnitude (r_i) (explained in the Step Detection Algorithm section) of the acceleration signals depends on the location of the accelerometers attached to the body [54]. As acceleration signals in the RADAR-MDD-KCL data set were collected by mobile phones, the variable locations of phones when attached to participants’ bodies (such as in the hand, handbag, and pocket) affected the magnitude of acceleration signals. Therefore, the magnitude of phone-collected acceleration signals cannot fully reflect the gait force.

Results of regression models and the likelihood test in the LTMM data set illustrated the importance of monitoring daily-life gait in real-world settings. Laboratory gait features and demographics in LTMM data only explained a small proportion of data variance of the GDS-15 score (R²=0.06), whereas long-term gait features extracted from 3-day activities could explain an extra 24% of data variance (R²=0.30). This finding supported that long-term daily-life walking has the potential to provide additional information for predicting depression symptom severity relative to laboratory gait characteristics and demographics. Further, this finding also indicated that the laboratory walking test may be affected by several factors such as subjective psychological factors and laboratory-controlled conditions, which may not fully reflect the condition of a participant’s mental health [27,29]. Since there were no laboratory tests in the RADAR-MDD-KCL data set, the comparison between laboratory gait features and long-term daily-life gait features was not performed in the RADAR-MDD-KCL. We will consider adding laboratory tests at enrollment in future digital depression studies.

Although we found that wearables and mobile phones have the potential to capture the associations between depression and daily-life gait patterns, both devices have some limitations. Wearables could collect relatively complete walking data; however, wearing sensors may not be suitable for long-term monitoring. Mobile phones could be used for long-term monitoring without user burden, but the missing rate of mobile phone acceleration signals is relatively high. The findings of this study support that the links between gait and depression could still be revealed from the limited and sparse daily-life walking acceleration signals. Missingness is a common challenge in remote digital studies [55], which may be caused by high battery consumption, network traffic for uploading the raw acceleration signals, and the Android operating system moderation of resources. According to the findings of this study, a possible solution to reduce missingness is uploading gait cycles instead of uploading raw acceleration signals in future long-term monitoring research. This is not difficult to implement, as most current smartphones have real-time step detection functions or apps [56,57]. Furthermore, the self-reported PHQ-8 data may be subject to recall bias. We may consider implementing ecological momentary assessments with passive gait data collection in future research.

The hyperparameters in step detection and feature extraction need further investigation. We considered using a 1-minute window size for step detection and 50 seconds for continuous walking segment selection based on previous studies [34,44] and our experience. The feature window sizes for the two data sets are different due to the different study designs. However, the optimal hyperparameters are still unclear and will be investigated in future research.

Gait features extracted in this study were simple and statistically based, which were used to illustrate the importance of daily walking in our initial analysis. More features such as nonlinear features will be considered in future research.

Gait characteristics could be affected by some physical diseases, neurological disorders, and age [58-60]. Although none of the participants had any cognitive or gait/balance disorders in the LTMM data set and the number of comorbidities and age were considered as covariates in the RADAR-MDD-KCL data set, physical comorbidities and other comorbidities may have different impacts on the gait characteristics. We will consider a wider range of comorbidities and investigate them further in future research.

In summary, the findings of this study showed that significant links between depression symptom severity and daily-life gait characteristics could be captured in different data sets and by different accelerometer devices. Long-term daily-life walking patterns could provide additional value for understanding depression manifestations relative to gait patterns in laboratory walking tests, which illustrated the importance of long-term gait monitoring. The gait cadence of high-performance walking in daily life has the potential to be an indicator for monitoring depression severity, which may contribute to developing clinical tools to remotely monitor mental health in real-world settings.