This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in JMIR mHealth and uHealth, is properly cited. The complete bibliographic information, a link to the original publication on https://mhealth.jmir.org/, as well as this copyright and license information must be included.
Depression is a prevalent mental health challenge. Current depression assessment methods using self-reported and clinician-administered questionnaires have limitations. Instrumenting smartphones to passively and continuously collect moment-by-moment data sets to quantify human behaviors has the potential to augment current depression assessment methods for early diagnosis, scalable, and longitudinal monitoring of depression.
The objective of this study was to investigate the feasibility of predicting depression with human behaviors quantified from smartphone data sets, and to identify behaviors that can influence depression.
Smartphone data sets and self-reported 8-item Patient Health Questionnaire (PHQ-8) depression assessments were collected from 629 participants in an exploratory longitudinal study over an average of 22.1 days (SD 17.90; range 8-86). We quantified 22 regularity, entropy, and SD behavioral markers from the smartphone data. We explored the relationship between the behavioral features and depression using correlation and bivariate linear mixed models (LMMs). We leveraged 5 supervised machine learning (ML) algorithms with hyperparameter optimization, nested cross-validation, and imbalanced data handling to predict depression. Finally, with the permutation importance method, we identified influential behavioral markers in predicting depression.
Of the 629 participants from at least 56 countries, 69 (10.97%) were females, 546 (86.8%) were males, and 14 (2.2%) were nonbinary. Participants’ age distribution is as follows: 73/629 (11.6%) were aged between 18 and 24, 204/629 (32.4%) were aged between 25 and 34, 156/629 (24.8%) were aged between 35 and 44, 166/629 (26.4%) were aged between 45 and 64, and 30/629 (4.8%) were aged 65 years and over. Of the 1374 PHQ-8 assessments, 1143 (83.19%) responses were nondepressed scores (PHQ-8 score <10), while 231 (16.81%) were depressed scores (PHQ-8 score ≥10), as identified based on PHQ-8 cut-off. A significant positive Pearson correlation was found between screen status–normalized entropy and depression (
Our findings demonstrate that behavioral markers indicative of depression can be unobtrusively identified from smartphone sensors’ data. Traditional assessment of depression can be augmented with behavioral markers from smartphones for depression diagnosis and monitoring.
Depression is one of the most prevalent, complex, and heterogeneous mental health challenges of our time. In 2020, the World Health Organization (WHO) estimated that depression has impacted 264 million people worldwide [
For the past 30 years, clinician-administered and self-reported questionnaires remain the gold standard in the assessment and diagnosis of depression [
Today, smartphones and wearables offer a unique opportunity to overcome limitations in traditional depression assessment methods. Smartphones and wearables (eg, Fitbit, Oura Rings, and smartwatches) have become ubiquitous in the global population, they are inherently personal, and people are continuously monitored through their embedded sensors (eg, camera, accelerometer, global positioning system [GPS], Bluetooth, and many more) [
A growing body of research in smartphone and wearable sensing, human behavior modeling has improved our understanding of the relationship between mental health and biomarkers [
In the StudentLife study [
Another promising source of biomarkers is wearable devices [
Actigraphy-based biomarkers that quantify time sequences of rest and active behaviors with accelerometer sensors are known to be useful in predicting mood disorders such as depression and bipolar disorder [
Taken together, previous research has shown the potential of quantifying human behavior from smartphones and wearables data set as biomarkers. These biomarkers are insightful in understanding depression.
In this study, we aim to investigate the feasibility of predicting depression using digital biomarkers quantified from a smartphone data set. To this end, we explore the relationship between digital biomarkers and depression severity with statistical methods. We investigate whether depression can be predicted with digital biomarkers using supervised ML algorithms.
We utilized an existing data set collected in a longitudinal observational study with the Carat app [
The Carat app is a mobile sensing app, originally developed by a team of researchers from the University of Helsinki and the University of California, Berkeley, for smartphone energy consumption research [
The data set used in this study was a subset of the large-scale crowdsourced Carat app data set from anonymous volunteers. The study data set was collected for a multifaceted purpose, which includes studying the relationship between smartphone app usage and Big 5 personality traits [
All participants in this data set are Android-based smartphone users, who explicitly and voluntarily gave their consent from their mobile devices after they were informed about the purpose of the data collection, the data collection procedures, and management of the data set. The data set does not contain personally identifiable information, and was collected under the institutional review board license from the University of California, Berkeley and the University of Helsinki [
Besides battery consumption data, the Carat Android app unobtrusively collected participants’ time zone and time-stamped data, including foreground app usage (ie, app the participant has interacted with), internet connectivity (ie, connected and disconnected states), and screen lock and unlock logs. This data set was sampled at each 1% battery change (ie, while charging or discharging) on the participants’ smartphone. The Carat app also collected participant’s demographic information, including age, gender, education, and occupation via a self-report.
In addition to the mobile sensing and demographic variables, depression severity was assessed by a self-report instrument. Participants answered the 8-item Patient Health Questionnaire (PHQ-8) [
For each participant’s data set, we excluded days with at least 10 missing log intervals (ie, days where no data were logged by the Carat app for at least 10% battery charging or discharging periods). Next, we only included PHQ-8 responses from participants with at least 8 days of data within the preceding 2 weeks of PHQ-8 response. Consequently, the final data contained 629 participants, 1374 PHQ-8 responses with 13,898 days of participants’ data set.
Our data set is primarily categorized into screen status, internet connectivity, and foreground app usage logs. For data preprocessing, we converted the time stamps of the data set to local date and time, using the participants’ time zone. We computed digital biomarkers (herein features) by quantifying the per-participant hourly and daily behavioral patterns (ie, routines, irregularity, variability) from these data sets with simple counts, SDs, entropy [
We computed entropy to capture the degree of variability, complexity, disorder, and randomness in the participant behavior states from screen status (ie, on and off states), internet connectivity (ie, disconnected and connected states), and foreground app (ie, the frequency of use per app) over a 24-hour period of each day. Entropy was calculated using the Shannon entropy [
where
Regularity index quantifies routines in participant behaviors by capturing the similarity (or difference) in participant behaviors between the same hours across different days. For internet connectivity, for instance, the regularity index quantifies the routineness of the participant’s internet connectivity behavior at the same hours (eg, every 9 am) for all days. We determined the hourly values as follows: for screen status, the modal screen status for each hour; for internet connectivity, the modal connectivity state for each hour; and for foreground app usage, the number of distinct apps usage for each hour.
Following the regularity index computation method of Wang et al [
where
The SD features capture the variance of daily behavior between 4-day epochs based on the hour of the day. We defined morning as the 6-11th hour, afternoon as the 12-17th hour, evening as the 18-23rd hour, and night as the 0-5th hour of the day. We computed the count of each screen status, the count of each internet connectivity status, and the count of foreground app usage per day epoch. With these counts per day epoch, we computed the SD per day.
We also computed the day level count of each screen status, the count of each internet connectivity status, and the count of foreground app usage. Additionally, we computed the count of minutes until the first and last use of foreground app per day.
Before beginning the statistical analysis, we pooled (ie, aggregated) the extracted features within the preceding 2 weeks (ie, assessment window) of each PHQ-8 response from a participant. The pooling is to ensure that the timelines of the feature variables in the analysis are aligned with those of the PHQ-8 assessment window. The pooling was done as follows: for each PHQ-8 response, we pooled all entropy and regularity index features by computing the average feature values for all days within the PHQ-8 assessment window. Instead of average values for SD, we took a different approach due to the additive properties of SD measures. For SD features, we computed the pooled SD [
For correlation analysis, we used the pooled data to quantify the linear relationship between the features and depression severity (ie, PHQ-8 responses). The correlations were computed using the Pearson correlation coefficient. Full information maximum likelihood [
For association analysis, we used the bivariate linear mixed model (LMM) [
In the LMM, we used multiple imputation to handle missing data, taking into account the nested structure of the data set [
We developed population-based supervised ML classifiers to explore how the digital biomarkers/features predict the depression state of an individual. We also explored whether including participants’ self-reported demographics as features would improve the ML classifier performance.
To this end, we used 5 supervised ML models: random forest (RF), support vector machine (SVM) with radial basis function (RBF) kernel, XGBoost (XGB) [
All the ML modeling was performed using stratified and nested cross-validation [
The hyperparameter optimization in the inner cross-validation was done with grid search over a grid of parameters, where all combinations of hyperparameters are exhaustively considered. We use the F1 (macro averaged) score to select the most optimized hyperparameters.
It is worth noting that in the ML setup, we used stratified sampling in the nested cross-validation. The stratified sampling ensures the splitting of the data set into folds that have an equal proportion of each class (ie, labels 1 and 0). However, the proportion of each class is still dependent on its availability in the data set. We handled class imbalance in the training data set with the synthetic minority over-sampling technique (SMOTE) [
We used the permutation importance method [
We created 2 baseline classifiers to benchmark the performance of the ML classifiers. The first baseline is a random weighted classifier (RWC) with 10,000 randomly generated predictions based on a multinomial distribution of the nondepressed and depressed classes. The second baseline is a decision tree (DT) classifier trained using the same approach as the ML classifiers, but with age group and gender as features. The performance of the ML classifiers and baseline classifiers was measured using the following performance metrics: accuracy, precision, recall, AUC, F1 score, and Cohen κ. The precision, recall, and F1 scores were computed with an emphasis on predicting the depressed score (ie, label 1).
Data preprocessing and feature extraction pipeline were created with Python (version 3.7.6) and R (version 4.0.2) programming languages, using Snakemake [
Self-reported demographic data from the 629 participants included in our analyses show that 69/629 (10.97%) were females, 546/629 (86.8%) were males, and 14/629 (2.2%) were nonbinary or preferred not to disclose their gender.
For the participants’ age distribution, 73/629 (11.6%) were aged between 18 and 24, 204/629 (32.4%) were aged between 25 and 34, 156/629 (24.8%) were aged between 35 and 44, 166/629 (26.4%) were aged between 45 and 64, and 30/629 (4.8%) were aged 65 years and over. The participants were distributed across at least 56 different countries, including 91/629 (14.5%) from unknown countries, 199/629 (31.6%) from the USA, 66/629 (10.5%) from Finland, 32/629 (5.1%) from Great Britain, 42/629 (6.7%) from Germany, and 29/629 (4.6%) from India. The data set also has participants from varied educational and occupational backgrounds.
Summary statistics of participants who were included in the data analysis (N=629).
Variable | Value, n (%) | ||
|
|
||
|
18-24 | 73 (11.6) | |
|
25-34 | 204 (32.4) | |
|
35-44 | 156 (24.8) | |
|
45-64 | 166 (26.4) | |
|
≥65 | 30 (4.8) | |
|
|
||
|
Female | 69 (11.0) | |
|
Male | 546 (86.8) | |
|
Other or Rather not tell | 14 (2.2) | |
|
|
||
|
Elementary school/basic education | 9 (1.4) | |
|
High school/sixth form/other upper secondary level | 98 (15.6) | |
|
No education or rather not to tell | 5 (0.8) | |
|
Professional graduate degree/higher university degree (master’s or equivalent) | 193 (30.7) | |
|
Research graduate degree (PhD or equivalent) | 34 (5.4) | |
|
Undergraduate degree/lower university degree (bachelor’s or equivalent) | 228 (36.2) | |
|
Vocational school/trade school/other education leading to a profession | 62 (9.9) | |
|
|
||
|
Agricultural forestry or fishery | 1 (0.2) | |
|
Clerical support | 14 (2.2) | |
|
Craft and trade or plant and machine operations | 8 (1.3) | |
|
Entrepreneur or freelancer | 30 (4.8) | |
|
Manager | 59 (9.4) | |
|
No suitable option or rather not to tell | 34 (5.4) | |
|
Professional | 227 (36.1) | |
|
Retired | 39 (6.2) | |
|
Sales or services | 29 (4.6) | |
|
Staying at home (eg, with kids) | 5 (0.8) | |
|
Student | 74 (11.8) | |
|
Technician or associate professional | 90 (14.3) | |
|
Unemployed or between jobs | 19 (3.0) | |
|
|
||
|
Unknown | 91 (14.5) | |
|
USA | 199 (31.6) | |
|
Finland | 66 (10.5) | |
|
Great Britain | 32 (5.1) | |
|
Germany | 42 (6.7) | |
|
Canada | 16 (2.5) | |
|
India | 29 (4.6) | |
|
Othera | 154 (24.5) |
aComprising 49 different countries with less than 15 participants, including South Africa, Morocco, Brazil, Philippines, Qatar, Japan, Russia, and Denmark.
We had 1374 PHQ-8 responses.
For the distribution of the PHQ-8 scores, 1143/1374 (83.19%) responses were nondepressed scores (PHQ-8 score <10), while 231/1374 (16.81%) were depressed scores (PHQ-8 score ≥10). The mean PHQ-8 score is 5.19 (SD 5.22; range 0-24).
The number of smartphone data set days was 13,898 for all 629 participants.
Distribution of participants’ contribution to the PHQ-8a responses (N=629).
Participants, n (%) | PHQ-8 responses, n |
316 (50.2) | 1 |
129 (20.5) | 2 |
57 (9.1) | 3 |
47 (7.5) | 4 |
40 (6.4) | 5 |
39 (6.2) | 6 |
1 (0.2) | 7 |
aPHQ-8: 8-Item Patient Health Questionnaire.
Distribution of participants’ smartphone data set days (N=629).
Days, n | Participants, n (%) |
8-14 | 364 (57.9) |
15-28 | 126 (20.0) |
29-42 | 53 (8.4) |
43-56 | 34 (5.4) |
57-70 | 29 (4.6) |
71-84 | 22 (3.5) |
85-98 | 1 (0.2) |
In all, we computed 22 features from the smartphone data set. All features were aggregated at the day level. For example, the
We found a significant positive correlation between screen status–normalized entropy and depression (
Regarding the association analysis, we found an ICC of 0.7584; thus, 75.84% of the variations in the features are explainable by the interindividual differences. We found a significant positive association between screen status–normalized entropy and depression (β=.48,
The overall performance of the ML classifiers trained with features only (ie, with no demographics data set) is listed in
As shown in
In terms of precision, recall, and F1 scores, which were computed with an emphasis on the predictive performance of the positive label (ie, depressed score, PHQ-8 ≥ 10), XGB was the best performing classifier, followed by RF and KNN. XGB, RF, and KNN performed better than the RWC and DT baselines, as shown in
Likewise, with AUC and Cohen κ performance metrics, which take into consideration both positive and negative labels (ie, nondepressed score, PHQ-8 <10), XGB, RF, and KNN classifiers had the best performance, as shown in
As shown in
When age group and gender were included with features as predictors, we observed a general improvement in all performance metrics for all classifiers, as shown in
Average and SDs of accuracy, precision, recall, F1, area under the curve, and Cohen κ metrics for 10-fold cross-validation, with features-only data set as predictors.
Metric | RFa, mean (SD) | XGBb, mean (SD) | SVMc, mean (SD) | LRd, mean (SD) | KNNe, mean (SD) |
Accuracy | 97.97 (0.37) | 98.14 (0.37) | 85.68 (1.16) | 59.27 (1.45) | 96.44 (0.52) |
Precision | 92.50 (1.78) | 92.51 (1.25) | 51.98 (2.58) | 20.29 (1.25) | 85.55 (1.97) |
Recall | 94.38 (1.86) | 95.56 (1.99) | 80.67 (2.36) | 57.25 (4.14) | 92.19 (2.24) |
F1 | 93.41 (1.19) | 94.00 (1.21) | 63.20 (2.29) | 29.95 (1.87) | 88.73 (1.63) |
Area under the curve | 98.83 (0.67) | 99.06 (0.54) | 89.47 (1.06) | 62.43 (2.22) | 94.69 (1.15) |
Cohen κ | 92.21 (1.41) | 92.90 (1.43) | 54.83 (2.92) | 9.66 (2.38) | 86.61 (1.93) |
aRF: random forest.
bXGB: XGBoost.
cSVM: support vector machine.
dLR: logistic regression.
eKNN: K-nearest neighbor.
Average and SDs of accuracy, precision, recall, F1, area under the curve, and Cohen κ metrics for 10-fold cross-validation, with features, age group, and gender data set as predictors.
Metric |
RFa, mean (SD) | XGBb, mean (SD) | SVMc, mean (SD) | LRd, mean (SD) | KNNe, mean (SD) |
Accuracy | 98.55 (0.40) | 98.56 (0.31) | 92.61 (0.46) | 60.37 (1.39) | 98.09 (0.26) |
Precision | 95.65 (1.59) | 94.93 (1.08) | 70.46 (1.63) | 21.40 (1.20) | 92.13 (1.41) |
Recall | 94.78 (1.59) | 95.62 (1.52) | 88.76 (3.19) | 60.00 (3.94) | 95.62 (1.56) |
F1 | 95.20 (1.31) | 95.27 (1.03) | 78.52 (1.41) | 31.54 (1.78) | 93.83 (0.85) |
Area under the curve | 99.01 (0.51) | 99.36 (0.33) | 95.45 (1.00) | 66.62 (3.06) | 97.07 (0.73) |
Cohen κ | 94.34 (1.55) | 94.42 (1.21) | 74.13 (1.66) | 11.74 (2.28) | 92.69 (1.00) |
aRF: random forest.
bXGB: XGBoost.
cSVM: support vector machine.
dLR: logistic regression.
eKNN: K-nearest neighbor.
Average and SDs of accuracy, precision, recall, F1, area under the curve, and Cohen κ metrics for the RWC and DT baselines.
Metric | RWCa, mean (SD) | DTb, mean (SD) |
Accuracy | 25.80 (0.33) | 46.80 (3.77) |
Precision | 15.21 (0.36) | 18.70 (0.66) |
Recall | 84.79 (0.86) | 74.33 (4.71) |
F1 | 25.80 (0.24) | 29.85 (0.75) |
Area under the curve | 50.00 (0.47) | 62.94 (1.38) |
Cohen κ | 0.00 (0.32) | 7.33 (1.26) |
aRWC: random weighted classifier; RWC metrics is the average and SD of 10,000 random predictions.
bDT: decision tree; DT metrics is the average for 10-fold cross-validation, with age group and gender only as features.
We present the mean permutation feature importance in predicting PHQ-8 depression score across the 10-fold cross-validation with the top 3 performing ML classifiers (ie, XGB, RF, and KNN) in
For the XGB classifier in
For the RF classifier in
Likewise, for the KNN classifier in
By ranking all important features for KNN, XGB, and RF classifiers, the top 5 most were the screen regularity index, screen status entropy, internet regularity index, screen status–normalized entropy, and the screen off count SD. App count SD is the least important feature for all classifiers (
Mean permutation feature importance across 10-fold cross-validation with the XGBoost machine learning classifier.
Mean permutation feature importance across 10-fold cross-validation with the random forest machine learning classifier.
Mean permutation feature importance across 10-fold cross-validation with the K-nearest neighbor machine learning classifier.
Our objective was to investigate the feasibility of predicting depression using multivariate digital biomarkers quantified from smartphone data sets collected in a real-world study. In this study, we used 13,898 days of smartphone data set, and 1374 PHQ-8 depression assessments from 629 participants to explore the feasibility of detecting depression from participants’ behavioral markers (ie, digital biomarkers) quantified from their smartphones. We focused on finding the relationship between repeated measures of depression scores and participant’s digital biomarkers and developing predictive models to classify depressed and nondepressed symptom severity scores.
This data set was collected from a heterogeneous geographic (ie, from at least 56 different countries), occupational, and educational population, with high interindividual differences (ie, 75.84% interclass correlation).
Despite this heterogeneity, digital biomarkers extracted from participants’ smartphone data set were able to predict participants’ depression state (ie, depressed or nondepressed) with high predictive performance using ML models. The ML models achieved the following: precision, 85.55%-92.51%; recall, 92.19%-95.56%; F1, 88.73%-94.00%; AUC, 94.69%-99.06%; Cohen κ, 86.61%-92.90%; and accuracy, 96.44%-98.14%. These findings show that predictive modeling of mental health using digital biomarkers is not only possible in small homogenous populations [
Moreover, we found that the predictive performances of ML classifiers improved when demographic characteristics were included among predictors, indicating that such variables should also be included in clinical applications. Previous studies suggest a relationship between demographic factors, smartphone usage behavior, and depression [
Interestingly, tree-based, nearest neighbor–based classifiers had superior performance over linear classifiers, including SVM with RBF kernel, corroborating the existence of nonlinear relationships between digital biomarkers and depression. This finding further supported the correlation finding, which failed to replicate previous results reported in Saeb et al [
Given the high ICC, we tested whether LMM, a much robust method for finding linear relationships, can identify additional linear relationships. However, the results from the association analyses further showed that a unit increase in the screen status–normalized entropy positively increases the average depression score (β=.48,
The heterogeneity and inconsistency in correlation findings (ie, linear relationships) in the field are common issues [
Nevertheless, both the correlation findings and the feature importance analysis in the prediction models clearly showed that participants’ phone screen (lock and unlock) behaviors, such as routinely and randomly locking and unlocking phone screen, and internet connectivity behaviors played the most important role in predicting their depression state. The findings in this study are also supported by prior research that investigated the relationship between screen interactions and mental health [
Given the crowdsourced nature of the deployment of the Carat app, the sample size in the data set is small (N=629) and may not be representative of the general population. Despite the data set having a fair distribution of age groups, with a spread over several countries, it is biased toward highly educated and professional occupations. The data set is also biased toward males in gender distribution. Future research with a larger sample size and a balanced gender distribution could explore correlations, associations, and prediction performance for population subgroups.
Clinical diagnosis of depression was not an inclusion criterion for our sample population. The data set also does not contain a clinical or self-reported baseline assessment of depression and has scarce high depression scores. Because of the crowdsourced rolling recruitment nature of participants, the data set contained an unequal number of repeated depression assessments for all participants. Future research should benefit from replicating the experiment in a clinical population and a more controlled experimental design. With a clinical baseline data set, future research could study the differences in features between depressed and nondepressed groups.
The correlation and association between behavioral patterns extracted from the data set in this study and depression do not necessarily imply causal relationships. For example, the correlation between screen status–normalized entropy and depression may be caused by other confounding variables. In addition, the correlation and association between screen status–normalized entropy and depression are not strong and may not generalize in other populations. Further research is needed to establish the extent to which such behaviors cause or are a consequence of depression.
Lastly, the data set was collected from Android participants only, and the long-term use of the Carat app could influence participants’ behavior [
Replicating the findings from this study with additional biomarkers from GPS and wearable sensor data sets and comparing their correlation and biomarker predictive importance will be interesting in future work. There would be a major design implication for depression intervention development if the behavioral markers from screen and internet connectivity achieve similar promising results as biomarkers from GPS and wearable devices. We hypothesize that screen interaction and internet connectivity data sets alone are less privacy intrusive, could better capture behaviors of immobile persons, and people may be more willing to donate such data sets to science. For example, Apple’s Screen Time and Google’s Digital Wellbeing app are processing and presenting such data to users to inform where and how users spent their time on smartphones.
In summary, this study sought to find whether we can detect changes in human behavior that would be indicative of depression using smartphones. In addition, we sought to find what objective measures of human behavior from smartphones are insightful in understanding depression. Our results established a positive statistically significant linear correlation and association between depression and screen status–normalized entropy behavior quantified from smartphone data sets. Our findings also establish that behavioral markers extracted from smartphone data sets can predict whether or not a participant is depressed based on the PHQ-8 depression score, and that phone screen and internet connectivity behaviors were the most insightful behaviors that influence depression in participants. The findings in this study are supported by previous research findings and contribute to compelling evidence on the utility of digital biomarkers in augmenting traditional assessment of depression, thus enabling continuous and passive monitoring of the complex vectors of depression.
Description of Features Extracted from the Smartphone Dataset.
Extended Results for Statistical Analysis.
Extended Results for Machine Learning Analysis.
area under the curve
decision tree
intraclass correlation
K-nearest neighbor
linear mixed model
logistic regression
machine learning
8-Item Patient Health Questionnaire
random forest
random weighted classifier
support vector machine
XGBoost
This research is supported by the Academy of Finland 6Genesis Flagship (Grant No. 318927), SENSATE (Grant Nos 316253, 320089), Infotech Institute University of Oulu Emerging Project, and Nokia Foundation (Jorma Ollila Grant for EP). We thank the Carat Project for making their data set available for this study, and all participants who contributed to the Carat Project.
KOA, DF, and EP contributed to the conceptualization of the study and bulk data transfers from Carat project archive servers. EP and EL were principally involved in the Carat Project. KOA and JV contributed to data preparation, feature extraction, and machine learning analysis. KOA and YT contributed to the statistical analysis. KOA and DF prepared the original draft. All authors critically reviewed and edited the draft. All authors read and approved the final manuscript.
None declared.