Skip to main content
NCBI home page
NIHPA Author Manuscripts logoLink to NIHPA Author Manuscripts
. Author manuscript; available in PMC: 2024 Mar 1.
Published in final edited form as: Ment Health Phys Act. 2023 Feb 23;24:100512. doi: 10.1016/j.mhpa.2023.100512

Associations between daily step count trajectories and clinical outcomes among adults with comorbid obesity and depression

Emily A Kringle 1,*, Danielle Tucker 2, Yichao Wu 2, Nan Lv 1, Thomas Kannampallil 3, Amruta Barve 1, Sushanth Dosala 1, Nancy Wittels 1, Ruixuan Dai 4, Jun Ma 1
PMCID: PMC10191421  NIHMSID: NIHMS1882219  PMID: 37206660

Abstract

Purpose:

To examine the relationship between features of daily measured step count trajectories and clinical outcomes among people with comorbid obesity and depression in the ENGAGE-2 Trial.

Methods:

This post hoc analysis used data from the ENGAGE-2 trial where adults (n=106) with comorbid obesity (BMI ≥30.0 or 27.0 if Asian) and depressive symptoms (Patient Health Questionnaire-9 score ≥10) were randomized (2:1) to receive the experimental intervention or usual care. Daily step count trajectories over the first 60 days (Fitbit Alta HR) were characterized using functional principal component analyses. 7-day and 30-day trajectories were also explored. Functional principal component scores that described features of step count trajectories were entered into linear mixed models to predict weight (kg), depression (Symptom Checklist-20), and anxiety (Generalized Anxiety Disorder Questionnaire-7) at 2-months (2M) and 6-months (6M).

Results:

Features of 60-day step count trajectories were interpreted as overall sustained high, continuous decline, and disrupted decline. Overall sustained high step count was associated with low anxiety (2M, β=−0.78, p<.05; 6M, β=−0.80, p<.05) and low depressive symptoms (6M, β=−0.15, p<.05). Continuous decline in step count was associated with high weight (2M, β=0.58, p<.05). Disrupted decline was not associated with clinical outcomes at 2M or 6M. Features of 30-day step count trajectories were also associated with weight (2M, 6M), depression (6M), and anxiety (2M, 6M); Features of 7-day step count trajectories were not associated with weight, depression, or anxiety at 2M or 6M.

Conclusions:

Features of step count trajectories identified using functional principal component analysis were associated with depression, anxiety, and weight outcomes among adults with comorbid obesity and depression. Functional principal component analysis may be a useful analytic method that leverages daily measured physical activity levels to allow for precise tailoring of future behavioral interventions.

Keywords: physical activity, activity tracker, anxiety, body weight, activity

Introduction

Multimorbidity is a growing public health concern that places adults at high risk for poor quality of life, high healthcare costs, and mortality (King et al., 2018; Lebenbaum et al., 2018; Wang et al., 2018). Obesity and depression frequently co-occur: adults with obesity are 32% more likely to have depression than those without (Pereira-Miranda et al., 2017), and 43% of adults with depression have obesity (Pratt & Brody, 2014). Further, adults with mild to severe obesity are 4.5 to 14.5 times more likely to have multimorbidity relative to those without obesity (Kivimäki et al., 2017), and adults with multimorbidity have 2.3 times the risk of depressive disorder relative to those without (Read et al., 2017). Although several lifestyle interventions exist for adults with multimorbidity, the evidence for behavioral interventions shows only modest effects on depression, and small effects on behavioral outcomes (e.g., health behaviors, medication adherence) (Smith et al., 2021). Understanding the relationship between lifestyle behaviors and outcomes associated with multimorbidity is needed to bolster the effects of interventions.

Physical activity is a lifestyle behavior that is widely associated with both obesity, and depression (Jakicic et al., 2019; Pearce et al., 2022). Being physically active is associated with reduced risk for multimorbidity among adults with obesity (Srivastava et al., 2021) and reduced odds of having depressive disorder among adults with multimorbidity (Andrade-Lima et al., 2020). Although physical activity improves outcomes associated with multimorbid conditions, only a small proportion of randomized controlled behavioral intervention trials enroll adults with multiple chronic conditions; in fact, approximately 68.3% of these studies specifically excluded adults with multimorbidity between 2000 to 2014 (Stoll et al., 2019). Despite recommendations to tailor physical activity interventions for multimorbidity (Dekker et al., 2019), evidence that guides the tailoring of physical activity interventions within the context of multimorbidity is scant.

Advancements in wearable activity trackers allow for daily measurement of physical activity metrics such as step count. These activity trackers capture longitudinal information which is often collapsed into aggregate summary statistics to describe linear mean change over time (Ringeval et al., 2020). However, these trajectories may contain important information that informs intervention tailoring within the context of multimorbidity. For example, trends in the direction or pace of change or day-to-day variability may be linked with specific clinical outcomes. Emerging analyses of behavioral interventions in populations without multimorbidity suggest that distinct step count trajectories exist and that age, body mass index (BMI), having type 2 diabetes, and general health perception predict trajectory group membership (Cooke et al., 2020; Imes et al., 2018). These group-based trajectory analyses suggest a relationship between step count trajectory and weight but have not yet explored the impact on other important health outcomes. Additionally, a growing body of literature suggests that day-to-day variability exists (Nicolai et al., 2010). However, there is conflicting evidence about the relationship between physical activity variability and health outcomes (e.g., (Hooker et al., 2020; Saeb et al., 2015)). Decomposing step count trajectories to identify features of step count trajectories can leverage longitudinal data to deepen our understanding of the relationship between physical activity trajectories, variability, and clinical outcomes.

Functional principal component analysis (fPCA) is an innovative analytic approach that can be used to identify the main features, or functional principal components of step count trajectories over time. These functional principal components may have predictive utility for health outcomes. Traditionally, parametric mixed effects nonlinear models are used when dealing with longitudinal data. fPCA is inherently nonparametric (Wang et al., 2016), which provides more flexibility in modeling the tremendous amount of information contained in the infinite dimensional trajectories. The resulting scores of fPCA jointly describe individual trajectories and can be used in regression models to examine the relationship between features of step count trajectories and clinical outcomes. fPCA (Chen et al., 2017; Wang et al., 2016; Yao et al., 2005) has been used to investigate the relationship between features of diurnal (within-day) physical activity patterns in adults and clinical outcomes, including BMI, cancer status, sleep, quality-of-life, and diabetes-related biomarkers (Xu et al., 2019; Zeitzer et al., 2017; Zeitzer et al., 2013). The purpose of the present study was to examine the relationship between features of day-to-day step count trajectories and physical and mental health outcomes in a sample of adults with comorbid obesity and depression.

Methods

Study design and data

Data collected as part of the ENGAGE-2 randomized clinical trial (ClinicalTrials.gov, #NCT03841682) were suitable for exploring the relationship between features of step count trajectories and health outcomes. ENGAGE-2 was designed to test neurobiological mechanisms and clinical outcomes associated with an integrated collaborative care intervention that aimed to treat adults with comorbid obesity and depression (Lv et al., 2020). Data were collected between March 2019 and August 2021. Participants were randomized (2:1) to receive an integrated behavior therapy or usual care. Assessment of clinical and behavioral outcomes occurred at baseline (0), 2-months (2M), and 6-months (6M). All participants, regardless of group assignment, provided up to 6 months of daily step count data via a wearable activity tracker (Fitbit Alta HR, San Francisco, CA). This allowed all participants to self-monitor their physical activity levels. Participants in the intervention group received tailored counseling based on physical activity data from their activity tracker. The primary outcomes of ENGAGE-2 were published previously (Lv, Ajilore, et al., 2022). The purpose of this posthoc analysis is to (1) characterize features of step count trajectories among adults with comorbid obesity and depression, and (2) explore the relationship between features of step count trajectories and clinical outcomes.

Participants

Adults (≥18 years) were recruited from internal medicine outpatient clinics of the University of Illinois Hospital and Health Sciences System (UI Health). Participants were included if they met criteria for both obesity (BMI ≥30.0 or ≥27.0 if Asian) and depression (Patient Health Questionnaire-9 [PHQ-9] score ≥10). Those with other psychiatric conditions, alcohol or substance abuse, and pre-existing diabetes, cardiovascular disease, cancer, or severe medical comorbidities or terminal illnesses were excluded (detailed criteria are reported in (Lv et al., 2020)). This research was approved by the University of Illinois at Chicago IRB, conducted in compliance with the Declaration of Helsinki, and all participants provided written consent to participate.

Interventions

Participants assigned to either the treatment or control group received usual medical care and information about behavioral health and weight management services available through UI Health. Additionally, participants assigned to the treatment group completed 9 individual sessions of the Integrated Coaching for Better Mood and Weight version 2 (I-CARE2) with a trained health coach over 6 months. Sessions were delivered on a weekly basis for the first 4 weeks. The remaining sessions were delivered during weeks 6, 8, 12, 16, and 20. I-CARE2 integrates established two evidence-based intervention programs: the Diabetes Prevention Program-based Group Lifestyle Balance™ video program for weight loss (Diabetes Prevention Program Research Group, 2002; Ma et al., 2013) and the PEARLS program for depression care management (Ciechanowski et al., 2004). Details of the integrated intervention are described in Lv et al (2020).

Measures

Daily step count was measured using a wearable activity tracker, Fitbit Alta HR. Participants received the tracker during study orientation and were instructed to sync their data to the study database during 7-days at the 0, 2, and 6-month timepoints. Participants were also encouraged to share their Fitbit data with the study between assessment timepoints. Clinical outcomes were measured by blinded assessors and included weight, depression, and anxiety. Weight (in kilograms) was measured following a standard protocol (PhenX Toolkit, 2011). The Symptom Checklist-20 (SCL-20) and Generalized Anxiety Disorder Scale (GAD-7) are valid and reliable measures of depression and anxiety severity, respectively (Glass, 1978; Goldberg et al., 1976; Spitzer et al., 2006). The SCL-20 consists of 20 statements during which participants rate the level of distress caused by the symptom over the past 2 weeks using a 0 to 4-point scale. A mean score less than 0.5 indicates remission of depressive symptoms (Glass, 1978; Goldberg et al., 1976). The GAD-7 consists of 7 statements during which participants rate the frequency of anxiety symptoms over the past 2 weeks using a 0 to 3-point scale. Scores are summed (possible range 0 to 21) and high scores indicate high anxiety symptoms (Spitzer et al., 2006).

Statistical Analyses

To explore the relationship between features of daily step count trajectories and clinical outcomes, three types of analyses were conducted: (1) fPCA (Chen et al., 2017; Wang et al., 2016; Yao et al., 2003; Yao et al., 2005; Zhou et al., 2022) using Fitbit data collected over the first 60 days of the trial, (2) group least absolute shrinkage and selection operator (group LASSO) variable selection (Meier, 2020; Yuan & Lin, 2007), and (3) linear modeling to regress fPCA scores on clinical outcomes. All analyses were conducted using R (version 4.0.3, Vienna, Austria). Before undertaking the fPCA analyses, Fitbit data were assessed for validity. Duration of device wear time was determined using minute-by-minute readings of heart rate and step counts. If there was a valid heart rate reading or non-zero step count during one minute, that minute was included in the wear time count. Step count on a particular day was considered valid if the Fitbit was worn for ≥10 hours. Participants were included in the analysis if they had at least 24 valid days during the first 60 days of the trial. These criteria were selected giving consideration to the robustness of fPCA to data sparseness and conventional practice with accelerometer physical activity data (Bergman & Hagströmer, 2020). To further explore the relationship between features of step count trajectories and future clinical outcomes, analyses were repeated using step count data during the first 7 and 30 days of the trial. For these analyses, participants were considered to have valid data if they provided 3 of 7 or 12 of 30 valid days, respectively.

fPCA was used identify features of step count trajectories, i.e. their functional principal components. Details of the modeling approach are included in the online supplementary file. Briefly, we considered each participant’s step count trajectory to be an observation of a stochastic process; that is, a random curve over time with a mean and a covariance function. An eigenfunction decomposition was used to estimate the true covariance function. The estimated eigenfunctions define the functional principal components of the observed trajectories and thereby jointly describe the between-person variance over time. Each participant is assigned a functional principal component score for each estimated eigenfunction. These functional principal component scores jointly describe each individual’s trajectory and may then be used as continuous variables in regression models. The number of functional principal components was selected based on the number required to explain 99% of the between-person variance over time. fPCA was used to identify features of step count trajectories using data from only the first 7, 30, and 60 days of the trial, respectively. Specifically, the PACE algorithm for fPCA (Wang et al., 2016; Zhou et al., 2022) was used to properly handle the sparse data and the possible presence of measurement errors.

Linear regression models were fit to examine the relationship between features of step count trajectories and future clinical outcomes. Separate models were fit for each outcome (weight, depression, anxiety) and each fPCA analysis (7-day, 30-day, 60-day), resulting in a total of 9 models. Group LASSO variable selection (Meier, 2020; Yuan & Lin, 2007) was used to determine whether step count trajectories contributed to the model, and to select covariates to include in the models, while minimizing collinearity. These methods are described in detail in Supplementary File 1. Briefly, for each model, all functional principal components were grouped together so that the group LASSO algorithm either entirely included or entirely excluded them. Simultaneously, LASSO variable selection was performed on all covariates (age, sex, race/ethnicity, education, group assignment, antidepressant medication use, COVID-19 shutdown, baseline score on corresponding outcome). Group LASSO was conducted using 5-fold cross validation for tuning of hyperparameters (details of this approach are included in the supplementary file). Linear regression models were then fit, which included only the selected predictors. Model residuals were examined and when assumptions of normality were violated, the Box Cox transformation (Box & Cox, 1964) was implemented, and the model was re-fit. Non-transformed models are reported in the results sections and, where indicated, transformed models are included in the supplementary file.

Results

Participants

A total of 88 out of 106 participants included in the parent study had sufficient valid Fitbit data to be included in this posthoc analysis (Figure 1). Baseline characteristics are located in Table 1. Participants had mean (standard deviation [SD]) age of 46.8 (12.1) years, were predominantly female (76.1%), and were racially and ethnically diverse (53.4% were African American and 20.5% were Hispanic/Latinx). At baseline, participants had a mean BMI of 36.8 (5.9) indicative of obesity and 78.4% of the sample were considered to have moderate depression (PHQ-9 score of 10 to 14). Apart from minutes per day of light physical activity reported on the 7-Day Physical Activity Recall, there were no differences in demographic or baseline clinical measures between participants who did and did not have valid data.

Fig. 1.

Fig. 1.

Open in a new tab

CONSORT flowchart illustrating the number of participants screened, randomized, and included in the present analysis. Among participants randomized in the parent trial (n=106), 88 provided sufficient Fitbit data for inclusion in the present analysis (intervention arm n=58; control arm n=30).

Table 1.

Participant characteristics

Characteristic Participants included n=88 Participants not included n=18 P Value
Age, years, mean ± SD 46.8 ± 12.1 47.8 ± 11.2 0.75
Female, n (%) 67 (76.1) 14 (77.8) 0.88
Race/Ethnicity, n (%) 0.71
Non-Hispanic White 15 (17.1) 4 (22.2)
African American 47 (53.4) 11 (61.1)
Asian/Pacific Islander 2 (2.3) 0 (0)
Hispanic 18 (20.5) 3 (16.7)
Other (e.g., decline to state, multirace) 6 (6.8) 0 (0)
Education, n (%) 0.12
High school/GED or less 9 (10.2) 5 (27.8)
College: 1 to 3 years 35 (39.8) 8 (44.4)
College: 4 years or more 25 (28.4) 4 (22.2)
Post college 19 (21.6) 1 (5.6)
Income, n (%) 0.91
<$35,000 27 (30.7) 7 (38.9)
$35,000 to <$55,000 22 (25) 4 (22.2)
$55,000 to <$75,000 13 (14.8) 2 (11.1)
≥$75,000 26 (29.6) 5 (27.8)
BMI, kg/m2, mean ± SD 36.8 ± 5.9 38.6 ± 6.7 0.25
Weight, kg, mean ± SD 100.5 ± 15 106.4 ± 15.7 0.13
Waist circumference, cm, mean ± SD 112.1 ± 12.1 115.9 ± 15.1 0.25
PHQ-9 score, mean ± SD 12.7 ± 2.8 13.8 ± 2.7 0.12
10–14 (moderate depression), n (%) 69 (78.4) 12 (66.7)
15–19 (moderately severe depression), n (%) 15 (17.1) 6 (33.3)
≥20 (severe depression), n (%) 4 (4.6) 0 (0) 0.21
SCL-20 score, mean ± SD 1.2 ± 0.6 1.2 ± 0.8 0.85
GAD-7 score, mean ± SD 7 ± 4.7 6.8 ± 5.3 0.87
0–4 (minimal anxiety), n (%) 26 (29.6) 8 (44.4)
5–9 (mild anxiety), n (%) 39 (44.3) 4 (22.2)
10–14 (moderate anxiety), n (%) 18 (20.5) 5 (27.8)
15–21 (severe anxiety), n (%) 5 (5.7) 1 (5.6) 0.36
Current use of ADM, n (%) 17 (19.3) 2 (11.1) 0.41
SBP, mmHg, mean ± SD 122.3 ± 15.3 123.9 ± 23.3 0.78
DBP, mmHg, mean ± SD 76.9 ± 9.3 77.9 ± 17.4 0.80
7-DPAR light PA, minutes/day 920.9 ± 82.3 842.4 ± 77.1 <.001
7-DPAR moderate PA, minutes/day 33 ± 41.2 36.3 ± 44 0.76
7-DPAR hard PA, minutes/day 0.7 ± 2.4 13.7 ± 50.3 0.29
7-DPAR very hard PA, minutes/day 0.8 ± 5.1 0.3 ± 1 0.38
7-DPAR moderate + hard + very hard PA, minutes/day 34.6 ± 43.7 50.3 ± 60.8 0.31
Fitbit step count, daily mean over 7 days, mean ± SD 7386±3600 8625 ± 3372 0.21
Open in a new tab

BMI = Body Mass Index; PHQ-9 = Patient Health Questionnaire-9; SCL-20 = Symptom Checklist-20; GAD-7 = Generalized Anxiety Disorder Questionnaire-7; ADM = anti-depressant medication; SBP = systolic blood pressure; DBP = diastolic blood pressure; 7-DPAR = 7-Day Physical Activity Recall; PA = physical activity

Data validity

On average valid days, participants wore the Fitbit for 20.0 hours (SD=4.4 hours). Participants included in the 60-day analysis (n=84) had an average of 49 (SD=10) valid days of Fitbit data. Those included in the 7-day (n=87) and 30-day (n=85) had an average of 6 (SD=1) and 27 (SD=5) valid days of Fitbit data, respectively.

60-Day Trajectories vs. Clinical Outcomes

Three functional principal components explained a cumulative 99% of variance in 60-day step count trajectory. High scores on these components were interpreted as (1) overall sustained high step count, (2) continuous decline in step count throughout the 60 days, and (3) interrupted decline in step count (Table 2). Figure 2 depicts step counts associated with each component relative to the sample mean. These functional principal components were included in all models predicting both 2-month and 6-month outcomes based on the LASSO group variable selection (Table 3). At 2-months, overall high step count was associated with low anxiety symptoms (β = −0.78, 95% CI = −1.57, −0.00, p<.05), and continuous decline in step count was associated with high weight (β = 0.58, 95% CI = 0.02, 1.14, p<.05). At 6-months, overall high step count was associated with low depressive symptoms (β = −0.15, 95% CI = −0.27, −0.03, p<.05) and low anxiety (β = −0.80, 95% CI = −1.53, −0.07, p<.05).

Table 2.

Principal component score summaries

Principal Component Mean (SD) Range Cumulative Variance Descriptor
7-Day Step Count Trajectories (Baseline), n=87 1 −219.09 (8625.57) −16753.44, 31413.47 73% Overall sustained high
2 −158.64 (4311.87) −19663.84, 12873.79 95% Continuous increase
3 8.24 (1643.95) −8298.1, 4484.50 99% Weekend warrior
30-Day Step Count Trajectories n=85 1 −520.89 (18630.90) −32023.90, 86010.05 91% Overall sustained high
2 185.67 (4313.17) −17293.40, 17855.05 97% Continuous decline
3 −20.16 (1993.48) −5078.53, 8324.10 98% Disrupted increase
4 −55.14 (1940.99) −6218.58, 7823.74 100% Overly ambitious increase
60-Day Step Count Trajectories n=84 1 −1174.12 (26076.93) −38929.35, 136513.80 88% Overall sustained high
2 32.57 (7769.12) −24738.22, 25558.66 97% Continuous decline
3 121.64 (3767.69) −14002.35, 14441.75 99% Interrupted decline
Open in a new tab

Note. Descriptors characterize high scores for each component. An individual with a low (negative) score on the component would have the opposite pattern. For example, a negative score on Principal Component 1 would indicate an overall sustained low step count for the individual.

Fig. 2.

Fig. 2.

Open in a new tab

60-day step count trajectories.

Table 3.

Association between principal component scores and clinical outcomes

7-Day Trajectories
Principal Component 1 2 3
2-Month Outcomes
ǂBMI NS NS NS
ǂWeight (kg) NS NS NS
ǂSCL-20 NS NS NS
ǂGAD-7 −0.30 (−1.36, 0.75) −0.39 (−1.47, 0.69) −0.08 (−1.17, 1.01)
6-Month Outcomes
ǂBMI 0.49 (−0.90, 1.88) −0.58 (−1.97, 0.82) 0.97 (−0.45, 2.39)
ǂWeight (kg) 0.76 (−2.74, 4.27) −0.01 (−3.52, 3.5) 1.78 (−1.78, 5.34)
ǂSCL-20 *−0.12 (−0.26, 0.01) −0.05 (−0.19, 0.08) −0.06 (−0.20, 0.08)
ǂGAD-7 −0.53 (−1.57, 0.52) 0.29 (−0.80, 1.37) −0.79 (−1.88, 0.31)
30-Day Trajectories
Principal Component 1 2 3 4
2-Month Outcomes
ǂBMI −0.10 (−0.28, 0.08) *0.18 (−0.01, 0.37) 0.10 (−0.09, 0.30) 0.12 (−0.07, 0.30)
ǂWeight (kg) −0.22 (−0.73, 0.29) ** 0.53 (0.00, 1.06) 0.27 (−0.27, 0.81) 0.31 (−0.21, 0.83)
SCL-20 NS NS NS NS
ǂGAD-7 ** −0.89 (−1.69, −0.09) −0.02 (−0.82, 0.79) −0.30 (−1.15, 0.56) 0.06 (−0.75, 0.87)
6-Month Outcomes
ǂBMI −0.13 (−0.44, 0.17) −0.04 (−0.34, 0.27) 0.06 (−0.25, 0.38) *0.27 (−0.04, 0.58)
ǂWeight (kg) −0.47 (−1.32, 0.37) −0.11 (−0.96, 0.73) −0.28 (−0.58, 1.14) ** 0.85 (0.00, 1.71)
ǂSCL-20 ** −0.14 (−0.25, −0.02) 0.04 (−0.08, 0.15) *0.11 (−0.01, 0.23) 0.01 (−0.12, 0.13)
ǂGAD-7 ** −0.80 (−1.54, −0.07) 0.42 (−0.35, 1.19) 0.31 (−0.49, 1.11) −0.36 (−1.12, 0.40)
60-Day Trajectories
Principal Component 1 2 3
2-Month Outcomes
ǂBMI *−0.17 (−0.35, 0.02) *0.17 (−0.02, 0.37) 0.10 (−0.08, 0.28)
ǂWeight (kg) *−0.42 (−0.93, 0.09) ** 0.58 (0.02, 1.14) 0.24 (−0.27, 0.75)
SCL-20 −0.09 (−0.20, 0.03) −0.02 (−0.14, 0.10) 0.07 (−0.04, 0.19)
ǂGAD-7 ** −0.78 (−1.57, 0.00) −0.38 (−1.18, 0.43) 0.21 (−0.57, 1.00)
6-Month Outcomes
BMI *−0.26 (−0.57, 0.04) ** 0.33 (0.01, 0.65) −0.22 (−0.53, 0.08)
ǂWeight (kg) *−0.70 (−1.53, 0.13) *0.73 (−0.13, 1.58) −0.67 (−1.52, 0.18)
SCL-20 ** −0.15 (−0.27, −0.03) −0.05 (−0.17, 0.07) *0.11 (−0.02, 0.23)
ǂGAD-7 ** −0.80 (−1.53, −0.07) −0.40 (−1.17, 0.38) *0.66 (−0.07, 1.39)
Open in a new tab

Note: 7-day trajectories with 3 or more valid days, n=87; 30-day trajectories with 12 or more valid days, n=85; 60-day trajectories with 24 or more valid days, n=84; Values represent β (95% CI); NS=Principal Components not selected for inclusion in the model by LASSO methodology

ǂ

Transformed models included in supplementary files

*

P<.10

**

P<.05

7-Day Baseline Trajectories vs. Clinical Outcomes

Three functional principal components explained a cumulative 99% of between-person variance in 7-day step count trajectory. High scores on these components were interpreted as (1) overall sustained high step count, (2) continuous increase in step count throughout the 7 days, and (3) weekend warriors who had low step count on weekdays and high step count on weekends (Table 2). Supplementary file Figure S1 depicts step counts associated with each component relative to the sample mean. Based on the group LASSO variable selection and linear regression models, no functional principal components were associated with clinical outcomes (either not selected for model inclusion or p>.05) at 2- or 6-months (Table 3).

30-Day Trajectories vs. Clinical Outcomes

Four functional principal components explained a cumulative 100% of between-person variance in 30-day step count trajectory. High scores on these components were interpreted as (1) overall sustained high step count, (2) continuous decline in step count throughout the 30 days, (3) disrupted increase, and (4) unsustained early increase in step count at the beginning of the 30 days (Table 2). Supplementary file Figure S2 depicts step counts associated with each component relative to the sample mean. Based on the group LASSO variable selection, these functional principal components were excluded from the 2-month models predicting depression but were included in all other 2-month and 6-month models (Table 3). At 2-months, overall high step count was associated with low anxiety (β = −0.89, 95% CI = −1.69, −0.09, p<.05) and continuous decline in step count was associated with high weight (β = 0.53, 95% CI = 0.00, 1.06, p<.05). At 6-months, overall high step count was associated with low depressive symptoms (β = −0.14, 95% CI = −0.25, −0.02, p<.05) and anxiety (β = −0.80, 95% CI −1.54, −0.07, p<.05). Further, having an unsustained early increase in step count was associated with high weight (β = 0.85, 95% CI = 0.00, 1.71, p<.05) at 6 months.

Exemplar: Interpreting functional principal components

Because functional principal components each describe only one feature of an individual’s step count trajectory over time, it is important to note that each participant received a score for each component. For example, Figure 3 depicts 60-day plots for 2 participants. One participant had high scores on all 3 components, which can be interpreted as a high overall step count that decreased over time and was disrupted around day 35. Conversely, the other participant had low scores on functional principal components 1 and 2, and an average score on functional principal component 3. This trajectory can be interpreted as a low overall step count that remained relatively stable over time and was not disrupted.

Fig. 3.

Fig. 3.

Open in a new tab

Individual step count trajectory exemplars.

Discussion

Step count trajectories among participants in the ENGAGE-2 trial were characterized by features that describe overall sustained step count levels, direction of change over time, and disruptions in the direction of change. A continuous decline in step count over 60 and 30 days was associated with high 2-month weight. High overall sustained step count levels over 60 and 30 days were associated with low anxiety symptoms at 2-months, and with low anxiety and low depression symptoms at 2-months and 6-months. These findings build on prior evidence suggesting that physical activity trajectories influence weight and mental health outcomes, and guide toward possible targets for enhancing treatment efficacy of existing interventions designed to treat comorbid obesity and depression (Lv, Kringle, et al., 2022).

fPCA is a granular, nonparametric approach to analyzing day-to-day physical activity trajectories that builds on more common group-based trajectory model approaches applied in prior studies. Results from prior studies also suggested that increasing physical activity trajectories are associated with decreased BMI (Cooke et al., 2020; Imes et al., 2018). In addition to aligning with findings from group-based trajectory models, the present findings provide insight into additional features of step count trajectories that may explain variance in clinical outcomes. For example, people who had a greater unsustained early increase in step count during the first week of the trial had higher weight at the 6-month timepoint. This suggests that although an overall increasing trajectory in steps is associated with a low weight, too quick of an initial increase in step count may dampen the impact on weight. This could be attributed to difficulty maintaining long-term behavior change when initial goals are too ambitious. In fact, recent updates to goal setting theory caution against setting performance-based goals (e.g., achieve a particular step count) for populations who are habitually inactive (Swann et al., 2021). Rather, goals that focus on enhancing knowledge about strategies to accumulate steps may support a more gradual increase in step count, long-term maintenance of the behavior, and improvements in weight-related outcomes (Swann et al., 2021).

The present findings are also salient as they relate to the growing global population with multimorbidity. Ma et al. (2017) demonstrated that among people with comorbid obesity and depression, distinct profiles exist in which one condition may be more prominent than the other (Ma et al., 2017). It is notable that different characteristics of step count trajectories were associated with different types of clinical outcomes. Although the overall sustained step count level was associated with anxiety and depression outcomes, the direction and magnitude of day-to-day step count were associated with weight-related outcomes. Understanding these relationships may allow an intervention to be tailored to emphasize maintaining a high physical activity level for individuals with depression-dominant profiles, while emphasizing incremental increases in physical activity goals for individuals with obesity-dominant profiles.

Identifying features of day-to-day step count trajectories measured by a commercially available activity tracker (Fitbit Alta HR) also affords opportunities to better leverage these intensive longitudinal step count data within behavior change research and practice. Fitbit and other wearable activity trackers are commonly used as part of both intervention strategies (i.e. self-monitoring) and outcomes measures in physical activity interventions across the lifespan (St Fleur et al., 2020). Existing literature suggests that challenges during both intervention (Balbim et al., 2021) and outcomes measurement (Feehan et al., 2018) must be carefully considered when using commercially available activity trackers, such as Fitbit, in any capacity during physical activity interventions, including adherence to device use and accuracy of step count (Feehan et al., 2018) or activity expenditure estimation (Germini et al., 2022). fPCA provided an opportunity to overcome several of these challenges, because it is robust to sparse data and emphasizes features of individual trajectories over time rather than aggregate step counts. The findings suggest that a commercially available activity tracker, such as the Fitbit Alta HR, may adequately detect features of step count trajectories over time that are associated with clinical outcomes. Future research in this area may lead to identification of activity patterns or trajectories that place people at risk for poor outcomes (for example, consistently decreasing step count over time) and enable the delivery of tailored interventions that bolster clinical outcomes.

This posthoc analysis has several limitations. Participants were only required to sync their Fitbit data to the study database for 7 days at each study timepoint, and providing daily data over the entire study was encouraged, but optional. This limited the number of participants who met the requirements for inclusion in the present analysis. Although there were no baseline group differences between those who provided daily data and those who did not, it is possible that this impacted the present findings. Additionally, although a strength of fPCA is its robustness to sparse data, 10% of the included sample contributed data on fewer than half (and more than 40%) of possible days. Finally, this trial was not prospectively designed to detect the relationship between daily measured step count trajectories and clinical outcomes. Although we controlled for group assignment in our analysis, it is possible that different trajectory characteristics would be identified in a study prospectively designed for that purpose. Therefore, these posthoc findings should be viewed as exploratory. Replication in future prospective trials is critical for specifying key characteristics of trajectories at specified timepoints which trigger precise intervention adaptation.

Despite these limitations, the present findings demonstrate that day-to-day step count trajectories can be characterized using fPCA. Further, different features of step count trajectories may be associated with specific clinical outcomes. That is, overall high levels of step count were associated with low anxiety and low depression, while a sustained decline in step count over time was associated with high weight. Future studies which replicate and build on this analysis should further elucidate the relationship between these features of step count trajectories and clinical outcomes. Employing measurement and rigorous statistical and data science methods that capitalize on daily measured step counts and other 24-hour behaviors (e.g., sedentary time, sleep) are vital for advancing the development of personalized precision behavioral medicine interventions that efficiently and effectively improve health among adults with comorbid obesity and depression.

Supplementary Material

1
2

Table 4.

Association between principal component scores and self-reported moderate to very hard physical activity

7-Day Trajectories
Principal Component 1 2 3
ǂBL *** 20.36 (11.96, 28.75) 2.95 (−5.55, 11.46) ** 10.07 (1.69, 18.46)
ǂM2 7.33 (−6.57, 21.22) 6.70 (−5.63, 19.02) 4.35 (−8.39, 17.09)
ǂM6 0.16 (−8.43, 8.74) −4.16 (−13.04, 4.72) −7.01 (−15.62, 1.61)
30-Day Trajectories
Principal Component 1 2 3 4
ǂM2 5.69 (−2.77, 14.14) 4.23 (−2.89, 11.35) *−6.69 (−14.69, 1.30) *** 11.7 (4.34, 19.06)
ǂM6 ***14.70 (5.00, 24.39) 2.58 (−5.92, 11.09) −4.52 (−13.58, 4.54) *−7.62 (−16.09, 0.84)
60-Day Trajectories
Principal Component 1 2 3
ǂM2 0.47 (−0.12, 1.06) ** 0.69 (0.09, 1.29) 0.04 (−0.51, 0.59)
ǂM6 *** 16.66 (7.34, 25.99) 1.85 (−7.71, 11.42) 3.75 (−4.94, 12.44
Open in a new tab

*Note: 7-day trajectories with 3 or more valid days, n=87; 30-day trajectories with 12 or more valid days, n=85; 60-day trajectories with 24 or more valid days, n=84; Values represent β (95% CI)

ǂ

Transformed models included in supplementary files

*

P<.10

**

P<.05

***

P<.01

Highlights.

  • Functional principal component analyses identified features of step count trajectories.

  • Continuous decline in step count over time was associated with high weight.

  • High sustained step count was associated with low anxiety and depression symptoms.

Acknowledgements:

The authors would like to acknowledge the participants who engaged in the study without whom this research would not be possible. Research reported in this publication was supported by the National Heart Lung and Blood Institute, the National Institute of Mental Health, and the Office of the Director of the National Institutes of Health under award numbers UH3HL132368, R61 MH119237, T32 HL134634, and K23 HL159240. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Footnotes

Declaration of interests

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Jun Ma reports financial support was provided by University of Illinois Chicago. Emily Kringle reports financial support was provided by University of Illinois Chicago. Jun Ma (HM) and Thomas Kannampallil (Pfizer) reports a relationship with Health Mentor Inc (San Jose, CA) and Pfizer Inc that includes: consulting or advisory.

Competing interests: Dr. Jun Ma is a paid scientific consultant for Health Mentor, Inc (San Jose, CA). Dr. Thomas Kannampallil is a paid consultant for Pfizer, Inc, outside of this work. All other report no conflicts of interests (EK, DT, YW, NL, AB, SD, NW, RD).

Trial Registration: ClinicalTrials.gov NCT04524104. Registered 15 February 2019, https://clinicaltrials.gov/ct2/show/NCT03841682

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

References

  1. Andrade-Lima A, Werneck AO, Szwarcwald CL, Schuch FB, Stubbs B, Bastos AA, & Silva DR (2020). The role of physical activity in the association between multimorbidity and depressive symptoms: Data from 60,202 adults from the Brazilian National Health Survey. Journal of Psychosomatic Research, 134, 110122. 10.1016/j.jpsychores.2020.110122 [DOI] [PubMed] [Google Scholar]
  2. Balbim GM, Marques IG, Marquez DX, Patel D, Sharp LK, Kitsiou S, & Nyenhuis SM (2021). Using Fitbit as an mHealth intervention tool to promote physical activity: Potential challenges and solutions. JMIR mHealth and uHealth, 9(3), e25289. 10.2196/25289 [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Bergman P, & Hagströmer M (2020). No one accelerometer-based physical activity data collection protocol can fit all research questions. BMC Medical Research Methodology, 20, 141. 10.1186/s12874-020-01026-7 [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Box G, & Cox D (1964). An analysis of transformations. Journal of the Royal Statistical Society: Series B, 26(2), 211–243. 10.1111/j.2517-6161.1964.tb00553.x [DOI] [Google Scholar]
  5. Chen K, Zhang X, Petersen A, & Müller H-G (2017). Quantifying infinite-dimensional data: Functional data analysis in action. Statistics in Biosciences, 9(2), 582–604. 10.1007/s12561-015-9137-5 [DOI] [Google Scholar]
  6. Ciechanowski P, Wagner E, Schmaling K, Schwartz S, Williams B, Diehr P, Kulzer J, Gray S, Collier C, & Logerfo J (2004). Community-integrated home-based depression treatment in older adults. JAMA, 291(13), 1569. 10.1001/jama.291.13.1569 [DOI] [PubMed] [Google Scholar]
  7. Cooke AB, Rahme E, Defo AK, Chan D, Daskalopoulou SS, & Dasgupta K (2020). A trajectory analysis of daily step counts during a physician-delivered intervention. Journal of Science and Medicine in Sport, 23(10), 962–967. 10.1016/j.jsams.2020.04.010 [DOI] [PubMed] [Google Scholar]
  8. Dekker J, Buurman BM, & van der Leeden M (2019). Exercise in people with comorbidity or multimorbidity. Health Psychology, 38, 822–830. 10.1037/hea0000750 [DOI] [PubMed] [Google Scholar]
  9. Diabetes Prevention Program Research Group. (2002). The Diabetes Prevention Program (DPP). Diabetes Care, 25, 2165–2171. 10.2337/diacare.25.12.2165 [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Feehan LM, Geldman J, Sayre EC, Park C, Ezzat AM, Yoo JY, Hamilton CB, & Li LC (2018). Accuracy of Fitbit devices: Systematic review and narrative syntheses of quantitative data. JMIR mHealth and uHealth, 6(8), e10527. 10.2196/10527 [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Germini F, Noronha N, Borg Debono V, Abraham Philip B, Pete D, Navarro T, Keepanasseril A, Parpia S, De Wit K, & Iorio A (2022). Accuracy and acceptability of wrist-wearable activity-tracking devices: Systematic review of the literature. Journal of Medical Internet Research, 24(1), e30791. 10.2196/30791 [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Glass RM (1978). Psychiatric screening in a medical clinic. Archives of General Psychiatry, 35(10), 1189. 10.1001/archpsyc.1978.01770340039003 [DOI] [PubMed] [Google Scholar]
  13. Goldberg D, Rickels K, Downing R, & Hesbacher P (1976). A comparison of two psychiatric screening tests. British Journal of Psychiatry, 129(1), 61–67. 10.1192/bjp.129.1.61 [DOI] [PubMed] [Google Scholar]
  14. Hooker SA, Oswald LB, Reid KJ, & Baron KG (2020). Do physical activity, caloric intake, and sleep vary together day to day? Exploration of intraindividual variability in 3 key health behaviors. Journal of Physical Activity and Health, 17(1), 45–51. 10.1123/jpah.2019-0207 [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Imes CC, Zheng Y, Mendez DD, Rockette-Wagner BJ, Mattos MK, Goode RW, Sereika SM, & Burke LE (2018). Group-based trajectory analysis of physical activity change in a US weight loss intervention. Journal of Physical Activity and Health, 15(11), 840–846. 10.1123/jpah.2017-0484 [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Jakicic JM, Kraus WE, Powell KE, Campbell WW, Janz KF, Troiano RP, Sprow K, Torres A, & Piercy KL (2019). Association between bout duration of physical activity and health: Systematic review. Medicine & Science in Sports & Exercise, 51(6), 1213–1219. 10.1249/mss.0000000000001933 [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. King DE, Xiang J, & Pilkerton CS (2018). Multimorbidity trends in United States adults, 1988–2014. Journal of the American Board of Family Medicine, 31(4), 503–513. 10.3122/jabfm.2018.04.180008 [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Kivimäki M, Kuosma E, Ferrie JE, Luukkonen R, Nyberg ST, Alfredsson L, Batty GD, Brunner EJ, Fransson E, Goldberg M, Knutsson A, Koskenvuo M, Nordin M, Oksanen T, Pentti J, Rugulies R, Shipley MJ, Singh-Manoux A, Steptoe A, … Jokela M (2017). Overweight, obesity, and risk of cardiometabolic multimorbidity: pooled analysis of individual-level data for 120 813 adults from 16 cohort studies from the USA and Europe. The Lancet Public Health, 2(6), e277–e285. 10.1016/s2468-2667(17)30074-9 [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Lebenbaum M, Zaric GS, Thind A, & Sarma S (2018). Trends in obesity and multimorbidity in Canada. Preventive Medicine, 116, 173–179. 10.1016/j.ypmed.2018.08.025 [DOI] [PubMed] [Google Scholar]
  20. Lv N, Ajilore OA, Ronneberg CR, Venditti EM, Snowden MB, Lavori PW, Xiao L, Goldstein-Piekarski AN, Wielgosz J, Wittels NE, Barve A, Patel AS, Eckley TL, Stetz P, Gerber BS, Smyth JM, Simmons JM, Rosas LG, Williams LM, & Ma J (2020). The ENGAGE-2 study: Engaging self-regulation targets to understand the mechanisms of behavior change and improve mood and weight outcomes in a randomized controlled trial (Phase 2). Contemporary Clinical Trials, 95, 106072. 10.1016/j.cct.2020.106072 [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Lv N, Ajilore OA, Xiao L, Venditti EM, Lavori PW, Gerber BS, Snowden MB, Wittels NE, Ronneberg CR, Stetz P, Barve A, Shrestha R, Dosala S, Kumar V, Eckley TL, Goldstein-Piekarski AN, Smyth JM, Rosas LG, Kannampallil T, … Ma, J. (2022). Mediating effects of neural targets on depression, weight, and anxiety outcomes of an integrated collaborative care intervention: The ENGAGE-2 mechanistic pilot randomized clinical trial. Biological Psychiatry Global Open Science, Online ahead of print. 10.1016/j.bpsgos.2022.03.012 [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Lv N, Kringle EA, & Ma J (2022). Integrated behavioral interventions for adults with comorbid obesity and depression: A systematic review. Current Diabetes Reports, 22(4), 157–168. 10.1007/s11892-022-01458-z [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Ma J, Xiao L, Lv N, Rosas LG, Lewis MA, Goldhaber-Fiebert JD, Venditti EM, Snowden MB, Lesser L, & Ward E (2017). Profiles of sociodemographic, behavioral, clinical and psychosocial characteristics among primary care patients with comorbid obesity and depression. Preventive Medicine Reports, 8, 42–50. 10.1016/j.pmedr.2017.07.010 [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Ma J, Yank V, Xiao L, Lavori PW, Wilson SR, Rosas LG, & Stafford RS (2013). Translating the Diabetes Prevention Program Lifestyle Intervention for Weight Loss into primary care. JAMA Internal Medicine, 173(2), 113. 10.1001/2013.jamainternmed.987 [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Meier L (2020). Fitting user-specified models with group lasso penalty. In (Version 0.4–7) https://rdrr.io/cran/grplasso/ [Google Scholar]
  26. Nicolai S, Benzinger P, Skelton DA, Aminian K, Becker C, & Lindemann U (2010). Day-to-day variability of physical activity of older adults living in the community. Journal of Aging & Physical Activity, 18, 75–86. [DOI] [PubMed] [Google Scholar]
  27. Pearce M, Garcia L, Abbas A, Strain T, Schuch FB, Golubic R, Kelly P, Khan S, Utukuri M, & Laird Y (2022). Association between physical activity and risk of depression: A systematic review and meta-analysis. JAMA psychiatry, 79(6), 550–559. 10.1001/jamapsychiatry.2022.0609 [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. Pereira-Miranda E, Costa PRF, Queiroz VAO, Pereira-Santos M, & Santana MLP (2017). Overweight and obesity associated with higher depression prevalence in adults: A systematic review and meta-analysis. Journal of the American College of Nutrition, 36(3), 223–233. 10.1080/07315724.2016.1261053 [DOI] [PubMed] [Google Scholar]
  29. Toolkit PhenX. (2011). Measures from the PhenX Toolkit version February 4 2011, Ver 4.2 (www.phenxtoolkit.org). PhenX (consensus measures of Phenotypes and eXposures) is supported by NHGRI award No. U01 HG004597, 2011 (accessed January 15, 2015. In. [Google Scholar]
  30. Pratt LA, & Brody DJ (2014). Depression and obesity in the U.S. adult household population, 2005–2010 (1941–4935). (NCHS Data Brief, Issue. [PubMed] [Google Scholar]
  31. Read JR, Sharpe L, Modini M, & Dear BF (2017). Multimorbidity and depression: A systematic review and meta-analysis. Journal of Affective Disorders, 221, 36–46. 10.1016/j.jad.2017.06.009 [DOI] [PubMed] [Google Scholar]
  32. Ringeval M, Wagner G, Denford J, Paré G, & Kitsiou S (2020). Fitbit-based interventions for healthy lifestyle outcomes: Systematic review and meta-analysis. Journal of Medical Internet Research, 22(10), e23954. 10.2196/23954 [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Saeb S, Zhang M, Karr CJ, Schueller SM, Corden ME, Kording KP, & Mohr DC (2015). Mobile phone sensor correlates of depressive symptom severity in daily-life behavior: An exploratory study. Journal of Medical Internet Research, 17(7), e175. 10.2196/jmir.4273 [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Smith SM, Wallace E, Clyne B, Boland F, & Fortin M (2021). Interventions for improving outcomes in patients with multimorbidity in primary care and community setting: A systematic review. Systematic Reviews, 10(1). 10.1186/s13643-021-01817-z [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Spitzer RL, Kroenke K, Williams JBW, & Löwe B (2006). A brief measure for assessing generalized anxiety disorder. Archives of Internal Medicine, 166(10), 1092. 10.1001/archinte.166.10.1092 [DOI] [PubMed] [Google Scholar]
  36. Srivastava S, Joseph K J V, Dristhi D, & Muhammad T (2021). Interaction of physical activity on the association of obesity-related measures with multimorbidity among older adults: A population-based cross-sectional study in India. BMJ Open, 11(5), e050245. 10.1136/bmjopen-2021-050245 [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. St Fleur RG, St. George SM, Leite R, Kobayashi M, Agosto Y, & Jake-Schoffman D. (2020). Use of Fitbit devices in physical activity intervention studies across the life course: Narrative review JMIR mHealth and uHealth, 9(5), e23411. 10.2196/23411 [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Stoll CRT, Izadi S, Fowler S, Philpott-Streiff S, Green P, Suls J, Winter AC, & Colditz GA (2019). Multimorbidity in randomized controlled trials of behavioral interventions: A systematic review. Health Psychology, 38, 831–839. 10.1037/hea0000726 [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Swann C, Rosenbaum S, Lawrence A, Vella SA, McEwan D, & Ekkekakis P (2021). Updating goal-setting theory in physical activity promotion: A critical conceptual review. Health Psychology Review, 15(1), 34–50. 10.1080/17437199.2019.1706616 [DOI] [PubMed] [Google Scholar]
  40. Wang J-L, Chiou J-M, & Müller H-G (2016). Functional data analysis. Annual Review of Statistics and Its Application, 3(1), 257–295. 10.1146/annurev-statistics-041715-033624 [DOI] [Google Scholar]
  41. Wang L, Si L, Cocker F, Palmer AJ, & Sanderson K (2018). A systematic review of cost-of-illness studies of multimorbidity. Applied Health Economics and Health Policy, 16(1), 15–29. 10.1007/s40258-017-0346-6 [DOI] [PubMed] [Google Scholar]
  42. Xu SY, Nelson S, Kerr J, Godbole S, Johnson E, Patterson RE, Rock CL, Sears DD, Abramson I, & Natarajan L (2019). Modeling temporal variation in physical activity using functional principal components analysis. Statistics in Biosciences, 11(2), 403–421. 10.1007/s12561-019-09237-3 [DOI] [Google Scholar]
  43. Yao F, Müller H-G, Clifford AJ, Dueker SR, Follett J, Lin Y, Buchholz BA, & Vogel JS (2003). Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics, 59(3), 676–685. 10.1111/1541-0420.00078 [DOI] [PubMed] [Google Scholar]
  44. Yao F, Müller H-G, & Wang J-L (2005). Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100(470), 577–590. 10.1198/016214504000001745 [DOI] [Google Scholar]
  45. Yuan M, & Lin Y (2007). Model selection and estimation in the Gaussian graphical model. Biometrika, 94(1), 19–35. 10.1093/biomet/asm018 [DOI] [Google Scholar]
  46. Zeitzer JM, Blackwell T, Hoffman AR, Cummings S, Ancoli-Israel S, Stone K, & Group O. F. i. M. S. R. (2017). Daily patterns of accelerometer activity predict changes in sleep, cognition, and mortality in older men. The Journals of Gerontology: Series A, 73(5), 682–687. 10.1093/gerona/glw250 [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Zeitzer JM, David R, Friedman L, Mulin E, Garcia R, Wang J, Yesavage JA, Robert PH, & Shannon W (2013). Phenotyping apathy in individuals with Alzheimer disease using functional principal component analysis. American Journal of Geriatric Psychiatry, 21(4), 391–397. 10.1016/j.jagp.2012.12.012 [DOI] [PMC free article] [PubMed] [Google Scholar]
  48. Zhou Y, Bhattacharjee S, Carroll C, Chen Y, Dai X, Fan J, Gajardo A, Hadjipanetli P, Han K, Ji H, Zhu C, Lin S-C, Dubey P, Muller H-G, & Wang J-L (2022). fdapace: Functional data analysis and empirical dynamics. In (Version 0.5.9) https://cran.r-project.org/web/packages/fdapace/fdapace.pdf

Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

1
NIHMS1882219-supplement-1.pdf (262.6KB, pdf)
2
NIHMS1882219-supplement-2.pdf (111KB, pdf)

RESOURCES