Characterizing daily physical activity patterns with unsupervised learning via functional mixture models

Abstract

Physical inactivity is a significant public health concern. Consideration of inter-individual variations in physical activity (PA) trends can provide additional information about the groups under study to aid intervention design. This study aims to identify latent profiles (“phenotypes”) based on daily PA trends among adults living in. This was a secondary analysis of 724 person-level days of accelerometry data from 133 urban-dwelling adults (89% Latinx, age = 19–77 years). We used Actigraph accelerometers and the Actilife software to collect and process 24-hour PA data. We implemented a probabilistic clustering technique based on functional mixture models. Multiple days of data per person were averaged for entry into the models. We evaluated step counts, moderate-intensity PA (MOD), total activity and sedentary minutes as potential model variables. Bayesian Information Criterion (BIC) index was used to select the model that provided the best fit for the data. A 4-cluster resolution provided the best fit for the data (i.e., BIC=−3257, improvements of Δ = 13 and Δ = 7 from 3- and 5-cluster models, respectively). MOD provided the greatest between-cluster discrimination. Phenotype 1 (N = 61) was characterized by a morning peak in PA that declined until bedtime. Later bedtimes and the highest daily PA volume were distinct for phenotype 2 (N = 18), along with a similar peak pattern. Phenotype 3 (N = 29) membership was associated with the lowest PA levels throughout the day. Phenotype 4 was characterized by a more evenly distributed PA during the day, and later waking/bedtimes. Our findings point to distinct, interpretable PA phenotypes based on temporal patterns. Functional clustering of PA data could provide additional actionable points for tailoring behavioral interventions.

Introduction

It is estimated that 21–31% of the adults worldwide do not engage in sufficient physical activity (PA) for optimal health(Dumith et al., 2011; Guthold et al., 2018; World Health Organization, 2021). Physical inactivity and similarly sedentary behavior are associated with adverse health outcomes (e.g., cardiovascular and metabolic diseases) (Feng et al., 2023; Niemelä et al., 2019), and co-morbidities (e.g., poor sleep, depressive symptomologyBull et al., 2020; Chastin et al., 2019; Ekelund et al., 2019a, b; Healy et al., 2008). Effective intervention on these behaviors typically requires tailored approaches that consider contextual (e.g., living environment) and person-level (e.g., behavioral determinants) factors that can influence one’s behavior(Bauman et al., 2012). Similarly, inter-individual variations in how habitual PA patterns unfold over the course of a day could provide meaning information for tailoring such interventions (e.g., just-in-time adaptive interventions). For example, sys tematic analyses of the relationship between PA, sedentary behavior, and chronotype (“peak times of the day according to one’s circadian rhythm” (Horne & Ostberg, 1976)), indicate that evening chronotypes are associated with less PA and more time in sedentary activities, compared to morning chronotypes (Sempere-Rubio et al., 2022). This link moreover appears to be independent of differences in light exposure or seasonality associated with geographic location, as well as type of population under study.(Sempere-Rubio et al., 2022).

However, there has been scarce research investigating potential homogenous profiles or clusters (“phenotypes”) of habitual PA behavior using quantitative methods that explicitly account for the daily temporality of PA. This approach is different than using daily (or weekly) summary scores (e.g., total steps or minutes of activity) and instead considers the entire PA trajectory without aggregation. Such a modeling approach has the potential to identify phenotypes that are more informative about the PA behavior of the individuals and groups under study, which in return could increase their interpretability and actionability when tailoring interventions. Numerous traditional cross-sectional clustering techniques have been implemented for phenotyping PA behavior to date (Lam & Garcia, 2021; Rovniak et al., 2010; Todd et al., 2016; Vagni & Cornwell, 2018). These techniques typically rely on aggregated PA scores (e.g., total daily steps or minutes of activity), and cluster the observed time-series data using either geometric distance-based methods (e.g., k-means clustering), or by creating features that summarize the activity patterns within the given time window (e.g., principal component analysis; PCA). However, this results in the omission of the temporal dynamics of the data during the clustering process(Bouveyron et al., 2015; Pulido et al., 2021). Instead, using a more flexible clustering technique that can explicitly model these temporal dynamics could enable more informative and actionable PA phenotypes.

To this end, we investigate a clustering approach based on discriminative functional mixture models (FMMs)(Bouveyron et al., 2015), which belong to the family of functional data analytic (FDA) techniques(Reiss et al., 2017). In this framework, the unit of analysis is a collection of discrete observations over time (i.e., data curves or functions), as opposed to scalar data points(Ramsay & Dalzell, 1991). Accordingly, FMMs model a set of observed data curves from a heterogenous sample into K homogenous clusters based on similarity(Bouveyron et al., 2015). As such, potential inter-individual differences in the temporal trends explicitly inform the phenotype-assignment process. This aspect makes FMMs particularly useful for capturing within-individual temporal fluctuations (e.g., changes in PA behavior over the course of the day). Moreover, FMMs are a probabilistic clustering method and allow consideration of the confidence bounds of a given cluster assignment. They can also distinguish between distinct latent trajectories with a few predictors and allow parsimony(Bouveyron et al., 2015). Other FDA-based methods have been implemented for studying circadian rhythms using accelerometry data(McDonnell et al., 2021), phasic variations in gait patterns(Lee et al., 2019), and other medical data scenarios that involve frequently sampled, interdependent data(Sørensen et al., 2013; Ullah & Finch, 2013). However, to our knowledge, no previous study has investigated FMMs to identify possible phenotypes of PA trajectories.

Among the PA parameters available from accelerometers, step counts and moderate-to-vigorous intensity activity (MVPA) have been studied for cut-off points linked to health outcomes, supporting the development of public health guidelines, recommendations for goal-setting and intervention design (Bull et al., 2020; Ekelund et al., 2019a; Tudor-Locke et al., 2008, 2013). For example, previous analyses of accelerometry data from nationally representative cohorts (e.g., National Health and Nutrition Examination Survey; NHANES) concluded that accumulating ~ 8,000 steps within a day corresponds to 30 min of MVPA (Tudor-Locke et al., 2011). The same study indicated that ~ 7,000 steps/day corresponded to obtaining the 150 min of weekly MVPA recommended by the Centers for Disease Control and Prevention(Tudor-Locke et al., 2011). A recent meta-analysis echoed these findings, (del Pozo Cruz et al., 2022) reporting a marked reduction in all-cause mortality up to ~ 7,500 daily steps (hazard ratio = 0.57), with marginal gains observed beyond ~ 11,000 steps/day. This is also in line with the upper threshold of the recommended weekly MVPA (i.e., 150–300 min per week) by the World Health Organization (WHO)(Bull et al., 2020). Finally, studies using the isotemporal substitution model to investigate time reallocation over the course of a 24-hour period indicate that substitution of sedentary time with higher intensity PA is associated with more favorable health outcomes (Grgic et al., 2018). This suggests a dose response relationship and further motivates the focus on MVPA.

Current guidelines do not indicate any thresholds for sedentary behavior, which is defined as activities that expend < 1.5 METs (e.g., sitting, lying down, standing still) (Ainsworth et al., 2011). Nevertheless, the general recommendation is to reduce its overall daily volume(Bull et al., 2020), and evidence indicates that replacing sedentary behavior with PA of any intensity is beneficial (Benatti & Ried-Larsen, 2015; Ekelund et al., 2019b). Similarly, an increasing body of evidence points to the necessity of “breaking” sedentary time throughout the day to minimize the detrimental effects on various health outcomes (Bailey & Locke, 2015; Duran et al., 2023; Giurgiu et al., 2020). These recent findings are particularly relevant to the research question addressed in this study, as they point to the importance of the distribution of PA throughout the course of the day, as opposed to the mere total daily volume.

Accordingly, this study aimed to investigate interpretable and potentially actionable phenotypes of daily PA trajectories using accelerometry. As an exploratory technique, clustering models intrinsically assume unobserved heterogeneity in the data due to latent differences between the data points (i.e., participants) (Bouveyron et al., 2018; Patton & Weller, 2023; Ullah & Finch, 2013). They therefore assess whether the data can be separated into latent, homogeneous subgroups based these differences(Bauer et al., 2022; Benassi et al., 2020; Patton & Weller, 2023). In line with this premise, we expected to observe multiple homogenous phenotypes characterized by differences in the temporal patterns of daily PA, and explored the number of clusters and the structures they would take in this sample. Given that the clusters are informed by trajectories, rather than the total sum of the daily PA parameters, we further expected similarities among the identified phenotypes with respect to the day-level sums for some of the PA parameters.

Methods

Study sample

The study sample included adults enrolled into an ancillary study of Convoy Q or one of the three pilot studies of Precision in Symptom Self-Management (PriSSM) Center (Bakken et al., 2019) at Columbia University Irving Medical Center (CUIMC) between 2018 and 2020. Convoy Q was an observational cross-sectional study of cognitive health among sexual and gender minority (SGM) adults. Enrollment criteria included SGM adults ages 18–85 years without any past or current diagnosis of cognitive impairment or severe mental disorder (e.g., psychosis). The PriSSM Center pilot studies investigated health disparities among the Latinx population and focused on (1) sleep health and disturbance among women ages 40 or older (N = 53); (2) sleep health outcomes associated with exposure to discrimination-related stress among gender minority (i.e., transgender and nonbinary) adults 18 or older (N = 38); and (3) improving sleep disturbance and fatigue among adults 50 or over (N = 26) living with HIV through a fatigue self-management program. Complete inclusion and exclusion criteria are described elsewhere(Ensari et al., 2021). Data from these participants were combined to allow adequate data heterogeneity in the overall sample for the present analysis, motivated by the a priori research question.

Data collection

All procedures were approved by the institutional review boards of the CUIMC and the New York State Psychiatric Institute. Informed consent was obtained from all participants. Demographic data (e.g., age, race/ethnicity) were collected using self-report. PA data were collected using Actigraph (wGT3X-BT) accelerometers, worn on participants’ non-dominant wrist (Montoye et al., 2020; Straczkiewicz et al., 2019). Raw data were collected in 60-sec epochs, validated and processed using the Actilife software following published guidelines(Troiano et al., 2008). Participants were asked to keep a log of the times they got out of bed in the morning and went to bed at night each day. We primarily relied on the software-detected awakening and bed times, and confirmed against the participant-reported times and Actigraph’s light sensor for discrepancies as recommended(Martin & Hakim, 2011). For handling missingness in the data, a valid day was classified as a day with at least 8 h of wear time during waking hours (i.e., outside of the individual’s primary sleep period), providing a total weartime range of 8–24 h in the data sample. The use of 8 h as the cut-off is motivated by our preliminary sensitivity analyses indicating no significant differences in the within-individual means or variability (SD) in the PA outcomes when compared to a 10-hour cut-off, therefore providing more data for analysis, as well as previous studies conducted by others who similarly implemented an 8-hour weartime cut-off (Airlie et al., 2022; Prescott et al., 2020). Days with unrealistically low activity counts suggesting likely non-wear (e.g., < 500 steps for the entire 24-hour period), often corresponding to first day of data collection, (Burchartz et al., 2023) were similarly excluded. All participants with at least 3 valid days of data were included in the analyses.

Model outcome variable

Inspection of the accelerometry data indicated that none of the participants had engaged in any vigorous-intensity PA. Consequently, we first considered the following variables as the potential outcome variable in the FMMs: step counts, total activity (i.e., sum of light and moderate intensity PA), total sedentary minutes (SED), total sedentary bout minutes (i.e., total sedentary time accumulated in bouts of ≥ 10 min; SEDB), and axis 1 vector magnitude counts (VM1). As expected, several of the variables were highly correlated in the overall study sample: step counts and VM1 (r = 0.95), MOD and VM1 (r = 0.96), total activity and VM1 (r = 0.89), total activity and step counts (r = 0.88), MOD and step counts (r = 0.90), SED and step counts (r=−0.86), total activity and SED (r=−0.97), total activity and SEDB (r=−0.88), MOD and SED (r=−0.76), total activity and MOD (r = 0.78). For interpretability and given the strong corre lations, we excluded VM1 from further consideration. The SED and SEDB variables by nature create data matrices with zero-inflation (i.e., excess zeros) and overdispersion, which can lead to unreliable model estimates and invalid model inference (Al-Taweel & Algamal, 2022; Campbell, 2021). Moreover, given our focus on PA and similarly strong correlations, we did not further evaluate these variables. Accordingly, total activity, steps, and MOD were evaluated in the subsequent analyses using separate models.

Data analysis

Clustering analysis within an FDA framework involves 3 steps: (1) Processing of the longitudinal data to be clustered by reconstructing into their “functional” form, (2) Model selection and inference, (3) Evaluation of the phenotypes identified from the final model in step 2 via comparisons. We describe below these steps in further detail.

Data processing

Processing of the data refers to the conversion of scalar, discrete data points into a data curve (or “function”), thus making the unit of analysis an entire trajectory of data points, i.e., smoothed functions. To accomplish this, the general trend in the longitudinal data is synthesized and smoothed using basis functions (e.g., B-splines, Fourier). For the purposes of our analyses, each participant’s data were averaged across their available days and as such each row in the data matrix corresponds to a participant represented by a sample path of 24 data points (i.e., 24 h). These sample paths were processed using a Fourier basis to smooth the curves, as the Fourier basis functions are considered appropriate for data varying over a continuum and might have some periodicity. The obtained curves, depicted in Fig. 1, are then used in the subsequent clustering step.

Fig. 1.

Fourier basis functions (i.e., the periodicities in the observed curves) representing the 24-hour activity pattern of each participant. Each curve represents 1 participant (N = 133)

Model inference and selection

The FMM-based clustering algorithm (“funFEM”) aims to predict, for each observed data curve, probability of membership to one of K homogeneous groups (“clusters”) in a latent subspace that is assumed to be the most discriminative subspace for the K clusters (Bouveyron et al., 2015). The most discriminative subspace, and therefore the optimal cluster membership, is determined by minimizing within-cluster variance and maximizing between-cluster variance (Fisher, 1936). The selection of the optimal K is done via iterative testing and comparison of model fit indices between competing models (Pulido et al., 2021) and as well inspection of posterior probabilities of cluster membership (i.e., higher values indicating higher confidence with which the assignment was made). Accordingly, we fit FMMs estimating up to K = 6 clusters and using variables of MOD and steps in separate models. The selection of the best fitting model was based on the Bayesian Information Criterion (BIC) as this has been recommended for FMM selection in this context (Bouveyron et al., 2015), as well as model posterior probabilities of cluster membership for each participant. Selection of the most discriminative outcome variable in the final model was based first on visual inspection of cluster separation and then through a one-way analysis of variance (ANOVA) to assess the total variance in hourly PA explained by the interaction of cluster and hour.

Characterization of phenotypes

To characterize the phenotypes identified by the best-fitting model, we assessed differences in hourly- and total daily steps, total activity, MOD, and SED, using pairwise t-tests adjusted for multiple observations with Bonferroni correction. In addition, we assessed self-reported fatigue, pain, sleep disturbance scores using the Patient-Reported Outcomes Measurement Information System (PROMIS) questionnaires (Ameringer et al., 2016; Cella et al., 2010; Full et al., 2019) and demographic factors of age, body mass index (BMI), education, employment (employed full-time or parttime, unemployed, on disability, homemaker/volunteer work), relationship status (in a committed partnership or single), and household count (number of people living in the household) as potential predictors of the phenotypes using multinomial logistic regression for whom the data were available. Finally, as a post-hoc inspection of potential bias in the clustering process due to study source, we evaluated whether there was a significant association between phenotype assignment and belonging to one of the four studies, using an overall χ2 test of independence and pairwise post-hoc comparisons. The significance level for all statistical tests was set at p < 0.05.

Results

Sample characteristics

One participant had only 2 days of accelerometry data and thus was excluded from the analysis, resulting in a final sample of 133 individuals. Descriptive statistics for demographic variables, awakening and bed times by phenotype are provided in Table 1. The median age was 56 years (mean absolute deviation (MAD) = 14.82, Range = 19–77), and 89.5% (N = 119) of the participants self-identifying as Latinx (any race). Participants on average had 5.44 days of data (SD = 1.71, Range = 3–9 days), providing a total of 724 days of accelerometer data for analysis.

Table 1.

Frequency and median (median absolute deviation) values for demographic variables, awakening and bed times by phenotype

Phenotype (N)	Age (years)	Weight (lbs)	Male Gender	Awakening time (24 h)	Bed time (24 h)
1 (61)	59 (11.9)	160 (28.9)	17 (27.9%)	07:32 (1.80)	21:00 (4.32)
2 (18)	54 (10.4)	158 (30.7)	5 (27.8%)	07:14 (1.43)	06:58 (10.01)
3 (29)	64 (11.9)	158 (33.7)	9 (31.0%)	07:59 (3.19)	07:20 (10.43)
4 (25)	47 (22.2)	161 (35.6)	7 (28.0%)	09:13 (1.84)	02:20 (2.06)

lbs = pounds

Clustering model results

A 4-cluster resolution with Fourier basis provided the best fit for the data (BIC = −3257, improvements of Δ = 13 and Δ = 7 from 3- and 5-cluster models, respectively), providing support for our primary hypothesis. Figure 1 depicts the Fourier basis functions (i.e., the periodicities in the observed curves) representing each participant. A visualization of the 4 functional clusters and orientation of the participant scores (i.e., model coefficients) projected into the subspaces are provided in Fig. 2. MOD variable was used as the outcome variable in the final model as it provided the greatest separation between clusters. Results of the pairwise t-tests comparing hour-level PA parameters were statistically significant (See Supplementary Table 1). For a visual comparison, plots of the functional subspaces identified from FMMs using step counts, total activity and SEDB as the outcome variable are provided in Supplementary Fig. 1. Median individual membership probability was 0.99 (MAD = 0.01, Range = 0.51–1.00), indicating a high level of confidence with which each participant was assigned to each cluster.

Fig. 2.

Individual participant scores (i.e., FMM coefficients) projected within the 4 discriminative functional subspaces according to the Fourier basis functions. Each dot represents 1 participant (N = 133)

Characterization of the phenotypes

The 24-hour trajectories of MOD, total activity, and SED for all 4 phenotypes are depicted in Fig. 3. Medians for hour- and day-level step counts, total activity, and SED minutes are provided in Table 2. Boxplots in Fig. 4 provide a visual comparison of the between- and within-phenotype variance. Phenotype 1 comprised the largest cluster (N = 61) and its trajectory was characterized by an initial peak in activity earlier in the day upon waking, followed by a decline (i.e., from ~ 11:00 am onward) over the remainder of the day. The participants associated with this phenotype accumulated a median 135 min of MOD and 10,337 step counts per day. Phenotype 2 (N = 18) was associated with the highest levels of total activity, MOD, and step counts both at the day- and hour-level. The median MOD among the participants associated with this phenotype was 295 min. Though the period of waking hours was similar that of phenotype 1, phenotype 2 was characterized by a sharper peak-and-dip pattern in activity levels. This indicates that these individuals were more likely to accumulate their PA during a narrower time period (See Fig. 3). Phenotype 3 (N = 29) was associated with the lowest volume of MOD and total activity, based on both the 24-hour trajectories and overall day-level medians. Consequently, membership to this phenotype was associated with higher sedentary levels compared to other phenotypes, based on both total accumulated (SED) and bout-minutes (SEDB) of sedentary time (See Table 2). Finally, median age for phenotype 3 was higher compared to the other phenotypes (i.e., 64 vs. 47–53.5 years). Phenotype 4 (N = 25) was characterized by more evenly distributed total activity patterns throughout the day, in contrast to the peak-and-decline pattern observed for phenotype 1. However, the day-level summary scores were comparable between the 2 phenotypes, indicated by almost identical SEDB values (i.e., 110 vs. 109 min). Membership to phenotype 4 was also associated with a daily median of 183 min of MOD, and later awakening and bed times relative to other phenotypes.

Fig. 3.

Total (light- and moderate intensity) activity, MOD and SED minutes over 24 h depicted using locally weighted scatterplot smoothing (LOESS) for each functional phenotype. Shaded grey areas indicate 95% confidence intervals

Table 2.

Multivariate PA summary statistics (i.e., medians and mean absolute deviation; MAD) at the hour and day level for the 4 phenotypes (N₁=22, N₂=51, N₃=29, N₄=26)

PA variable	Hour - level		Day - level
	Median (MAD)	Range	Median (MAD)	Range
MOD
Phenotype 1	8.75 (5.56)	0–37	135 (57.82)	30–349
Phenotype 2	18.833 (11.73)	0–57.4	295.5 (134.17)	19–867
Phenotype 3	3 (2.96)	0–21.5	56 (32.61)	0–186
Phenotype 4	12.75 (6.30)	0–36.66	183.5 (78.57)	30–518
Total Activity
Phenotype 1	39.57 (10.85)	0–60	614 (176.42)	157–1027
Phenotype 2	46.25 (12.60)	2–59.75	743.5 (160.12)	117–1138
Phenotype 3	29.75 (12.97)	0–56.5	486 (185.32)	84–915
Phenotype 4	41.75 (8.52)	0–59.25	605.5 (194.22)	137–1353
SED
Phenotype 1	19.75 (10.74)	0–60	338 (114.16)	64–908
Phenotype 2	13.75 (12.47)	0.25–58	278 (126.02)	52–723
Phenotype 3	29.143 (11.61)	0–60	495 (189.77)	106–942
Phenotype 4	17.75 (8.52)	0–60	307 (91.92)	53–635
Step counts
Phenotype 1	641.14 (352.93)	0–2008.5	10,675 (4170.55)	2,434 – 20,740
Phenotype 2	996.5 (514.46)	8.25–2526.57	16,224 (537.51)	1,665 – 37,969
Phenotype 3	367.85 (248.01)	1–1629	6,340.5 (2998.5)	1,105 – 14,982
Phenotype 4	738.42 (307.03)	0–2217.5	11,593 (4134.97)	1,590 – 26,529

Total Activity = light-moderate-vigorous intensity physical activity, MOD = moderate-intensity physical activity, SED = sedentary total minutes. MAD = Mean absolute deviation

Fig. 4.

Distribution of daily waketime sums for PA variables by phenotype. The bottom, middle and upper hinges of the boxplots indicate the first, 2nd (median) and 3rd quartiles, respectively

Pairwise comparison of the phenotypes

T-tests of day-level scores between the phenotypes indicated statistically significant differences in step counts for all pairwise comparisons (See Table 3). Total activity minutes significantly differed in all comparisons except for phenotypes 1 and 4, and SED similarly differed in all comparisons but between phenotypes 2 and 4. Of note, SEDB were comparable among phenotypes 1,2, and 4 both at the hour- and day level, and only differed in comparison to phenotype 3 (See Table 3 and Supplementary Table 1).

Table 3.

Complete results of the posthoc pairwise t-tests comparing day-level PA variables among phenotypes (n1 = 327, n2 = 86, n3 = 169, n4 = 122)

PA variable	Comparison groups	t-statistic	df	Adjusted p-value
Step counts	Phenotype 1–2	−8.68	103.81	< 0.00001
	Phenotype 1–3	12.73	441.00	< 0.00001
	Phenotype 1–4	−2.60	183.92	0.01
	Phenotype 2–3	14.29	103.85	< 0.00001
	Phenotype 2–4	6.04	154.20	< 0.00001
	Phenotype 3–4	−10.63	181.15	< 0.00001
Total	Phenotype 1–2	−5.06	119.47	< 0.00001
Activity	Phenotype 1–3	7.58	347.49	< 0.00001
	Phenotype 1–4	−0.95	183.00	0.344
	Phenotype 2–3	9.55	146.12	< 0.00001
	Phenotype 2–4	3.43	189.08	0.001
	Phenotype 3–4	−6.11	221.50	< 0.00001
MOD	Phenotype 1–2	−10.60	92.89	< 0.00001
	Phenotype 1–3	17.90	484.61	< 0.00001
	Phenotype 1–4	−5.66	165.80	< 0.00001
	Phenotype 2–3	15.56	90.34	< 0.00001
	Phenotype 2–4	6.89	128.41	< 0.00001
	Phenotype 3–4	−15.03	150.53	< 0.00001
SEDB	Phenotype 1–2	3.53	134.82	0.002
	Phenotype 1–3	−9.04	265.51	< 0.00001
	Phenotype 1–4	2.91	234.41	0.008
	Phenotype 2–3	−10.01	222.69	< 0.00001
	Phenotype 2–4	−0.98	175.17	0.328
	Phenotype 3–4	10.17	288.06	< 0.00001

Posthoc analyses

Phenotype 3 was associated with older age compared to phenotype 4 (t = 3.02, p = 0.024). Age did not differ significantly across other pairwise comparisons, and likewise the distribution of sex (i.e., assigned at birth) was similar (i.e., p > 0.05). The complete results of the multinomial regression analyses including point estimates, 95% confidence intervals, and the p-values, are provided in Supplementary File 2. Higher sleep disturbance scores were associated with slightly greater odds of being in phenotype 1 vs. phenotype 2 (OR = 1.09, p = 0.041; see Supplementary Table 2 for full results). There were no significant effects for the PROMIS fatigue or pain scores (See Supplementary Tables 3–4). Higher BMI was associated with greater odds of being in phenotype 4 vs. 2 (OR = 1.24, p = 0.037), whereas higher household count was associated with greater odds of being in phenotype 4 vs. 1 (OR = 1.41 p = 0.043). The overall χ2 statistics for the remaining factors (i.e., employment, education, relationship status) were not significant (χ2 = 11.482, df = 12, p = 0.488; χ2 = 11.48, df = 12, p = 0.488; χ2 = 4.5435, df = 3, p = 0.2084, respectively). Finally, the proportions of the phenotype assignments within each of the 4 pilot studies is provided in Supplementary Table 9. The overall X² statistic for the post-hoc evaluation was significant at p = 0.040, however; the adjusted pairwise comparisons indicated no significant differences across the study samples, suggesting lack of apparent bias in phenotype assignment due to specific study.

Discussion

In this study, we investigated phenotypes of daily PA trajectories among a sample of adults across the age spectrum using a functional data clustering framework that considers entire data curves as the unit of analysis. Our analyses indicated 4 distinct phenotypes characterized by differences in the temporal distribution of multiple PA parameters. The findings demonstrate that consideration of longitudinal patterns through appropriate analytic techniques can improve our understanding of how PA patterns unfold over time.

Functional PA phenotypes

The results from the FMMs indicated 4 distinct, homogeneous PA phenotypes characterized by differences in the trend of the activity and furthermore in the total daily durations. The activity pattern of phenotype 1 (i.e., peak in activity during mid-morning, decline toward evening, higher sedentary minutes leading up to bedtime) could represent the profile of the working adult with traditional daytime work schedule. In comparison, phenotype 4 might be representative of the younger adults with less traditional work schedules or in school. This suggestion is in part based on the younger median age and the shift in the circadian patterns where the median awakening and bedtimes were later in comparison to other phenotypes. Of note, phenotype 4 was distinctly characterized by a trajectory of a more evenly distributed total activity over the course of the day, though the day-level medians were comparable to those of phenotype 1. Phenotype 2 was the smallest cluster and associated with the largest total activity and MOD, as well as a smaller decline in activity toward bedtime. However, the overall pattern of awakening and bedtimes was similar to that of phenotype 1. The relatively smaller proportion of phenotype 2 membership is in line with the reported population level prevalence of adults engaging in sufficient amount of daily and weekly PA. Finally, phenotypes did not differ with respect to the distribution of gender or age, except for the older age associated with phenotype 3 membership compared to phenotype 4. Given that phenotype 3 was also associated with the lowest PA levels, these findings are collectively in accordance with the literature indicating an age-related reduction in PA and increase in sedentary levels, with substantial declines among older adults (i.e., 65 + years)(Bull et al., 2020; Dumith et al., 2011; Troiano et al., 2008).

Implications of the phenotypes

To further contextualize the identified phenotypes, we rely on PA level “zones” proposed in the literature (Tudor-Locke et al., 2008) that are based on a hierarchy of cut-off points for steps/day: 1) < 5,000 steps/day (sedentary); 2) 5,000–7,499 steps/day (low active); 3)7,500–9,999 steps/d (somewhat active); 4) 10,000–12,499 steps/day (active); and 5) 12,500 steps/day (highly active). According to these categories, members of phenotype 1 (i.e., 10,013 steps/day) would be equally likely to fall within the “active” and “somewhat active” zones. Phenotype 3 membership (6,287 steps/day) would be associated with the “low active” or “sedentary” zones. Previous research further estimated a daily step count of < 7,500 as the minimal threshold for accumulating ~30 min of MOD and being considered “physically active” (Tudor-Locke et al., 2013). Accordingly, phenotype 3 is further associated with the lowest likelihood of meeting the PA guidelines for adults and thus the highest risk of deleterious health effects associated with physical inactivity. In contrast, phenotypes 2 and 4 represent “highly active” profiles and are most likely to accumulate the weekly 150 min of MVPA recommended by PA guidelines (Bull et al., 2020), based on both step counts and MOD scores (See Table 3). Of note, total SEDB scores were comparable across phenotypes 1, 2 and 4 both at the hour- and day-level (i.e., p > 0.05; See Table 3). Given that total activity was comparable between phenotypes 1 and 4, but MOD was significantly higher for phenotypes 2 and 4, this suggests that phenotype 1 was associated with the highest amount of light-intensity activity throughout the day. Given the body of evidence on favorable cardiometabolic outcomes and reduced all-cause mortality linked to regular light-intensity activity(Chastin et al., 2019; Clark et al., 2022; Healy et al., 2008), these findings have important implications particularly for populations who might not be able to engage in sufficient amounts of daily- or weekly MVPA to meet the PA guidelines. For these individuals, shifting the focus from attaining a certain amount of MVPA per day to instead maintaining a positive light intensity–sedentary time balance (i.e., spending more time in light-intensity than sedentary time) might be a more feasible approach to attenuate the deleterious health consequences of sedentary time.

Generalizability of the study sample and phenotypes

The high correlation between total activity and sedentary minutes (r=−0.97) in the overall sample is in line with findings from others reporting high correlations between accelerometry-determined light-intensity activity and sedentary minutes (r=−0.96, N = 169)(Healy et al., 2008). Given that total activity includes both light- and moderate intensity PA in our sample, this similarity might be because light intensity PA accounted for more of the total activity counts in our sample. From a modeling perspective, this could also help explain why MOD as the outcome variable had greater discriminant ability than other variables. That is, MOD might have provided the sensitivity for detecting relevant PA while reducing likelihood of including activity and movements that might not be considered as clinically meaningful. None of the participants in this study had vigorous-intensity PA and this finding is in line with those from previous studies conducted with various populations (Ekblom-Bak et al., 2022; Howard et al., 2015; Pratt et al., 2020; Rao et al., 2016; Troiano et al., 2008) reporting marginal or no vigorous-intensity PA among adults. From this perspective, the habitual daily PA patterns observed in our study sample overall were similar to other studies with samples comprising a variety of demographic backgrounds reported in the literature. Of note, moderate- and vigorous intensity PA are typically reported as an aggregate (i.e., MVPA) in the literature, which limits our ability to compare vigorous-intensity PA findings on their own. It is possible that moderate- and vigorous intensity PA outcomes are differentially associated with health outcomes and behaviors (e.g.,(Kodama et al., 2009), motivating the rationale to analyze and report these variables separately.

Consideration of additional factors

There are other factors that could be associated with phenotype membership likelihood. In post hoc analyses, phenotype 1 was associated with higher sleep disturbance compared to phenotype 2 (Median = 47.0 and 42.3, respectively). There were also no retired individuals in phenotype 2, and the median BMI (21.3) was the lowest. In contrast, phenotype 3 was associated with the highest fatigue scores. These factors could collectively explain the relatively higher volumes of PA characterizing phenotype 2 and the relatively lower volume of PA observed in phenotype 3. While the study participants resided in urban neighborhoods (e.g., New York City) where use of public transportation and walking are more common primary modes of commuting vs. driving, information on car access or use habits could provide additional valuable information for contextualizing the phenotypes. Similarly, we do not have more detailed data on social or built-in environment, such as proximity to PA-promoting facilities, which can be associated with PA behavior (Josey & Moore, 2018). The self-reported scores on fatigue, pain, or perceived general health were not substantially associated with phenotype membership, though some of the results may have reached our criterion for statistical significance with a larger, more well-powered sample. Accordingly, these findings should be approached with caution given their exploratory nature and limited availability of data for some of the variables.

Limitations

We acknowledge some limitations of this study. First, accelerometry data were averaged across the available number (3–9) of days per participant. This was because the FMM used in this work does not allow nested/hierarchical data (i.e., multiple rows of data per individual). An alternative approach might be to conduct a 2-step functional clustering which involves dimension reduction via functional PCA (fPCA) followed by conducting a classical cross-sectional clustering analysis (e.g., k-means) on the dimensions (“features”) identified in step 1. However, this approach reduces the temporal dimension of the data to create orthogonal features, and as such has 2 limitations. First, it does not allow consideration of the entire daily trajectory of the individual’s activity patterns, which is counterintuitive to the a priori goal of this work. Second, the new dimensions produced from the dimension reduction are not as interpretable as the FMM approach. Another limitation is that our sample size was relatively small with 133 participants and 3–9 days of data per person. Future research would benefit from investigating the stability of the identified phenotypes over longer periods of time, as well as any within-individual variability that might have clinical implications. Another limitation is the lack of details regarding the type (e.g., leisure, occupational, transportation) of the PA accumulated by the participants. Knowledge of this aspect can be helpful, for example, when tailoring the timing and type of recommendations delivered in an intervention that aims to increase overall PA levels. Similarly, we did not have information on daytime sleep (e.g., naps) as most participants did not record these in their logs. Thus, we were not able to assess potential differences in daytime sleep patterns between the identified phenotypes. Finally, the study included a convenience sample of primarily Latinx adults and higher proportions of SGM adults (~ 40%) and those living with HIV (~ 20%) than the general population. While the pairwise comparisons did not indicate significant influence of the study on cluster assignment, it is possible that one might identify additional phenotypes with a different participant sample composition. Future investigations are warranted to assess whether the phenotypes identified in our analyses could generalize to other adult populations. For example, using larger cohort-based samples of greater diversity with respect to sociodemographic background can facilitate a more comprehensive understanding of these phenotypic PA patterns. This would be useful for informing the tailoring of effective interventions to increase PA and decrease sedentary behavior across a wide range of patient profiles.

Conclusion

This work implemented a functional data analytic approach to identify potentially meaningful clusters of daily PA trajectories. The results from the FMMs indicated 4 distinct, homogeneous PA phenotypes. Some of the attributes of these phenotypes have been previously alluded to in the literature, and we further delineate other novel attributes through the evaluation of their trajectories. The median membership probability of 0.99, indicating high confidence in cluster assignments. MOD as the outcome variable had the greatest discriminant performance, suggesting it might provide a better balance of specificity and sensitivity compared to other variables. The methodological approach in this work contributes to the literature that has thus far relied on aggregated summary scores on PA for characterizing PA behavior. Identification of phenotypes that consider the temporal variations in naturally occurring PA patterns can inform the design of more efficacious behavioral interventions that are tailored at the right level.

Supplementary Material

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/s10865-024-00519-w.