ALACRITY Phase I Data Analysis

• ALACRITY Phase I data is a longitudinal mHealth dataset collecting passive sensor and daily EMA reports from middle-aged and older adults with mood disorders.
• It employs advanced time-series methods, including change-point detection, co-segmentation, and MOSUM-based hotspot identification, to pinpoint clinically meaningful stress episodes.
• Machine learning models, particularly random forest and boosting, substantially improve stress period prediction accuracy compared to traditional methods.

The ALACRITY Phase I data comprise a comprehensive, longitudinal mHealth dataset collected from middle-aged and older adults with mood disorders (and, in most cases, chronic pain), designed to support research on the detection and prediction of emotionally stressful periods using passively sensed behavioral data in conjunction with self-reported stress. Data were captured via smartphones and wearables, summarized at daily resolution, and include both multimodal passive sensor streams and daily ecological momentary assessment (EMA) stress self-reports. The dataset supports development, validation, and benchmarking of advanced time-series methods—including co-segmentation, multivariate change point detection, and interval-based hotspot identification—for extracting clinically meaningful periods of stress from complex, nonstationary behavioral data.

1. Cohort, Devices, and Data Collection Protocols

Participants and Monitoring

The ALACRITY Phase I paper enrolled 48 adults aged 45–75 (per (Kim et al., 14 Feb 2025), broader cohort per (Kim et al., 8 Nov 2025)), all diagnosed with a DSM-5 mood disorder; 60% also reported chronic pain. Each subject was provided with an Android smartphone (or, in select protocols, a wearable device) configured with continuous passive-sensing applications. The monitoring window ranged from 50–140 consecutive days; each day, participants completed an EMA survey at bedtime.

Data Streams and Features

Colleted data include:

• Passive-sensing (summarized daily):
  • Mobilization: Total daily step count, seconds spent walking (active time)
  • Sleep: Sleep duration (sec), sleep interruption count
  • Sociability: Conversation percentage (fraction of day with detected speech), conversation duration (sec)
  • Location: Travel diameter (m), time spent traveling (sec), radius of gyration (m)
  • Device usage: Total activity-stream uptime, total location-stream uptime
• Self-reports (EMA):
  • Stress level (Yₜ) ∈ {1,…,5}
  • Arousal (Aₜ) ∈ {1,…,5}
  • Valence (Vₜ) ∈ {1,…,5}
  • Adjusted stress (Ŷₜ): continuous, via transformation

A tabular summary of the main variables:

Name	Type	Definition
Step count	Continuous	Total daily steps
Active time	Continuous	Seconds walking/day
Sleep duration	Continuous	Seconds asleep/day
Sleep interruption	Continuous	# restless periods/night
Conversation %	Continuous	% of day with voice detected
Conversation time	Continuous	Seconds of voice/day
Travel diameter	Continuous	Max distance covered/day (m)
Travel time	Continuous	Seconds moving/day
Radius of gyration	Continuous	Area covered/day (m)
Activity uptime	Continuous	Device activity uptime/day
Location uptime	Continuous	Location stream uptime/day
Stress (Yₜ)	Ordinal	1 (low) – 5 (high)
Arousal (Aₜ)	Ordinal	1 (calm) – 5 (excited)
Valence (Vₜ)	Ordinal	1 (unpleasant) – 5 (pleasant)

All raw streams were aggregated to a single daily summary per feature per participant.

2. Data Pre-processing and Quality Control

Missingness and Bias Correction

Passive sensor readings were subjected to device-use bias due to non-wear and non-use; unreliable days were flagged by the two-stage "2SpamH" algorithm, which detects irregularities using auxiliary indicators (screen-unlock counts, battery variance, app usage) and applies bias-correction only to "reliable" points. Remaining days flagged as missing were imputed using MissForest (a non-parametric, mixed-type imputation method).

Transformation of Self-Reported Stress

As many change-point and distributional analysis methods assume continuously distributed data, ordinal stress scores (Yₜ) were mapped to latent Gaussian residuals (Zₜ) via a randomized inverse-CDF (probit) transform:

$$\begin{align*} Uₜ &:= \hat{F}(Yₜ^-) + Wₜ \cdot \hat{P}(Yₜ), \quad Wₜ \sim \text{Uniform}(0,1) \ Zₜ &:= \Phi^{-1}(Uₜ) \end{align*}$$

where $\hat{F}$ is the empirical CDF and $\hat{P}$ the empirical discrete mass at $Yₜ$.

Alignment and Feature Construction

All data streams were aligned on the daily grid without need for interpolation or normalization across subjects. Model features comprised the passively sensed vector $Xₜ$ and (in some approaches) a post-hoc segment label $Sₜ$ summarizing co-segment period membership.

3. Segmentation, Change-Point Analysis, and "Hotspot" Detection

Nonparametric Change-Point Detection

Change points $\{\tau_k\}$ in passive features were estimated using nonparametric multivariate methods (Matteson & James 2014). For each candidate split, the empirical energy distance between segments was computed: $$\hat{\mathcal{E}}(\mathbf{X}_n, \mathbf{Y}_m; \alpha) = \frac{2}{n + m} \sum_{i=1}^n \sum_{j=1}^m \left\| X_i - Y_j \right\|^{\alpha} - \frac{1}{\binom{n}{2}} \sum_{i < j} \left\| X_i - X_j \right\|^{\alpha} - \frac{1}{\binom{m}{2}} \sum_{i < j} \left\| Y_i - Y_j \right\|^{\alpha}$$ The optimal split maximizes the corresponding goodness-of-fit statistic $\hat{Q}$ and is tested for significance using permutation (R=499, $\alpha=1$).

This process is equivalently formulated as a penalized optimization: $$\min_{\{\tau_k\}} \sum_{k=1}^{K} C\left( Z_{(\tau_{k-1}+1):\tau_k} \right) + \beta\,K$$ with $C(\cdot)$ a divergence-based segment cost, $\beta$ selected per permutation threshold.

Co-Segmentation and Segment Refinement

Detected change points in $Xₜ$ partition the paired $(Xₜ, Yₜ)$ time series into co-segments. These are further refined by:

• Testing within-segment $X \rightarrow Y$ association (OLS/F-test for $\beta_k = 0$).
• Chow tests for parameter constancy across adjacent segments.
• Distributional tests (Pearson $\chi^2$, $Z$-test) for $Yₜ$ distributional changes.

Segments failing association or distributional change are merged. The process yields final co-segments believed to have distinct $X-Y$ associations.

MOSUM-Based Hotspot Detection

An alternative algorithm (Kim et al., 8 Nov 2025) constructs statistical "hotspots" by applying an extended moving sum (MOSUM) scheme to both passive and self-report residuals. For each day $k$ and window $G$:

• Compute difference statistics for means ($d\bar{X}(k)$) and variances ($dS_X^2(k)$), scaled to local standard deviation/variance.
• Construct the multivariate detectors (e.g., Joint-MOSUM, Bi-MOSUM):
  • $J_X(k) = [T_X^{(1)}(k), T_X^{(2)}(k)]'$
  • $D_X^2(k)$: Mahalanobis distance using local covariances.
  • Bivariate detectors (cross-mean, cross-variance) for $X$ and transformed $Y$.

Hotspot intervals are defined either by threshold crossing: $$H_\text{thrs} = \{ k : \max [D_{YX}^2(k), D_{YX^2}^2(k), D_{Y^2 X}^2(k), D_{Y^2 X^2}^2(k)] > D_n(G, \alpha) \}$$ or by bootstrapped confidence intervals enclosing detected change-points.

4. Machine Learning for Stress Period Prediction

Feature Usage and Class Assignment

After segmentation, each day $t$ is annotated with its passive-sensing vector $Xₜ$ and segment label $Sₜ$; the latter is assigned ordinally by comparing segment mean adjusted stress ($\bar{\hat{Y}}$). The objective is to classify days into $N^*$ stress periods (typically 2 or 3).

Model Architecture and Validation

Candidate classifiers included:

• Multinomial logistic regression
• Linear discriminant analysis (LDA)
• Support vector machines (radial kernel)
• Random forest (ntree=500)
• Gradient boosting (depth=1, 100 trees)

Performance is validated under rolling-window splits (5-day holdout; up to 50 splits/subject), evaluating accuracy, macro-precision/recall, and per-class F₁.

A summary of mean model performance (illustrative group of six patients, step size $s=2$):

Method	Recall	Precision	Accuracy	F₁(Class 1)	F₁(Class 2)	F₁(Class 3)
Reg	0.42	0.39	0.43	0.38	0.30	0.18
SVM	0.56	0.51	0.58	0.55	0.44	0.22
LDA	0.63	0.60	0.64	0.62	0.53	0.35
RF	0.68	0.66	0.70	0.69	0.60	0.48
Boost	0.69	0.67	0.71	0.68	0.59	0.47
Resp	0.48	0.46	0.49	0.47	0.39	0.30
Pred	0.51	0.50	0.53	0.52	0.42	0.31

Random forest and boosting after segmentation substantially outperform benchmarks (gain in accuracy ΔAcc ≈ +0.21 over baseline clustering on reported stress).

5. Methodological Challenges and Limitations

Key challenges specific to this dataset and analytic context:

• Nonstationarity: Behavioral and stress distributions drift on timescales of weeks to months; segmentwise methods adapt to these dynamics, whereas global models underperform.
• Asynchronous change: Passive and stress signals' mean/variance shifts often misalign in time, confounding pointwise CPD and conventional models.
• Weak/mixed signals: Day-to-day behavioral variance may mask subtle stress-related changes; multivariate detectors (e.g., Mahalanobis) are required to aggregate cross-feature information.
• Imputation and Device Bias: Passive data are susceptible to spurious low values from device idle/off states; "2SpamH" and MissForest are necessary for rigorous bias correction.
• Hotspot interpretability: MOSUM-based hotspots are intervals, not precise change-points; this acknowledges intrinsic uncertainty and variable temporal lags in behavioral-stress relationships.
• Model-free approaches: Both segmentation and hotspot algorithms emphasize model independence, precluding strong claims of behavioral causality.

A plausible implication is that, for mHealth stress detection, interval-focused analytic strategies more robustly surface clinically meaningful episodes than single-time-point methods.

6. Empirical Findings and Implications

Analysis of ALACRITY Phase I data showed:

• Predictive value of passive streams: Location features (travel diameter, radius of gyration), sociability (conversation %), and sleep interruption emerged as most predictive of stress-period transitions early in segments.
• Superiority of segmentwise learning: Segmenting time series before modeling yields up to 20–22% improvement in classification accuracy, recall, and precision over self-report or unsegmented regression.
• Tree-based learners excel: Random forest and boosting more effectively capture nonlinearities and heterogeneity associated with segmentwise dynamics.
• No across-subject normalization: Each time series is analyzed within-subject, in unnormalized but bias-corrected original units, supporting personalized stress-detection paradigms.

Recommendations for practice include aggregation of passive streams to the frequency of EMA, routine application of nonparametric change-point and hotspot detection, and periodic model retraining to adapt to behavioral drift.

In summary, the ALACRITY Phase I dataset provides a high-resolution, multi-modal framework for research on adaptive and interpretable stress detection methodologies. It demonstrates that methods accounting for local, time-varying associations between passively measured behavior and self-reported stress yield significant improvements over global or unsegmented approaches in real-world mobile health data contexts.