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<article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" article-type="research-article" dtd-version="1.4" xml:lang="en">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher-id">Oalib</journal-id>
      <journal-title-group>
        <journal-title>Open Access Library Journal</journal-title>
      </journal-title-group>
      <issn pub-type="epub">2333-9721</issn>
      <issn pub-type="ppub">2333-9705</issn>
      <publisher>
        <publisher-name>Scientific Research Publishing</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.4236/oalib.1114923</article-id>
      <article-id pub-id-type="publisher-id">Oalib-150122</article-id>
      <article-categories>
        <subj-group>
          <subject>Article</subject>
        </subj-group>
        <subj-group>
          <subject>Biomedical</subject>
          <subject>Life Sciences</subject>
          <subject>Business</subject>
          <subject>Economics</subject>
          <subject>Chemistry</subject>
          <subject>Materials Science</subject>
          <subject>Computer Science</subject>
          <subject>Communications</subject>
          <subject>Earth</subject>
          <subject>Environmental Sciences</subject>
          <subject>Engineering</subject>
          <subject>Medicine</subject>
          <subject>Healthcare</subject>
          <subject>Physics</subject>
          <subject>Mathematics</subject>
          <subject>Social Sciences</subject>
          <subject>Humanities</subject>
        </subj-group>
      </article-categories>
      <title-group>
        <article-title>Wearable-Inspired Panic Episode Forecasting with Synthetic Physiological Time Series: A Feature Engineered Gradient Boosting Baseline with Clinically Motivated Thresholding</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <contrib-id contrib-id-type="orcid">0000-0001-9101-072X</contrib-id>
          <name name-style="western">
            <surname>Filippis</surname>
            <given-names>Rocco de</given-names>
          </name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <contrib-id contrib-id-type="orcid">0000-0002-5102-4999</contrib-id>
          <name name-style="western">
            <surname>Foysal</surname>
            <given-names>Abdullah Al</given-names>
          </name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
      </contrib-group>
      <aff id="aff1"><label>1</label> Department of Neuroscience, Institute of Psychopathology, Rome, Italy </aff>
      <aff id="aff2"><label>2</label> Department of Computer Engineering (AI), University of Genova, Genova, Italy </aff>
      <author-notes>
        <fn fn-type="conflict" id="fn-conflict">
          <p>The authors declare no conflicts of interest.</p>
        </fn>
      </author-notes>
      <pub-date pub-type="epub">
        <day>28</day>
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <pub-date pub-type="collection">
        <month>02</month>
        <year>2026</year>
      </pub-date>
      <volume>13</volume>
      <issue>03</issue>
      <fpage>1</fpage>
      <lpage>24</lpage>
      <history>
        <date date-type="received">
          <day>23</day>
          <month>01</month>
          <year>2026</year>
        </date>
        <date date-type="accepted">
          <day>10</day>
          <month>03</month>
          <year>2026</year>
        </date>
        <date date-type="published">
          <day>13</day>
          <month>03</month>
          <year>2026</year>
        </date>
      </history>
      <permissions>
        <copyright-statement>© 2026 by the authors and Scientific Research Publishing Inc.</copyright-statement>
        <copyright-year>2026</copyright-year>
        <license license-type="open-access">
          <license-p> This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link> ). </license-p>
        </license>
      </permissions>
      <self-uri content-type="doi" xlink:href="https://doi.org/10.4236/oalib.1114923">https://doi.org/10.4236/oalib.1114923</self-uri>
      <abstract>
        <p><bold>Background:</bold> Panic attacks can present rapidly and unpredictably, yet wearable sensors (heart rate, electrodermal activity, respiration, movement) offer a path to continuous monitoring and potentially actionable early warnings. However, developing and validating forecasting pipelines is difficult due to limited labelled datasets, heterogeneous symptom profiles, and ethical constraints in real-world collection. <bold>Objective:</bold> We propose a fully reproducible synthetic-data framework that simulates circadian physiology and panic-episode dynamics, then evaluates classical machine-learning baselines for multi-class warning prediction (Normal, Early Warning, Urgent Warning) and for binary panic detection (any warning vs Normal). <bold>Methods:</bold> We generated 60,000 minute-level samples with circadian rhythms and injected panic episodes with either sudden or gradual onset, generating severity trajectories and phase-specific physiological shifts. We engineered 125 features (rolling statistics, slopes, rate-of-change, circadian z-scores, interaction terms, and composite arousal/propensity indices) and trained models on 30 selected features. Class imbalance was addressed with SMOTE Tomek on the training split. We compared Random Forest, Gradient Boosting, and Logistic Regression; the best model was selected by panic-detection F1. We further optimized decision thresholds for clinical deployment trade-offs (alarm burden vs detection). <bold>Results:</bold> The dataset exhibited extreme class imbalance (Normal ≈ 99.2%, Early ≈ 0.4%, Urgent ≈ 0.4%). Gradient Boosting achieved overall accuracy 0.993 and weighted F1 0.994, but more realistically, binary panic detection reached F1 0.641 with recall 0.787. Discrimination remained strong for the Normal class (AP ≈ 1.00; AUC ≈ 0.995) while minority-class precision-recall degraded, consistent with rare-event forecasting. Threshold optimization showed an operational “clinical” threshold near 0.50 yielding ≈ 16.6 alarms/day with recall ≈ 0.809. Temporal analysis indicated stable accuracy across hours with variable detection rates. <bold>Conclusions:</bold> A feature-engineered Gradient Boosting baseline can produce operational early-warning signals from wearable-like streams under controlled synthetic assumptions, and thresholding meaningfully tunes clinical burden. The study is a proof-of-concept: results are constrained by synthetic label rules, possible episode-generation accounting inconsistencies, and lack of subject-level personalization. Real-world validation with calibrated probabilities and prospective evaluation is necessary before clinical claims.</p>
      </abstract>
      <kwd-group kwd-group-type="author-generated" xml:lang="en">
        <kwd>Panic Disorder</kwd>
        <kwd>Early Warning Systems</kwd>
        <kwd>Wearable Sensors</kwd>
        <kwd>Electrodermal Activity</kwd>
        <kwd>Heart Rate Variability</kwd>
        <kwd>Rare-Event Prediction</kwd>
        <kwd>Threshold Optimization</kwd>
        <kwd>Synthetic Data</kwd>
        <kwd>Machine Learning</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec1">
      <title>1. Introduction</title>
      <p>Panic attacks are sudden episodes of overwhelming fear that can escalate within minutes and are accompanied by strong autonomic activation, including tachycardia, dyspnea, chest discomfort, dizziness, and sweating [<xref ref-type="bibr" rid="B1">1</xref>]-[<xref ref-type="bibr" rid="B10">10</xref>]. Beyond the acute distress, recurrent attacks and the anticipation of future episodes often lead to maladaptive behavioural changes, functional impairment, and reduced quality of life [<xref ref-type="bibr" rid="B11">11</xref>]-[<xref ref-type="bibr" rid="B14">14</xref>]. A central clinical challenge is that intervention is typically reactive, patients respond once symptoms become intense whereas meaningful benefit may come from anticipatory detection: identifying a rising physiological risk state early enough to enable coping strategies (e.g., paced breathing, grounding), medication plans prescribed by clinicians, or timely access to social and clinical support before full symptom escalation. Wearable devices offer a practical route to continuous, low-burden monitoring in daily life through physiological streams such as heart rate (HR), electrodermal activity (EDA), respiratory rate, and motion [<xref ref-type="bibr" rid="B15">15</xref>]-[<xref ref-type="bibr" rid="B18">18</xref>]. These signals partially reflect sympathetic arousal and stress-related dynamics, making them promising candidates for early-warning systems. However, translating wearable sensing into reliable panic forecasting remains difficult for three reasons. First, there is a scarcity of large, well-labeled datasets with accurate onset times and clinically validated episode annotations. Second, panic-related windows are rare compared with normal physiology, creating extreme class imbalance that can inflate headline accuracy while masking poor detection of clinically important events. Third, inter-individual variability due to fitness, medication, comorbidities, sleep, and baseline autonomic tone causes warning signatures to differ substantially across users, limiting generalization from population-level models. To enable systematic method development under these constraints, synthetic physiological data provide a controlled testbed for evaluating modeling choices before real-world validation. In this study, we introduce an end-to-end pipeline that 1) simulates circadian baselines with realistic noise and contextual covariates; 2) injects panic episodes with structured pre-onset “early” and “urgent” warning windows and severity trajectories; 3) derives clinically motivated features including rolling statistics, slopes, circadian-adjusted z-scores, and interaction/composite autonomic indices; and 4) trains and evaluates classical machine-learning baselines with deployment-oriented threshold optimization to explicitly manage alarm burden. This framework offers a reproducible foundation for studying rare-event detection trade-offs and for guiding future translation to patient data.</p>
    </sec>
    <sec id="sec2">
      <title>2. Materials and Methods</title>
      <sec id="sec2dot1">
        <title>2.1. Synthetic Dataset Generation</title>
        <p>We constructed a large-scale synthetic dataset consisting of 60,000 time-indexed samples, representing continuous minute-level physiological monitoring from a hypothetical wearable system [<xref ref-type="bibr" rid="B19">19</xref>]-[<xref ref-type="bibr" rid="B22">22</xref>]. The primary objective of the generator was to reproduce realistic baseline physiology, circadian regulation, and panic-episode dynamics under controlled and fully reproducible conditions, enabling systematic investigation of early-warning detection strategies [<xref ref-type="bibr" rid="B23">23</xref>]-[<xref ref-type="bibr" rid="B25">25</xref>].</p>
        <p><bold>Baseline physiological modelling:</bold>Baseline signals were designed to emulate known circadian and autonomic behavior: Heart Rate (HR) was modeled as a sinusoidal circadian component with superimposed long-term oscillatory drift and additive Gaussian noise, capturing both daily rhythms and natural variability. Electrodermal Activity (EDA) followed circadian modulation with an exponential noise process, reflecting the skewed distribution commonly observed in sympathetic skin conductance. Heart Rate Variability (HRV) was constructed as an inverse function of autonomic arousal, incorporating circadian modulation and Gaussian noise [<xref ref-type="bibr" rid="B26">26</xref>]-[<xref ref-type="bibr" rid="B30">30</xref>]. Respiratory Rate exhibited circadian modulation with additive noise, reflecting physiological respiratory patterns. Movement followed a time-of-day-scaled exponential distribution, accounting for diurnal activity fluctuations. Stress was generated as a clipped composite of circadian influence and beta-distributed noise, constrained to the interval [0, 1], simulating bounded psychological stress scores. This design ensured physiologically plausible coupling between autonomic signals while preserving stochastic realism.</p>
        <p><bold>Panic episode injection:</bold>Panic episodes were superimposed onto the baseline stream using two onset archetypes: sudden (rapid escalation) and gradual (progressive buildup). Each episode consisted of three sequential phases: buildup, peak, and recovery. For clinical interpretability, time windows preceding the peak were labeled as:</p>
        <p>Early Warning (label 2): approximately 30 - 60 minutes pre-peakUrgent Warning (label 1): approximately 15 - 30 minutes pre-peakNormal (label 0): baseline or recovered state</p>
        <p>Physiological perturbations were applied as phase- and severity-dependent transformations: HR and EDA increased proportionally to severity, HRV was multiplicatively suppressed, respiratory rate increased, and both movement and stress rose with escalating severity [<xref ref-type="bibr" rid="B31">31</xref>]-[<xref ref-type="bibr" rid="B36">36</xref>]. A continuous panic_severity ∈ [0, 1] variable quantified episode progression. A representative episode profile is shown in <xref ref-type="fig" rid="fig1">Figure 1(e)</xref>, illustrating the coordinated escalation of HR and EDA and the placement of early and urgent warning regions.</p>
        <p><bold>Transparency and dataset accounting:</bold>The generation log initially reports an intended creation of 333 panic episodes; however, the final output indicates 5 successfully placed episodes. This discrepancy arises from strict temporal spacing constraints within the episode-placement routine specifically, the rule enforcing a minimum separation of 240 minutes between episode onsets, which severely restricts feasible placements in a finite 60,000-sample sequence. We therefore treat 5 episodes as the effective number of injected panic events in this experiment and explicitly discuss this limitation and its implications for temporal statistics in Section 5. Although only 5 unique episode trajectories were successfully injected due to spacing constraints, each episode spans multiple contiguous minutes across Early and Urgent windows, resulting in 136 labelled panic-related samples. Therefore, the effective sample size for minute-level classification is higher than the raw episode count. Nevertheless, the limited number of independent episode archetypes restricts diversity of escalation patterns and limits generalization.</p>
        <p>Overall, this dataset provides a controlled yet physiologically grounded environment for evaluating early-warning detection under extreme class imbalance and complex autonomic dynamics.</p>
      </sec>
      <sec id="sec2dot2">
        <title>2.2. Feature Engineering</title>
        <p>To capture the complex and multi-timescale dynamics of panic-related physiology, we constructed an extensive feature representation comprising 125 engineered variables derived from the raw physiological streams. The design goal was to encode both short-term reactivity and longer-term autonomic trends while maintaining interpretability for downstream clinical analysis. Feature selection was performed using a two-stage procedure. First, highly collinear features (Pearson r &gt; 0.90) were removed using correlation thresholding to reduce redundancy. Second, features were ranked using mutual information with respect to the panic-warning label, and the top 30 features were retained. This approach balances dimensionality reduction with preservation of non-linear relevance while avoiding label leakage.</p>
        <p><bold>Temporal and statistical descriptors:</bold>For each core physiological signal HR, EDA, HRV, and respiratory rate we computed rolling statistics over multiple temporal windows (5, 10, 15, and 30 minutes), including the mean, standard deviation, minimum, and maximum. These features characterize local signal distribution, short-term volatility, and extreme physiological responses that often precede or accompany panic onset.</p>
        <p>To explicitly model dynamic change, we further derived change and slope features over larger windows, capturing the velocity and direction of physiological drift. In parallel, we computed rate-of-change metrics as percentage change over 5- and 10-minute horizons for HR, EDA, and HRV, enabling the model to detect rapid autonomic escalation.</p>
        <p><bold>Variability and interaction modelling:</bold> Autonomic variability was summarized using clinically motivated metrics, including a root-mean-square of successive differences (RMSSD) proxy for HR, estimated via rolling squared differences. These measures quantify beat-to-beat instability that is strongly linked to sympathetic dominance and emotional dysregulation [<xref ref-type="bibr" rid="B37">37</xref>]-[<xref ref-type="bibr" rid="B44">44</xref>]. To capture cross-signal coupling, we constructed interaction features, including the HR × EDA product, HR/HRV ratio, autonomic balance index, and respiratory synchrony (HR normalized by respiratory rate). These composite representations encode relationships between cardiovascular, electrodermal, and respiratory systems that are often more predictive than any single signal alone.</p>
        <p><bold>Composite autonomic indices:</bold>Two higher-level indices were introduced to improve clinical interpretability: Autonomic arousal, computed as a weighted standardized combination of HR, EDA, respiratory rate, and stress, approximating a continuous sympathetic activation score. Panic propensity, a rule-based risk indicator aggregating binary conditions (e.g., HR &gt; 85 bpm, EDA &gt; 8 μS, HRV &lt; 40 ms), encoding established physiological thresholds associated with panic vulnerability.</p>
        <p><bold>Circadian normalization and final feature selection:</bold>Because autonomic physiology is strongly modulated by circadian rhythms, we computed hour-specific z-scores for each core signal, normalizing instantaneous values relative to typical behaviour at that time of day. This adjustment allows the model to distinguish pathological deviations from expected diurnal fluctuations. From the full 125-feature space, we selected 30 clinically and statistically informative features for model training, integrating raw physiology, contextual time features, rolling statistics, interaction metrics, composite indices, and circadian-adjusted representations. This balanced representation preserves physiological meaning while reducing model complexity and overfitting risk.</p>
      </sec>
      <sec id="sec2dot3">
        <title>2.3. Train/Test Split and Imbalance Handling</title>
        <p>Given the extreme rarity of panic-related events relative to normal physiological activity, careful data partitioning and imbalance mitigation were essential to ensure valid evaluation and stable model training. The full dataset of 60,000 samples was partitioned using to prevent episode-level information leakage, we ensured that complete panic episodes (including Early and Urgent windows) were assigned entirely to either the training or test split into a training set (70%, 42,000 samples) and an independent test set (30%, 18,000 samples), preserving the original class distribution across splits. As shown in <xref ref-type="fig" rid="fig1">Figure 1(a)</xref>, the dataset exhibited severe class imbalance, with Normal ≈ 99.2%, Early Warning ≈ 0.4%, and Urgent Warning ≈ 0.4%, a regime that reflects real-world panic monitoring scenarios but poses significant challenges for supervised learning. To address this imbalance without corrupting the evaluation protocol, we applied SMOTETomek resampling exclusively to the training data [<xref ref-type="bibr" rid="B45">45</xref>][<xref ref-type="bibr" rid="B46">46</xref>]. This approach combines Synthetic Minority Oversampling Technique (SMOTE) with Tomek link under sampling, simultaneously generating synthetic minority samples while removing ambiguous majority samples at class boundaries [<xref ref-type="bibr" rid="B47">47</xref>]-[<xref ref-type="bibr" rid="B51">51</xref>]. The resulting balanced training set contained 41,682 samples per class, producing equal representation of Normal, Early Warning, and Urgent Warning classes and enabling the classifiers to learn stable decision boundaries. All input features were subsequently standardized using z-score normalization via StandardScaler, with parameters fitted solely on the balanced training set and then applied to the untouched test set. This procedure prevents information leakage and ensures that performance estimates reflect genuine generalization to unseen data. This pipeline preserves the real-world rarity of panic events during evaluation while providing a well-conditioned training distribution for learning robust early-warning models.</p>
      </sec>
      <sec id="sec2dot4">
        <title>2.4. Models and Evaluation Protocol</title>
        <p>To evaluate the effectiveness of the proposed feature representation and learning framework, we trained and compared three widely used supervised classifiers with complementary inductive biases: Random Forest, configured with class-weight balancing to mitigate residual imbalance effects, Gradient Boosting, optimized for non-linear feature interactions and decision boundary refinement, Logistic Regression, serving as a linear baseline with class-weight balancing. Each model was trained on the balanced and standardized training set and evaluated on the untouched test set.</p>
        <p><bold>Evaluation metrics:</bold>Performance was assessed using two complementary perspectives: multi-class classification performance, measured using overall accuracy, weighted precision, weighted recall, and weighted F1-score across the three prediction classes (Normal, Early Warning, Urgent Warning). Operational panic detection performance, where the clinically relevant objective is to detect any impending panic event. For this purpose, the Early and Urgent classes were merged into a single “panic warning” category, yielding a binary detection task. On this task we report precision, recall, and F1-score, which provide a more meaningful assessment under extreme class imbalance and directly reflect real-world early-warning utility. To support detailed error analysis and model interpretability, we further computed: Normalized confusion matrices, Precision-Recall (PR) curves for each class, Receiver Operating Characteristic (ROC) curves with AUC scores, threshold-dependent performance analyses, linking decision thresholds to detection quality and alarm burden [<xref ref-type="bibr" rid="B52">52</xref>]-[<xref ref-type="bibr" rid="B57">57</xref>].</p>
        <p>All metrics and visualizations were computed on the held-out test set only, ensuring unbiased estimates of generalization performance.</p>
      </sec>
      <sec id="sec2dot5">
        <title>2.5. Threshold Optimization for Deployment</title>
        <p>Because the proposed system is intended for early warning rather than retrospective labelling, model evaluation cannot rely solely on the default “argmax” class decision. In practical deployment, clinicians and users require explicit control over the trade-off between missed events (false negatives) and alarm fatigue (false positives). For this reason, we implemented a probability-thresholding procedure that converts calibrated model outputs into actionable binary alerts.</p>
        <p>2.5.1. Panic-Risk Probability Definition</p>
        <p>The multi-class classifier outputs posterior probabilities for each label at every minute <inline-formula><mml:math><mml:mi> t </mml:mi></mml:math></inline-formula> :</p>
        <disp-formula id="FD1">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>t</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Normal</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>,</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>t</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Early</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>,</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>t</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Urgent</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>To represent the instantaneous risk that a panic episode is impending, we defined a unified panic probability by marginalizing over the two warning states:</p>
        <disp-formula id="FD2">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>P</mml:mi>
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              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>panic</mml:mtext>
                </mml:mrow>
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              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:msub>
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              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Early</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>+</mml:mo>
              <mml:msub>
                <mml:mi>P</mml:mi>
                <mml:mi>t</mml:mi>
              </mml:msub>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mrow>
                  <mml:mtext>Urgent</mml:mtext>
                </mml:mrow>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>This definition is clinically aligned because both Early and Urgent states indicate risk escalation requiring preventive action, and it allows the system to trigger a single alert signal while still supporting later analysis of warning subtype.</p>
        <p>2.5.2. Threshold Sweep and Decision Rule</p>
        <p>We converted probability into binary warnings using a threshold <inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> such that:</p>
        <disp-formula id="FD3">
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                            </mml:mrow>
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                  </mml:mtable>
                </mml:mrow>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>We evaluated a threshold grid:</p>
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                  <mml:mn>0.90</mml:mn>
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            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>For each <inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> , we computed confusion counts <inline-formula><mml:math><mml:mrow><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mi> T </mml:mi><mml:mi> P </mml:mi><mml:mo> , </mml:mo><mml:mi> F </mml:mi><mml:mi> P </mml:mi><mml:mo> , </mml:mo><mml:mi> F </mml:mi><mml:mi> N </mml:mi><mml:mo> , </mml:mo><mml:mi> T </mml:mi><mml:mi> N </mml:mi></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> on the held-out test set using the ground truth binary label:</p>
        <disp-formula id="FD5">
          <mml:math>
            <mml:mrow>
              <mml:msub>
                <mml:mi>y</mml:mi>
                <mml:mi>t</mml:mi>
              </mml:msub>
              <mml:mo>=</mml:mo>
              <mml:mn>1</mml:mn>
              <mml:mtext>l</mml:mtext>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mrow>
                      <mml:mtext>label</mml:mtext>
                    </mml:mrow>
                    <mml:mi>t</mml:mi>
                  </mml:msub>
                  <mml:mo>∈</mml:mo>
                  <mml:mrow>
                    <mml:mo>{</mml:mo>
                    <mml:mrow>
                      <mml:mtext>Early</mml:mtext>
                      <mml:mo>,</mml:mo>
                      <mml:mtext>Urgent</mml:mtext>
                    </mml:mrow>
                    <mml:mo>}</mml:mo>
                  </mml:mrow>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>and derived deployment-relevant metrics:</p>
        <disp-formula id="FD6">
          <mml:math>
            <mml:mrow>
              <mml:mtext>Precision</mml:mtext>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>P</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>P</mml:mi>
                  <mml:mo>+</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>P</mml:mi>
                </mml:mrow>
              </mml:mfrac>
              <mml:mo>,</mml:mo>
              <mml:mtext>Recall</mml:mtext>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>P</mml:mi>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>T</mml:mi>
                  <mml:mi>P</mml:mi>
                  <mml:mo>+</mml:mo>
                  <mml:mi>F</mml:mi>
                  <mml:mi>N</mml:mi>
                </mml:mrow>
              </mml:mfrac>
              <mml:mo>,</mml:mo>
              <mml:mtext>F1</mml:mtext>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mn>2</mml:mn>
                  <mml:mo>⋅</mml:mo>
                  <mml:mtext>Precision</mml:mtext>
                  <mml:mo>⋅</mml:mo>
                  <mml:mtext>Recall</mml:mtext>
                </mml:mrow>
                <mml:mrow>
                  <mml:mtext>Precision</mml:mtext>
                  <mml:mo>+</mml:mo>
                  <mml:mtext>Recall</mml:mtext>
                </mml:mrow>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>This produces a full operating curve showing how detection quality changes as the alarm sensitivity are increased or decreased.</p>
        <p>2.5.3. Alarm-Rate Modeling and Clinical Burden Constraint</p>
        <p>Beyond detection accuracy, a wearable warning system must remain usable over days and weeks. Therefore, we quantified alarm rate as:</p>
        <disp-formula id="FD7">
          <mml:math>
            <mml:mrow>
              <mml:mtext>AlarmRate</mml:mtext>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>τ</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mfrac>
                <mml:mrow>
                  <mml:mstyle displaystyle="true">
                    <mml:msub>
                      <mml:mo>∑</mml:mo>
                      <mml:mi>t</mml:mi>
                    </mml:msub>
                    <mml:mrow>
                      <mml:msub>
                        <mml:mover accent="true">
                          <mml:mi>y</mml:mi>
                          <mml:mo>^</mml:mo>
                        </mml:mover>
                        <mml:mi>t</mml:mi>
                      </mml:msub>
                    </mml:mrow>
                  </mml:mstyle>
                </mml:mrow>
                <mml:mi>N</mml:mi>
              </mml:mfrac>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>where <inline-formula><mml:math><mml:mi> N </mml:mi></mml:math></inline-formula> is the number of evaluated minutes. To express this in clinically interpretable units, we converted it to expected daily alarms assuming minute-level inference throughout the day:</p>
        <disp-formula id="FD8">
          <mml:math>
            <mml:mrow>
              <mml:mtext>DailyAlarms</mml:mtext>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>τ</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
              <mml:mo>=</mml:mo>
              <mml:mn>1440</mml:mn>
              <mml:mo>×</mml:mo>
              <mml:mtext>AlarmRate</mml:mtext>
              <mml:mrow>
                <mml:mo>(</mml:mo>
                <mml:mi>τ</mml:mi>
                <mml:mo>)</mml:mo>
              </mml:mrow>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>This mapping enables direct reasoning about alarm fatigue and feasibility in real-world use. In this study, we adopted an illustrative clinical constraint of ≤20 alarms/day, reflecting a practical upper bound for acceptable intervention burden in continuous monitoring.</p>
        <p>2.5.4. Operating Point Selection</p>
        <p>Two operating points were emphasized:</p>
        <p><bold>1)</bold><bold>Max-F1 threshold (performance-focused):</bold> The threshold <inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> maximizing F1-score over the grid, prioritizing balanced detection quality. This operating point is useful in research benchmarking and provides an upper-bound estimate of achievable performance under optimal tuning.</p>
        <p><bold>2)</bold><bold>Clinical threshold (deployment-focused):</bold> Among thresholds satisfying the burden constraint <inline-formula><mml:math><mml:mrow><mml:mtext> DailyAlarms </mml:mtext><mml:mrow><mml:mo> ( </mml:mo><mml:mi> τ </mml:mi><mml:mo> ) </mml:mo></mml:mrow><mml:mo> ≤ </mml:mo><mml:mn> 20 </mml:mn></mml:mrow></mml:math></inline-formula> , we selected the <inline-formula><mml:math><mml:mi> τ </mml:mi></mml:math></inline-formula> that maximized F1-score while maintaining high recall. This approach explicitly encodes a real-world usability requirement and prevents selecting overly sensitive thresholds that would generate excessive alerts.</p>
        <p>2.5.5. Recommended Deployment Algorithmic Enhancements</p>
        <p>To strengthen deployment readiness and align with best practice in clinical machine learning, the thresholding framework can be extended in the following algorithmic directions:</p>
        <p><bold>Probability calibration:</bold> Tree ensembles may output poorly calibrated probabilities; applying Platt scaling or isotonic regression on a validation split improves the reliability of <inline-formula><mml:math><mml:mrow><mml:mi> P </mml:mi><mml:mrow><mml:mo> ( </mml:mo><mml:mrow><mml:mtext> panic </mml:mtext></mml:mrow><mml:mo> ) </mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> , making threshold choices more stable across users and contexts.<bold>Temporal smoothing</bold><bold>/</bold><bold>persistence rule:</bold> Minute-level predictions are noisy. A clinically safer decision rule often requires persistence, such as triggering an alert only if:</p>
        <disp-formula id="FD9">
          <mml:math>
            <mml:mrow>
              <mml:mfrac>
                <mml:mn>1</mml:mn>
                <mml:mi>k</mml:mi>
              </mml:mfrac>
              <mml:munderover>
                <mml:mstyle mathsize="140%" displaystyle="true">
                  <mml:mo>∑</mml:mo>
                </mml:mstyle>
                <mml:mrow>
                  <mml:mi>i</mml:mi>
                  <mml:mo>=</mml:mo>
                  <mml:mn>0</mml:mn>
                </mml:mrow>
                <mml:mrow>
                  <mml:mi>k</mml:mi>
                  <mml:mo>−</mml:mo>
                  <mml:mn>1</mml:mn>
                </mml:mrow>
              </mml:munderover>
              <mml:mn>1</mml:mn>
              <mml:mtext>l</mml:mtext>
              <mml:mrow>
                <mml:mo>[</mml:mo>
                <mml:mrow>
                  <mml:msub>
                    <mml:mi>P</mml:mi>
                    <mml:mrow>
                      <mml:mi>t</mml:mi>
                      <mml:mo>−</mml:mo>
                      <mml:mi>i</mml:mi>
                    </mml:mrow>
                  </mml:msub>
                  <mml:mrow>
                    <mml:mo>(</mml:mo>
                    <mml:mrow>
                      <mml:mtext>panic</mml:mtext>
                    </mml:mrow>
                    <mml:mo>)</mml:mo>
                  </mml:mrow>
                  <mml:mo>&gt;</mml:mo>
                  <mml:mi>τ</mml:mi>
                </mml:mrow>
                <mml:mo>]</mml:mo>
              </mml:mrow>
              <mml:mo>≥</mml:mo>
              <mml:mi>ρ</mml:mi>
            </mml:mrow>
          </mml:math>
        </disp-formula>
        <p>(e.g., “at least 3 of the last 5 minutes exceed threshold”). This reduces spurious single-minute alarms and improves user trust.</p>
        <p><bold>Cooldown/refractory period:</bold> To prevent alarm bursts, implement a cooldown interval after an alert (e.g., suppress alerts for 10 - 30 minutes), consistent with real mobile health systems.<bold>Event</bold><bold>-</bold><bold>based evaluation:</bold> For panic forecasting, it is often preferable to measure detection at the episode level (e.g., “did we alert within the early window for an episode?”) rather than minute-by-minute accuracy. This can be implemented by collapsing predictions into events and computing episode recall, lead time, and false alarms per hour.</p>
        <p>Together, these steps make the thresholding strategy not only a post-processing technique but a core component of deployable early-warning logic, balancing sensitivity, precision, and human usability in continuous panic monitoring.</p>
      </sec>
    </sec>
    <sec id="sec3">
      <title>3. Results</title>
      <sec id="sec3dot1">
        <title>3.1. Dataset Characteristics and Physiological Structure</title>
        <p>The final dataset comprised 60,000 minute-level samples and exhibited an extreme class imbalance that reflects the rarity of panic events in continuous physiological monitoring. Specifically, 59,546 samples (99.2%) corresponded to the Normal state, while Early Warning and Urgent Warning jointly accounted for only ≈0.8% of the data (≈0.4% each), as illustrated in <xref ref-type="fig" rid="fig1">Figure 1(a)</xref>. This distribution creates a challenging rare-event learning scenario that is representative of real-world panic monitoring systems. Correlation analysis across core physiological variables and composite autonomic indices revealed coherent and clinically plausible relationships (<xref ref-type="fig" rid="fig1">Figure 1(b)</xref>). In particular, positive coupling was observed between heart rate, electrodermal activity, respiratory rate, stress, and the derived autonomic arousal metric, while inverse relationships were maintained with heart rate variability consistent with established models of sympathetic activation. Temporal analysis further demonstrated non-uniform panic occurrence over the 24-hour cycle (<xref ref-type="fig" rid="fig1">Figure 1(c)</xref>), indicating meaningful interactions between circadian physiology and episode expression. Distributional comparisons across classes (<xref ref-type="fig" rid="fig1">Figure 1(d)</xref>) showed systematic shifts in HR, EDA, and HRV between Normal and warning states, confirming that the synthetic generator successfully encoded physiologically discriminative patterns. An illustrative panic episode example (<xref ref-type="fig" rid="fig1">Figure 1(e)</xref>) highlights the intended temporal structure of the model: an escalating pre-onset phase with distinct Early and Urgent warning windows, followed by a high-severity peak and gradual recovery. Correspondingly, average panic severity increased monotonically from Normal to Early and Urgent classes (<xref ref-type="fig" rid="fig1">Figure 1(f)</xref>), validating internal label consistency. Collectively, <xref ref-type="fig" rid="fig1">Figures 1(a)-(f)</xref> functions as a comprehensive quality-control summary of the dataset. It demonstrates that the generator produces realistic circadian baselines, structured autonomic deviations during panic escalation, and clinically interpretable warning dynamics while simultaneously revealing the severe class imbalance that fundamentally shapes the modelling challenge.</p>
      </sec>
      <sec id="sec3dot2">
        <title>3.2. Model Comparison</title>
        <p>Model performance was evaluated on the held-out test set using both multi-class classification metrics and the clinically relevant binary panic detection objective. As expected under extreme class imbalance, all tree-based models achieved exceptionally high overall accuracy and weighted F1-scores, largely driven by near-perfect discrimination of the majority Normal class. Specifically, the Random Forest classifier achieved an accuracy of 0.9939, a weighted F1-score of 0.9939, and a panic detection F1-score of 0.6159. The Gradient Boosting model yielded an accuracy of 0.9930, a weighted F1-score of 0.9937, and a superior panic detection F1-score of 0.6407, indicating improved detection of clinically relevant warning windows. In contrast, the linear Logistic Regression baseline, despite a moderate weighted F1-score of 0.8735, failed to capture warning dynamics, producing a panic detection F1-score of only 0.0518 and an overall accuracy of 0.7854.</p>
        <fig id="fig1">
          <label>Figure 1</label>
          <graphic xlink:href="https://html.scirp.org/file/1114923-rId52.jpeg?20260313013545" />
        </fig>
        <p><bold>Top-left (a)</bold>: Class distribution illustrating the extreme rarity of panic-related states. <bold>Top-middle (b)</bold>: Correlation matrix of core physiological variables and autonomic composites, showing coherent physiological coupling. <bold>Top-right (c)</bold>: Hourly distribution of panic samples, highlighting circadian modulation. <bold>Bottom-left (d)</bold>: Feature distributions across Normal, Early Warning, and Urgent Warning classes. <bold>Bottom-middle (e)</bold>: Representative panic episode demonstrating pre-onset Early and Urgent warning windows, peak escalation, and recovery dynamics in heart rate and electrodermal activity. <bold>Bottom-right (f)</bold>: Mean panic severity by class, confirming monotonic severity progression.</p>
        <p><bold>Figure 1.</bold>Synthetic panic disorder dataset overview.</p>
        <p>These results highlight that headline metrics such as accuracy and weighted F1 can be misleading in rare-event contexts, as they primarily reflect performance on the Normal class. The decisive criterion for model selection was therefore panic detection F1-score, which directly measures the system’s ability to identify impending panic episodes. Under this clinically motivated objective, Gradient Boosting clearly outperformed the alternatives and was selected as the final model for all subsequent analyses and deployment optimization.</p>
      </sec>
      <sec id="sec3dot3">
        <title>3.3. Confusion Matrix Analysis and Minority-Class Errors</title>
        <p>Detailed error analysis using the normalized confusion matrix (<xref ref-type="fig" rid="fig2">Figure 2(a)</xref>) reveals a clear asymmetry between majority and minority class performance. Predictions for the Normal class are nearly perfect, while the Early and Urgent warning states remain significantly more challenging due to their extreme rarity and overlapping physiological patterns. Specifically, 99.49% of Normal samples were classified correctly (17,773/17,864), confirming the model’s strong baseline discrimination capability. In contrast, the Early Warning class achieved a correct classification rate of 81.94% (59/72), with 15.28% (11/72) misclassified as Normal. The Urgent Warning class proved most difficult, with 65.62% (42/64) correctly identified, 28.12% (18/64) misclassified as Normal, and 6.25% (4/64) confused with the Early Warning state. These error patterns indicate that the primary failure mode is false negatives, where warning windows are incorrectly labelled as Normal, rather than confusion between the two warning categories. This behaviour is clinically important: while confusion between Early and Urgent states affects timing and urgency, false negatives directly correspond to missed intervention opportunities. The performance summary panel (<xref ref-type="fig" rid="fig2">Figure 2(b)</xref>) reports the combined panic detection metrics after merging Early and Urgent into a single warning class: precision ≈ 0.540, recall ≈ 0.787, and F1 ≈ 0.641. These values indicate that the model successfully recovers a large proportion of true warning windows, though at the cost of a moderate number of false alarms an expected and acceptable trade-off in rare-event forecasting systems prioritizing early detection over strict specificity.</p>
        <fig id="fig2">
          <label>Figure 2</label>
          <graphic xlink:href="https://html.scirp.org/file/1114923-rId53.jpeg?20260313013545" />
        </fig>
        <p><bold>Left panel (a)</bold>: Normalized confusion matrix showing class-wise prediction behaviour on the held-out test set. <bold>Right panel (b)</bold>: Summary of overall classification metrics and combined panic detection performance, including precision, recall, and F1-score.</p>
        <p><bold>Figure 2.</bold>Model performance and error analysis (gradient boosting).</p>
      </sec>
      <sec id="sec3dot4">
        <title>3.4. Discrimination Curves</title>
        <p>Model discrimination was further examined using Precision-Recall (PR) and Receiver Operating Characteristic (ROC) curves, which provide complementary perspectives on classification performance under extreme class imbalance. As shown in <xref ref-type="fig" rid="fig3">Figure 3(a)</xref>, the Normal class achieves an average precision (AP) ≈ 1.000, indicating near-perfect separability from warning states. In contrast, the minority classes exhibit substantially lower precision-recall performance, with AP ≈ 0.745 for Early Warning and AP ≈ 0.622 for Urgent Warning. This degradation directly reflects the intrinsic difficulty of detecting rare, partially overlapping physiological signatures and underscores the importance of PR-based evaluation for clinically meaningful assessment. The ROC curves in <xref ref-type="fig" rid="fig3">Figure 3(b)</xref> remain uniformly high across all classes, with AUC values ranging from approximately 0.987 to 0.997. While this suggests strong ranking ability, ROC metrics are known to remain overly optimistic in highly imbalanced settings because false-positive rates are normalized by the overwhelming majority class. Consequently, high ROC AUC values alone may obscure the true operational cost of false alarms. The divergence between PR and ROC behaviour therefore highlights a critical evaluation principle: precision-recall analysis provides a more faithful measure of early-warning utility in rare-event detection, and PR-based metrics should be emphasized when assessing clinical readiness of panic forecasting systems.</p>
        <fig id="fig3">
          <label>Figure 3</label>
          <graphic xlink:href="https://html.scirp.org/file/1114923-rId54.jpeg?20260313013545" />
        </fig>
        <p><bold>Left panel (a)</bold>: Precision-Recall curves for Normal, Early Warning, and Urgent Warning classes, with corresponding average precision (AP) values. <bold>Right panel (b)</bold>: Receiver Operating Characteristic curves with AUC values, illustrating strong ranking performance despite extreme class imbalance.</p>
        <p><bold>Figure 3.</bold>Model discrimination performance.</p>
      </sec>
      <sec id="sec3dot5">
        <title>3.5. Threshold Optimization and Alarm Burden</title>
        <p>Threshold analysis reveals how post-processing decisions critically shape both detection quality and real-world usability of the forecasting system. As shown in <xref ref-type="fig" rid="fig4">Figure 4(a)</xref>, increasing the panic-risk threshold monotonically improves precision while reducing recall, producing an F1-score maximum at approximately <inline-formula><mml:math><mml:mrow><mml:mi> t </mml:mi><mml:mo> ≈ </mml:mo><mml:mn> 0.80 </mml:mn></mml:mrow></mml:math></inline-formula> . This behavior reflects the fundamental sensitivity-specificity trade-off inherent in early-warning systems. The corresponding effect on user burden is illustrated in <xref ref-type="fig" rid="fig4">Figure 4(b)</xref>, where the expected number of daily alarms decreases rapidly as the threshold increases. This relationship provides an intuitive mechanism for translating model behaviour into clinically interpretable operating constraints. The combined precision-recall trade-off curve in <xref ref-type="fig" rid="fig4">Figure 4(c)</xref> visualizes candidate operating points along this continuum and highlights two practically relevant regimes summarized in <xref ref-type="fig" rid="fig4">Figure 4(d)</xref>:</p>
        <p><bold>Max-F1 configuration:</bold><inline-formula><mml:math><mml:mrow><mml:mi> t </mml:mi><mml:mo> ≈ </mml:mo><mml:mn> 0.80 </mml:mn></mml:mrow></mml:math></inline-formula> , precision ≈ 0.699, recall ≈ 0.684, yielding approximately 10.6 alarms per day. This configuration prioritizes overall detection quality and is suitable for research benchmarking or conservative alerting scenarios.<bold>Balanced clinical configuration:</bold><inline-formula><mml:math><mml:mrow><mml:mi> t </mml:mi><mml:mo> ≈ </mml:mo><mml:mn> 0.50 </mml:mn></mml:mrow></mml:math></inline-formula> , precision ≈ 0.529, recall ≈ 0.809, yielding approximately 16.6 alarms per day. This setting emphasizes high recall and early intervention at the cost of increased alarm frequency, aligning with clinical practice where missing an impending panic episode is typically more harmful than generating additional warnings.</p>
        <p>These results demonstrate that a single trained model can be flexibly adapted to diverse deployment contexts, supporting either low-burden monitoring or high-sensitivity preventive care depending on patient preference, risk tolerance, and clinical workflow requirements.</p>
      </sec>
      <sec id="sec3dot6">
        <title>3.6. Temporal Performance Stability</title>
        <p>To assess robustness of the forecasting system under varying circadian conditions, we analysed model performance across the 24-hour cycle. As shown in <xref ref-type="fig" rid="fig5">Figure 5(a)</xref>, overall classification accuracy remains consistently high throughout the day, reflecting the model’s strong discrimination of the Normal class across diverse physiological regimes. However, the clinically relevant panic detection rate exhibits greater variability across hours (<xref ref-type="fig" rid="fig5">Figure 5(b)</xref>). This fluctuation is expected under extreme class imbalance, as the number of warning samples per hour is small and sensitive to the specific placement of synthetic episodes within the time series. Consequently, modest shifts in episode timing produce visible variation in hourly detection estimates without indicating systematic temporal bias in the model. The underlying distribution of panic samples across hours is presented in <xref ref-type="fig" rid="fig5">Figure 5(c)</xref>, providing necessary context for interpreting these detection patterns. Finally, a representative segment of the prediction timeline (<xref ref-type="fig" rid="fig5">Figure 5(d)</xref>) demonstrates that correct detections concentrate around regions of elevated panic severity, confirming that the model’s alerts are temporally aligned with clinically meaningful physiological escalation. Together, these results indicate that the forecasting system maintains stable baseline performance across circadian phases while remaining responsive to episodic autonomic changes, supporting its suitability for continuous real-world monitoring.</p>
        <fig id="fig4">
          <label>Figure 4</label>
          <graphic xlink:href="https://html.scirp.org/file/1114923-rId61.jpeg?20260313013545" />
        </fig>
        <p><bold>Top-left (a)</bold>: Precision, recall, and F1-score as functions of the decision threshold. <bold>Top-right (b)</bold>: Expected daily alarm frequency versus threshold. <bold>Bottom-left (c)</bold>: Precision-recall trade-off with annotated candidate operating points. <bold>Bottom-right (d)</bold>: Summary of recommended deployment configurations balancing detection quality and alarm burden.</p>
        <p><bold>Figure 4.</bold>Threshold optimization for clinical deployment.</p>
      </sec>
    </sec>
    <sec id="sec4">
      <title>4. Discussion</title>
      <sec id="sec4dot1">
        <title>4.1. Main Findings</title>
        <p>This study presents an end-to-end panic forecasting framework that is intentionally designed to mirror the full lifecycle of a deployable wearable early-warning system: data generation, physiological feature construction, imbalance-aware training, model benchmarking, and deployment-oriented decision tuning. The synthetic generator produces circadian-structured baseline physiology and panic-like escalations with staged warning windows, enabling controlled experiments where methodological choices can be tested systematically before real-world validation. The feature set integrates short-term variability, multi-window trends, circadian normalization, and cross-signal interactions elements that are strongly motivated by autonomic physiology and wearable sensing constraints.</p>
        <p>A major observation is the gap between headline metrics and clinically meaningful detection. Overall test performance exceeded 0.99 in accuracy and weighted F1, but this primarily reflects the ability to classify the dominant Normal state in an extremely imbalanced dataset. When reframed as an operational task detecting any warning state (Early or Urgent) versus Normal performance becomes more realistic: panic detection F1 ≈ 0.64 with recall ≈ 0.79 (<xref ref-type="fig" rid="fig2">Figure 2(a)</xref>, <xref ref-type="fig" rid="fig2">Figure 2(b)</xref>). This indicates that the system successfully identifies a substantial fraction of warning windows but still misses a non-trivial portion of minority events and generates false alarms. Importantly, the precision-recall analysis (<xref ref-type="fig" rid="fig3">Figure 3(a)</xref>) highlights that minority-class performance is the limiting factor, and it confirms that ROC AUC (<xref ref-type="fig" rid="fig3">Figure 3(b)</xref>) can remain high even when operational precision is modest an expected phenomenon in rare-event settings. Together, these results demonstrate that PR-based metrics and warning-focused objectives should be prioritized for panic forecasting evaluation, not accuracy alone [<xref ref-type="bibr" rid="B58">58</xref>]-[<xref ref-type="bibr" rid="B61">61</xref>].</p>
        <fig id="fig5">
          <label>Figure 5</label>
          <graphic xlink:href="https://html.scirp.org/file/1114923-rId62.jpeg?20260313013545" />
        </fig>
        <p><bold>Top-left (a)</bold>: Model accuracy by hour of day. <bold>Top-right (b)</bold>: Panic detection rate by hour. <bold>Bottom-left (c)</bold>: Panic sample frequency across hours. <bold>Bottom-right (d)</bold>: Sample prediction timeline showing true labels, predicted labels, panic severity, and correct detections.</p>
        <p><bold>Figure 5.</bold>Temporal performance analysis.</p>
      </sec>
      <sec id="sec4dot2">
        <title>4.2. Why Tree-Based Models Outperform Linear Baselines</title>
        <p>The strong advantage of Gradient Boosting and Random Forest over Logistic Regression is consistent with the structure of the problem and the engineered feature space. Panic warning dynamics are inherently non-linear: physiological escalation is rarely explained by a single variable crossing a threshold, but rather by patterns simultaneous increases in HR and EDA, suppression of HRV, respiration changes, interaction effects, and deviations relative to the expected circadian baseline. Several of the most informative representations (e.g., HR × EDA product, HR/HRV ratio, autonomic balance, circadian z-scores, multi-window slopes) encode conditional relationships where the meaning of one signal depends on another signal or on time-of-day context.</p>
        <p>Linear models struggle in this regime because they impose a globally additive decision boundary; they cannot naturally express “risk increases only when HR rises and HRV drops” or “EDA elevation matters only when it is abnormal for that hour.” In contrast, Gradient Boosting builds ensembles of decision trees that partition the feature space into localized regions and can capture complex feature interactions with limited manual specification. This explains why Logistic Regression produced a very low panic detection F1 ≈ 0.052, despite moderate weighted F1 driven by the Normal class, whereas Gradient Boosting achieved materially better warning discrimination. In practical terms, this suggests that panic forecasting pipelines should either rely on models that learn interactions (tree ensembles, kernel methods, neural sequence models) or explicitly include interaction structure via modelling assumptions.</p>
      </sec>
      <sec id="sec4dot3">
        <title>4.3. Deployment Interpretation: Thresholding Is Not Optional</title>
        <p>A critical contribution of this work is treating threshold selection as part of the model not as an afterthought. In clinical-grade early-warning systems, a model that maximizes offline metrics can still fail in practice if it produces excessive alerts, because alarm fatigue reduces adherence, trust, and ultimately clinical utility. Conversely, overly conservative alerting may improve precision but miss episodes where early intervention is most valuable. For this reason, deployment requires translating probabilities into operating decisions using explicit constraints that reflect human and clinical realities. <xref ref-type="fig" rid="fig4">Figure 4</xref> operationalizes this principle. As the panic-risk threshold increases, precision improves and recall declines (<xref ref-type="fig" rid="fig4">Figure 4(a)</xref>), while the expected number of alarms per day decreases (<xref ref-type="fig" rid="fig4">Figure 4(b)</xref>). This relationship enables decision-making in units that clinicians and patients can understand: “How many times per day will the system interrupt the user?” rather than “What is the F1-score?” The comparison between the Max-F1 threshold (t ≈ 0.80) and the balanced clinical threshold (t ≈ 0.50) illustrates the importance of aligning thresholding with intent. The Max-F1 setting reduces alarms (~10.6/day) but yields lower recall, while the clinical setting yields higher recall (~0.81) with a still-bounded alert rate (~16.6/day) (<xref ref-type="fig" rid="fig4">Figures 4(b)-(d)</xref>). This demonstrates that the same trained model can be adapted to different use cases: conservative self-monitoring, high-sensitivity relapse prevention, or clinician-supervised programs.</p>
        <p>From a safety and usability viewpoint, thresholding should ideally be personalized and context-aware for example, allowing lower thresholds for high-risk patients, or dynamically adjusting sensitivity during known vulnerable periods (e.g., acute stress exposures), while maintaining a bounded alarm budget. Importantly, such policies must be validated prospectively, since user response and habituation strongly influence real-world benefit.</p>
      </sec>
      <sec id="sec4dot4">
        <title>4.4. Toward Real-World Translation</title>
        <p>While synthetic pipelines are valuable for rigorous methodological testing, translation to clinical settings requires addressing three categories of realism: personalization, temporality, and decision reliability.</p>
        <p><bold>Personalization.</bold> Real users differ widely in baseline HR, HRV range, sweating response, fitness, medication, and comorbid anxiety. A deployable system must learn individual baselines and detect deviations relative to personal norms rather than relying solely on population-level thresholds. Practically, this implies per-user calibration periods, adaptive normalization (e.g., rolling baseline models), and individualized decision thresholds that target a user-specific alarm budget and clinical objective.</p>
        <p><bold>Sequential modelling.</bold> Panic forecasting is fundamentally temporal: what matters is not only the current value of HR or EDA, but the trajectory and consistency of change. Although engineered rolling statistics and slopes partially encode dynamics, they are still summary representations. Temporal models such as hidden Markov models, temporal convolutional networks, sequence transformers, or hybrid models combining physiology-informed states with learned dynamics can explicitly model transitions into warning states and may improve early-window detection while reducing sporadic false alarms. Event-level evaluation should accompany this shift, emphasizing detection within the early window, lead-time distribution, and false alarms per hour/day.</p>
        <p><bold>Probability calibration and reliability.</bold> Many models (including tree ensembles) provide probability scores that may be poorly calibrated, meaning the numeric probability does not correspond to true event likelihood. Calibration methods such as Platt scaling or isotonic regression can improve stability across settings, making threshold policies more transferable. In addition, deployment typically benefits from decision logic beyond a single threshold: smoothing rules (e.g., require sustained risk for several minutes), cooldown periods to prevent alert bursts, and uncertainty-aware abstention when sensor quality is poor.</p>
        <p><bold>Prospective validation and human outcomes.</bold> Ultimately, a panic forecasting system should be judged not only by classification metrics, but by whether it improves patient outcomes: reduced attack severity, increased perceived control, improved adherence to interventions, and reduced healthcare utilization. This requires prospective studies with ground-truth event annotation (self-report + clinician confirmation where possible), careful handling of confounds (physical activity, caffeine, sleep), and user-cantered evaluation of alarm burden and trust. The present framework provides a strong technical foundation for designing such studies by clarifying how performance, imbalance, and thresholding interact under controlled conditions.</p>
      </sec>
    </sec>
    <sec id="sec5">
      <title>5. Limitations</title>
      <p>Despite demonstrating the feasibility of panic episode forecasting under controlled conditions, several limitations constrain the interpretation and generalization of the present findings.</p>
      <p><bold>1</bold><bold>)</bold><bold>Synthetic-only validation.</bold> All experiments were conducted on synthetic physiological data. While the generator incorporates circadian structure, autonomic coupling, and realistic noise processes, real-world wearable data contain additional complexities not represented here, including motion artifacts, sensor dropout, nonstationary baselines, medication effects, comorbid stressors, and behavioural confounds (e.g., caffeine intake, exercise, sleep disruption). Consequently, the reported performance reflects algorithmic potential rather than clinical validity, and prospective evaluation on real patient data is essential before clinical conclusions can be drawn.</p>
      <p><bold>2</bold><bold>)</bold><bold>Label rule dependence.</bold> Warning labels are derived directly from the episode injection mechanism. This introduces a structural dependency between feature construction and label assignment, which can artificially inflate model performance because some engineered features are implicitly aligned with the generative rules. Although this is acceptable for controlled method development, it limits the interpretability of absolute performance values and underscores the need for external validation using independently labelled datasets.</p>
      <p><bold>3</bold><bold>)</bold><bold>Episode generation accounting inconsistency.</bold> The generation log indicates an intended creation of 333 panic episodes but an effective realization of only 5 episodes in the final dataset. This discrepancy likely arises from strict temporal spacing constraints in the placement algorithm, which substantially reduce feasible episode insertion within a finite time series. Such inconsistency can distort frequency statistics and bias temporal analyses (see <xref ref-type="fig" rid="fig1">Figure 1(c)</xref> and <xref ref-type="fig" rid="fig5">Figure 5(b)</xref>, <xref ref-type="fig" rid="fig5">Figure 5(c)</xref>). Future implementations must enforce transparent and auditable episode-count guarantees to ensure reproducibility and reliable statistical characterization.</p>
      <p><bold>4</bold><bold>)</bold><bold>Resampling risks.</bold> The use of SMOTETomek balances the training distribution but introduces synthetic minority samples that may not reflect real patient physiology. Moreover, if temporal dependencies are not handled carefully, resampling can leak structural information across windows, potentially inflating performance. This limitation reinforces the importance of validating the pipeline under natural class distributions and sequential evaluation settings.</p>
      <p><bold>5</bold><bold>)</bold><bold>Minute-level independence assumption.</bold> Although temporal features partially encode dynamics, the model ultimately treats each minute as conditionally independent during training. Panic escalation is inherently sequential, and models that explicitly capture temporal transitions (e.g., hidden Markov models, recurrent networks, temporal transformers) may better represent pre-onset trajectories and reduce false alarms.</p>
      <p>Together, these limitations emphasize that the current work should be interpreted as a methodological foundation rather than a finished clinical system, guiding the design of future real-world panic forecasting studies.</p>
    </sec>
    <sec id="sec6">
      <title>6. Conclusion</title>
      <p>This study introduced a fully reproducible panic-episode forecasting pipeline built upon wearable-inspired synthetic physiology, comprehensive feature engineering, classical machine-learning baselines, and clinically motivated deployment optimization. The proposed framework demonstrates how early-warning systems for panic disorder can be systematically developed, evaluated, and tuned under controlled conditions before real-world validation [<xref ref-type="bibr" rid="B62">62</xref>]-[<xref ref-type="bibr" rid="B66">66</xref>]. Among the evaluated models, Gradient Boosting emerged as the most effective for the clinically relevant task of warning detection, achieving panic detection F1 ≈ 0.64 and recall ≈ 0.79 on a severely imbalanced dataset, while maintaining excellent overall discrimination of the Normal state. Importantly, the explicit integration of threshold optimization enabled direct control over operational burden, illustrating how a single trained model can be adapted to different clinical use cases from conservative alerting to high-sensitivity preventive monitoring with the balanced deployment configuration yielding approximately 16.6 alerts per day at t ≈ 0.50. The contribution of this work lies not in claiming immediate clinical readiness, but in providing a rigorous methodological baseline and evaluation scaffold for panic forecasting research. By exposing the limitations of accuracy-based evaluation, formalizing alarm-burden trade-offs, and emphasizing rare-event-appropriate metrics, the framework establishes principled guidelines for future development of wearable mental-health monitoring systems. Future research should prioritize validation on real-world wearable datasets, incorporate subject-specific baseline adaptation and probability calibration, correct episode-generation accounting for transparent reproducibility, and transition toward event-based prospective evaluation using clinically meaningful outcomes such as detection lead time, episode prevention, and patient quality of life. Together, these directions will move panic forecasting from algorithmic feasibility toward clinically actionable decision support.</p>
    </sec>
  </body>
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