Cumulative Vigilance Score (CVS)

• Cumulative Vigilance Score (CVS) is a continuously updated, normalized behavioral index that quantifies vigilance using trial-wise performance metrics and calibrated reaction time thresholds.
• It employs a two-stage scoring process with a sliding window to capture both transient fluctuations and overall attention stability.
• High predictive correlations (up to R² = 0.91) in neural models highlight CVS’ potential for advanced vigilance monitoring in cognitive neuroscience.

The cumulative vigilance score (CVS) is a continuously updated, normalized behavioral index that quantifies a participant’s vigilance based on discrete performance labels in sustained attention tasks. CVS was introduced by Torkamani-Azar et al. as a way to capture trial-by-trial attention state fluctuations with high temporal specificity, enabling quantitative modeling of vigilance variability in association with neural signals such as resting-state EEG (Torkamani-Azar et al., 2019).

1. Construction of the Cumulative Vigilance Score

CVS is built on a two-stage scheme. First, each trial receives a trial-wise vigilance score (TVS), a discrete label encoding performance and reaction times. For every new trial $i$, the experimental context (e.g., a sustained attention to response task with Go/NoGo stimuli) informs error types—double-clicks, omission, commission, and single correct clicks. Two subject-specific reaction time thresholds are calibrated from the first 27 Go trials (no errors):

• $\mathrm{RT}_L = 250~\mathrm{ms}$, a fixed lower threshold,
• $$\mathrm{RT}_U = \overline{\mathrm{RT}^{(27)}} + 2\,\sigma_{\mathrm{RT}^{(27)}}$$, where $\overline{\mathrm{RT}^{(27)}}$ and $\sigma_{\mathrm{RT}^{(27)}}$ are the mean and standard deviation of RTs in the calibration phase.

TVS is then assigned as follows: $$\mathrm{TVS}_i = \begin{cases} 1 & \text{double-click or omission after double-click} \ 2 & \text{commission error (incorrect NoGo response)} \ 3 & \text{correct Go with }\mathrm{RT}_i > \mathrm{RT}_U \ 4 & \text{correct Go or NoGo with } \mathrm{RT}_L < \mathrm{RT}_i \leq \mathrm{RT}_U \ 5 & \text{correct Go with } \mathrm{RT}_i \leq \mathrm{RT}_L \end{cases}$$ This 1–5 scale discriminates between severe performance lapses and optimal, fast, correct responses.

The cumulative vigilance score, after $n \geq W$ trials, is computed as

$$\overline{\mathrm{TVS}_n} = \frac{1}{W} \sum_{i=n-W+1}^{n} \mathrm{TVS}_i$$

and normalized to $[0,1]$: $$\mathrm{CVS}_n = \frac{\overline{\mathrm{TVS}_n} - 1}{4}$$ CVS adapts over a sliding window $W$ (chosen as $W=36$ in the original study), updating as each new trial appends a new TVS and the oldest one is dropped.

2. Algorithmic Workflow

The CVS computation proceeds as follows:

1. Calibration: Use the first 27 Go trials (no errors) to compute $\overline{\mathrm{RT}^{(27)}}$ and $\sigma_{\mathrm{RT}^{(27)}}$, yielding $\mathrm{RT}_U$ and setting $\mathrm{RT}_L=250~\mathrm{ms}$.
2. Per-trial Scoring: For each subsequent trial, classify errors, measure RT where appropriate, and assign the TVS according to the defined rules.
3. Buffer Maintenance: Maintain a rolling buffer of the latest $W$ TVS values.
4. CVS Update: With every completed window, compute

$$\mathrm{CVS}_n = \frac{1}{4W} \sum_{i=n-W+1}^{n} (\mathrm{TVS}_i - 1)$$

The process yields a continuous-valued time series reflecting the most recent performance.

This sliding and normalization procedure translates abrupt or transient changes in performance into a smoothed measure suitable for dynamic behavioral and neural modeling (Torkamani-Azar et al., 2019).

3. Worked Example

Consider a window $W=5$ and the following sequence for trials $1$–$5$: $\{5, 4, 3, 2, 5\}$. The raw mean is

$$\overline{\mathrm{TVS}_5} = \frac{1}{5}(5+4+3+2+5) = 3.8$$

The CVS is then

$\mathrm{CVS}_5 = \frac{3.8 - 1}{4} = 0.70$

In the next window, suppose $\{5,5,5,4,5\}$, then

$$\overline{\mathrm{TVS}_{10}} = 4,\quad \mathrm{CVS}_{10} = 0.75$$

This illustrates how CVS responds to runs of suboptimal or optimal performance, balancing recent history with moment-to-moment variance.

4. Interpretation and Behavioral Significance

High CVS values near 1 indicate a sequence of rapid and accurate responses, signaling sustained attention and optimal vigilance. Low values approaching 0 result from consecutive errors, double-clicks, omissions, or excessive response times, indicative of vigilance lapses or fatigue. The window length $W$ governs the temporal responsiveness of the score: short windows track rapid fluctuations, while long windows confer stability at the cost of reduced temporal resolution. Thus, CVS captures both tonic vigilance and phasic lapses within the chosen time window (Torkamani-Azar et al., 2019).

5. Parameterization and Customization

The definition of CVS incorporates several modifiable hyperparameters:

Parameter	Typical Value	Purpose/Effect
Window length $W$	36 trials	Smoothing over ~73 s; higher $W$ stabilizes CVS, lower $W$ increases temporal acuity
$\mathrm{RT}_L$	250 ms	Separates anticipatory/impulsive from physiologically plausible responses
$\mathrm{RT}_U$	Calibration-derived	Baseline mean + 2 SD (personalized), penalizing excessive slowness
TVS Scale	$\{1,..,5\}$	Finer gradations sharpen CVS granularity; scale collapse reduces sensitivity

The selection of these parameters depends on experimental requirements, the trade-off between rapid detection of vigilance loss and score stability, and subject-specific factors. Alternative statistical strategies for $\mathrm{RT}_U$ (e.g., mean + 1 SD or quantile thresholds) are mentioned as plausible modifications, but the published approach uses mean + 2 SD (Torkamani-Azar et al., 2019).

6. Application in Predictive Modeling

In regression and neural-network analyses, CVS serves as a continuous behavioral target. Torkamani-Azar et al. extract for each subject the mean and variability of CVS ($\mathrm{CVSmean}$, $\mathrm{CVSvar}$), alongside hit-response time metrics, for subsequent prediction from baseline EEG features. Linear regression (with feature relevance analysis) and single-layer neural networks (trained with cross-validation) are deployed to relate resting-state EEG band-power ratios to CVS statistics, revealing that intrinsic spectrospatial properties of brain activity encode substantial information about a person’s capability for sustained vigilant performance. Notably, cross-validated $R^2$ up to 0.91 for $\mathrm{CVSmean}$ is achieved, signifying robust predictive utility (Torkamani-Azar et al., 2019).

7. Broader Implications and Benchmarking Role

CVS is constructed to be adaptable and experimentally transparent, offering a standardized behavioral read-out for sustained attention tasks. Its strong correlations with neurophysiological features suggest utility both as a calibration benchmark in BCI and vigilance monitoring contexts and as a foundational variable in studies probing the neural bases of attention. Its smooth, interpretable scaling facilitates integration into temporal analyses of performance variability. A plausible implication is that CVS, by combining error detection and reaction-time adaptation within a personalized, rolling framework, advances behavioral quantification beyond coarse accuracy-based indices, supporting high-sensitivity vigilance modeling in cognitive neuroscience and applied neuroengineering (Torkamani-Azar et al., 2019).