Predicting cognitive impairment using novel functional features of spatial proximity and circularity in the digital clock drawing test

This study demonstrates that novel mathematical functional features of spatial proximity and circularity derived from digital clock drawing tests can predict cognitive impairment with accuracy comparable to traditional summary statistics, offering a promising approach to enhance early detection strategies.

The Gist

Imagine you are trying to figure out if someone is having trouble with their memory or thinking skills. Traditionally, doctors might ask them to draw a clock on a piece of paper. A human doctor looks at the drawing and gives it a score: "Hmm, the numbers are a bit squished, and the hands are in the wrong place. That's a 6 out of 10."

This is the Clock Drawing Test (CDT). It's a classic tool, but it has a flaw: it relies on a human's opinion. One doctor might be stricter than another, and small, subtle mistakes might get missed.

Now, imagine instead of paper, the person draws on a digital tablet with a special smart pen. This pen doesn't just record the final picture; it records everything happening in real-time, 77 times every second. It knows exactly where the pen is, how hard they are pressing, and how long they pause.

This is the Digital Clock Drawing Test (dCDT).

The Problem with the Old Way

Researchers have been using this digital data to predict cognitive issues (like Mild Cognitive Impairment or Dementia). But so far, they've been treating the data like a grocery list. They'd count things like:

• "How long did it take?"
• "How many times did they lift the pen?"
• "How big was the circle?"

The problem with this "grocery list" approach is that it throws away the story. It's like judging a movie by only counting how many times the main character blinked, ignoring the plot, the acting, and the emotions. Also, if the person draws a messy clock or forgets a number, the computer often gets confused and has to guess (impute) the missing data, which isn't very reliable.

The New Idea: Listening to the "Song" of the Drawing

In this new study, the researchers decided to stop counting items and start listening to the music of the drawing. They treated the drawing not as a list of numbers, but as a continuous, flowing curve—a mathematical "song."

They invented three new ways to listen to this song:

1. The "Crowded Room" Test (Spatial Proximity / G-Function):

   • The Metaphor: Imagine the pen dots are people at a party.
   • The Healthy Way: A healthy person moves around the room smoothly. The "people" (dots) are spread out evenly.
   • The Impaired Way: A person with cognitive issues might get stuck in one corner, pacing back and forth nervously. The "people" (dots) are clumped tightly together.
   • The Feature: This new math tool measures how "clumped" the dots are. If the dots are huddled together, it suggests the person is hesitating or moving slowly in small areas, a sign of trouble.

2. The "Bumpy Road" Test (Circularity / Radius Function):

   • The Metaphor: Imagine drawing a perfect circle is like driving a car on a smooth, round track.
   • The Healthy Way: The car stays on the track perfectly. The road is flat and smooth.
   • The Impaired Way: The car wobbles, swerves, and hits bumps. The road is bumpy and uneven.
   • The Feature: This tool measures how "bumpy" the circle is. A wobbly, uneven circle suggests the brain is struggling with fine motor control and spatial planning.

3. The "Grip Strength" Test (Pressure Density):

   • The Metaphor: How hard are you squeezing the steering wheel?
   • The Idea: Does the person press too hard when they are stressed, or too lightly when they are confused?
   • The Result: Surprisingly, this study found that how hard they pressed didn't tell them much. The "grip" was similar for everyone, so this feature wasn't very helpful.

What Did They Find?

The researchers tested these new "musical" features on over 3,400 people from the famous Framingham Heart Study.

• The Result: The new "musical" features (how clumped the dots are and how bumpy the circle is) worked just as well as the old "grocery list" of features.
• The Bonus: Unlike the old method, these new features work even if the drawing is messy or incomplete. If someone forgets to draw the number "3," the old computer might crash or guess wrong. The new "musical" computer can still listen to the rhythm of the lines they did draw and make a good guess.

The Takeaway

Think of this like upgrading from a still photo to a high-definition video.

• The old way took a still photo of the finished clock and counted the pixels.
• The new way watches the video of the hand moving, feeling the hesitation, the wobble, and the flow.

By listening to the "song" of the drawing, doctors might soon be able to catch early signs of memory problems much sooner and more accurately, using a simple, non-invasive test that feels like just drawing a clock. It's a smarter, more sensitive way to see what the brain is really doing.

Technical Summary

1. Problem Statement

The Clock Drawing Test (CDT) is a standard, cost-effective screening tool for cognitive impairment (Mild Cognitive Impairment [MCI] and dementia). While digital versions (dCDT) capture high-resolution kinematic data (pen position, pressure, time) that traditional paper tests miss, current analytical approaches rely heavily on hand-engineered summary statistics (e.g., mean pressure, total time, symmetry scores).

These traditional approaches suffer from several limitations:

• Subjectivity: Feature selection and aggregation often involve analyst bias.
• Information Loss: Collapsing rich temporal and geometric trajectories into single summary values obscures subtle structural nuances in the drawing process.
• Data Dependency: Many summary features require complete drawings (e.g., specific digits or hands must be present), necessitating imputation for incomplete tests.
• Correlation Handling: Managing large sets of correlated features requires careful statistical handling to avoid overfitting.

The study aims to address these issues by introducing novel functional features that treat the drawing data as continuous mathematical functions rather than discrete summaries, thereby preserving temporal and geometric detail while remaining interpretable.

2. Methodology

Data Source and Pre-processing

• Cohort: Data was drawn from the Framingham Heart Study (FHS), comprising 3,415 participants.
• Task: Participants completed dCDT under two conditions: Command (draw from memory) and Copy (replicate a provided image).
• Data Capture: Digital pens recorded $(x, y)$ coordinates, pressure, and timestamps every 13 milliseconds.
• Pre-processing: Raw coordinates were linearly scaled and translated to a unit square to normalize drawing sizes while preserving aspect ratios. An image scale factor was retained as a covariate.
• Outcomes: Participants were classified as Cognitively Intact vs. Impaired (MCI or Dementia) based on adjudicated review. A secondary analysis distinguished MCI from Dementia.

Novel Functional Features

The authors proposed three functional features represented as mathematical curves, which are then reduced to low-dimensional scores via Functional Principal Component Analysis (FPCA) using the PACE (Principal Components Analysis through Conditional Expectation) algorithm:

1. Nearest-Neighbor G-function (Spatial Proximity):
   • Definition: The empirical cumulative distribution function of nearest-neighbor distances between all recorded pen points.
   • Significance: Captures the spatial clustering and dispersion of points. A rapidly rising G-function indicates tight clustering (often associated with hesitation or slower movement), while a flatter curve indicates dispersion. It is independent of stroke labeling.
2. Radius Function (Circularity):
   • Definition: The distance from the center of the clock-face to the pen tip as a function of the angle (0°–360°).
   • Significance: Quantifies deviations from a perfect circle (symmetry, waviness, tremors). A flat line represents a perfect circle; variability indicates morphological imperfections. It handles overlapping strokes via convex hull construction.
3. Pressure Density Function:
   • Definition: A non-parametric probability density function (Gaussian kernel smoothed) of the pressure values applied throughout the test.
   • Significance: Captures the full distribution of force application rather than just mean or standard deviation.

Modeling Framework

• Algorithm: Random Forest classifiers.
• Validation: Stratified 5-fold cross-validation with strict leakage control (FPCA was performed only on the training fold, and validation curves were projected onto training-derived eigenfunctions).
• Model Families Compared:
  1. Demographics only (Age, Sex, Education, APOE4, Cohort).
  2. Demographics + Literature-based Summary Features.
  3. Demographics + Time-based measures + Single Functional Feature (G, Radius, or Pressure).
  4. Demographics + Time-based measures + All Functional Features.
• Metrics: Area Under the Curve (AUC), Sensitivity, Specificity, and Shapley values for variable importance.

3. Key Contributions

• Functional Representation: Introduced a framework to model dCDT data as continuous functions (G-function, Radius, Pressure Density) rather than discrete summaries, preserving the richness of the raw trajectory data.
• Robustness to Incompleteness: Demonstrated that these functional features can be computed even when drawings are incomplete (e.g., missing digits or hands), reducing the need for data imputation.
• Interpretability: Provided clinically interpretable metrics where specific functional shapes correspond to specific cognitive/motor behaviors (e.g., clustering = hesitation; radius variability = motor tremor/visuospatial error).
• Leakage-Controlled Pipeline: Established a rigorous cross-validation protocol for functional data analysis to prevent information leakage during dimension reduction.

4. Results

Cognitively Intact vs. Impaired (Primary Outcome)

• Performance Parity: Models using the G-function and Radius function achieved predictive performance (AUC) comparable to models using large sets of traditional summary features.
  • Command Task: G-function AUC = 0.90; Radius AUC = 0.91; Summary Features AUC = 0.91.
  • Copy Task: G-function AUC = 0.90; Radius AUC = 0.91; Summary Features AUC = 0.90.
• Operating Characteristics:
  • G-function: Exhibited higher sensitivity (0.91) but lower specificity. It effectively flags impaired participants who exhibit clustered, hesitant movements.
  • Radius Function: Exhibited higher specificity (0.83 in copy task) and balanced sensitivity. It effectively identifies those with poor circularity and symmetry.
• Pressure Density: Showed limited incremental value. While the distribution differed slightly (impaired participants showed less peak pressure), it did not significantly improve classification over demographics alone or other functional features.
• Demographics: Age and FHS cohort were the strongest predictors overall, but adding functional features improved AUC by ~0.07–0.09 points over demographics alone.

MCI vs. Dementia (Secondary Outcome)

• Discrimination between MCI and Dementia was modest (best AUC ~0.78 with summary features in the copy task).
• Functional features performed similarly to summary features but did not significantly outperform them, likely due to the clinical overlap between MCI and early dementia and the smaller sample size for this subgroup.

Variable Importance

• Demographics (Age, Cohort) and Time-based measures (total time, ink time) were top predictors.
• Among functional features, FPC scores from the G-function and Radius function were top contributors.
• Pressure density scores ranked low in importance, consistent with the minimal group differences observed in the density plots.

5. Significance and Conclusion

This study demonstrates that interpretable functional features derived from digital pen data can match the diagnostic accuracy of complex, hand-engineered summary feature sets in detecting cognitive impairment.

• Clinical Utility: The approach offers a "screening-optimized" tool. The G-function's high sensitivity makes it ideal for catching potential cases (minimizing false negatives), while the Radius function's high specificity helps rule out false positives.
• Practicality: The method requires minimal pre-processing and is robust to incomplete drawings, making it highly suitable for real-world clinical settings where patients may not complete the full test.
• Future Direction: The study validates the use of functional data analysis (FDA) in digital biomarkers, suggesting that capturing the shape and structure of movement trajectories provides deeper insights into cognitive and motor control than static summary statistics.

Limitations: The cohort was predominantly White and from a single geographic location (Framingham), limiting generalizability. Additionally, the "intact" group included unflagged participants, potentially introducing label noise, though sensitivity analyses suggested robustness.