Theta-Beta Ratio in Attention Deficit Hyperactivity Disorder: A Multiverse Analysis

This multiverse analysis of two large datasets reveals that the theta/beta ratio is not a robust biomarker for ADHD, as previously reported group differences are largely driven by analytical choices, age, and individual alpha frequency rather than stable oscillatory dynamics.

The Gist

The Big Idea: Is the "ADHD Brain Radio" Broken?

For a long time, doctors and scientists have been trying to find a simple, objective way to diagnose Attention Deficit Hyperactivity Disorder (ADHD). Currently, diagnosis relies on asking parents and teachers, "Is the child fidgeting too much?" or "Can they sit still?" It's like judging a movie by reading a review rather than watching the film.

To fix this, researchers looked at brain waves (EEG). They noticed that in many children with ADHD, the brain seemed to be broadcasting on two specific radio stations at the wrong volume:

1. Theta (Slow waves): Like a slow, sleepy drone.
2. Beta (Fast waves): Like a busy, alert chatter.

The theory was that in ADHD, the "sleepy drone" is too loud, and the "busy chatter" is too quiet. Scientists created a simple math formula called the Theta/Beta Ratio (TBR) to measure this. If the number was high, they said, "Aha! This child has ADHD." This idea became so popular that the FDA even approved devices that use this ratio to help diagnose kids.

The Problem: The "Choose-Your-Own-Adventure" Trap

However, other scientists started noticing something weird. Sometimes the TBR test worked great; other times, it failed completely. It was as if the test gave different answers depending on who was holding the ruler.

This paper asks: Is the TBR a reliable tool, or does it just depend on how you measure it?

To find out, the authors didn't just run the test once. They ran it 576 different times on two massive groups of kids (nearly 1,500 in one group and 380 in another). This is called a "Multiverse Analysis."

The Analogy: Imagine you are trying to measure the height of a tree.

• Method A: You measure from the ground to the top branch.
• Method B: You measure from the base of the roots to the top branch.
• Method C: You measure only the trunk, ignoring the branches.
• Method D: You measure on a sunny day vs. a cloudy day.

If you try all 576 combinations of "how to measure," you get 576 different answers. The authors wanted to see if any of those answers consistently said, "This tree is definitely an ADHD tree."

The Findings: The "Magic Number" Doesn't Exist

After running all 576 versions of the test, the results were surprising:

1. No Consistent Difference: In almost every single scenario, the "ADHD group" and the "Healthy group" looked exactly the same. There was no reliable "high TBR" that separated the two groups.
2. It Depends on the Settings: The only time they found a difference, it wasn't because the kids had ADHD. It was because of how they calculated the number.
   • If they used a specific way to count the brain waves (ignoring the "background noise" of the brain), they found a difference.
   • If they changed the math slightly, the difference vanished.

The Metaphor: Imagine trying to hear a whisper in a noisy room.

• If you turn up the volume on the "slow" frequencies and turn down the "fast" ones, you might hear the whisper and think, "Aha! I found the signal!"
• But if you realize that the "whisper" was actually just the hum of the air conditioner (background noise) that changes depending on the time of day, you realize you weren't hearing a secret message at all.

The Real Culprit: The "Background Hum" (Aperiodic Signal)

The paper discovered that the TBR isn't actually measuring the "music" (the brain waves) as much as it is measuring the "static" or "background hum" of the brain.

• The Aperiodic Signal: Think of the brain's electrical activity like a radio station. There are specific songs playing (the Theta and Beta waves), but there is also a constant static hiss in the background.
• The Twist: Children with ADHD often move around more. This movement creates "static" in the recording. Also, as kids get older, their brain's "static" changes naturally.
• The Confusion: The TBR formula was accidentally counting this "static" as part of the "slow song." When the researchers corrected for the static (the background hum), the "ADHD difference" disappeared.

Why Does This Matter?

1. Stop Relying on the TBR: The paper concludes that the Theta/Beta Ratio is not a reliable standalone test for diagnosing ADHD. Using it alone is like trying to diagnose a broken car engine just by listening to the radio static; it's too easily fooled by outside factors.
2. The "One-Size-Fits-All" Doesn't Work: Every brain is different. Some kids have a naturally slower "radio frequency" (called Individual Alpha Frequency). If you use a fixed formula for everyone, you get the wrong answer.
3. Future Hope: The authors suggest that instead of a simple ratio, we need to look at the whole picture: the specific frequency of the brain, the background noise, and the age of the child.

The Bottom Line

The study is a massive "reality check" for the field of ADHD research. It shows that for years, scientists might have been seeing patterns that were actually just illusions created by how they did the math.

In short: The "Theta/Beta Ratio" is not a magic key to unlock the diagnosis of ADHD. It's a shaky compass that points in different directions depending on the weather. To truly understand ADHD, we need better maps that account for the unique terrain of every individual's brain.

Technical Summary

1. Problem Statement

Attention Deficit Hyperactivity Disorder (ADHD) affects 5–7% of children globally, yet diagnosis relies heavily on subjective clinical assessments. The Theta/Beta Ratio (TBR) derived from resting-state EEG has long been proposed as an objective neurobiological biomarker, based on the hypothesis that ADHD is characterized by elevated theta (4–8 Hz) and reduced beta (>14 Hz) activity.

Despite regulatory approval (e.g., FDA) of TBR-based diagnostic tools, recent literature has raised significant concerns regarding the robustness and generalizability of these findings. Previous studies have shown high heterogeneity, with effect sizes declining over time. The authors posit that these inconsistencies arise from researcher degrees of freedom (RDF)—the multitude of analytical choices (e.g., preprocessing pipelines, reference schemes, frequency band definitions, handling of aperiodic signals) that can arbitrarily influence TBR values. The study aims to determine whether TBR differences between ADHD and healthy controls represent a stable neurobiological phenomenon or are artifacts of specific methodological choices.

2. Methodology

The study employed a Multiverse Analysis approach to systematically evaluate the stability of TBR findings across the full spectrum of plausible analytical specifications.

• Datasets:
  • Main Sample: Healthy Brain Network (HBN) project ($N=1,499$), including Healthy Controls (HC), ADHD-Combined, and ADHD-Inattentive subtypes.
  • Validation Sample: A large-scale multicenter clinical study ($N=381$).
• Preprocessing:
  • Data were processed using the Automagic pipeline (MATLAB).
  • Steps included bad channel detection (PREP pipeline), filtering (0.5 Hz high-pass), line noise removal (ZapLine), and artifact rejection via Independent Component Analysis (ICA) using ICLabel.
  • Data were segmented into Eyes-Open (EO) and Eyes-Closed (EC) conditions.
• Feature Extraction:
  • Spectral Analysis: Fast Fourier Transform (FFT) over 1–40 Hz.
  • Aperiodic Separation: Power spectra were decomposed into periodic (oscillatory) and aperiodic (1/f) components using SpecParam (Fitting Oscillations & One-Over-F).
  • Three Power Metrics: Relative power (uncorrected), aperiodic-adjusted power (1/f-corrected), and the isolated aperiodic signal.
  • Individual Alpha Frequency (IAF): Estimated from posterior electrodes to define individualized frequency bands.
  • TBR Calculation: Calculated using both canonical bands (Theta: 4–8 Hz; Beta: 13–30 Hz) and IAF-relative bands (Theta: IAF-6 to IAF-4 Hz; Beta: IAF+2 to 30 Hz).
• Multiverse Design:
  • 576 distinct analytical specifications (universes) were generated per group contrast by varying:
    • Resting state condition (EO vs. EC).
    • Reference scheme (Average vs. Linked Mastoid).
    • Frequency band definition (Canonical vs. IAF-relative).
    • Aperiodic handling (Uncorrected, Adjusted, or Signal only).
    • Region of Interest (6 different scalp ROIs).
    • Inclusion criteria (Comorbidities, Medication status).
    • Regression models (varying interactions with Age, Gender, and IAF).
  • Statistical Analysis: Regression models tested main effects of diagnosis and interactions with covariates. Results were visualized via specification curves and possibility space plots. A bootstrap analysis was performed to rule out bias from unequal group sizes.

3. Key Contributions

• Systematic Quantification of RDF: This is one of the largest multiverse analyses in EEG research, testing 576 variations to map how analytical choices shape conclusions about ADHD biomarkers.
• Decomposition of TBR: The study explicitly separates oscillatory power from the aperiodic (1/f) background signal, addressing a critical confound in previous TBR literature.
• Dimensional vs. Categorical: The analysis was repeated using dimensional SWAN symptom scores, confirming that findings are consistent regardless of whether ADHD is treated as a discrete category or a continuous spectrum.
• Open Science: All code, data, and interactive Shiny apps for exploring the multiverse results are publicly available.

4. Key Results

• No Robust Main Effects: Across all 576 specifications in both datasets, there was no consistent main effect of ADHD diagnosis on TBR.
  • ADHD-Inattentive vs. HC: 0% of universes showed significant positive or negative TBR differences.
  • ADHD-Combined vs. HC: Only 1.91% of universes showed a significant positive difference; 0% showed a negative difference.
• Significance of Interactions: Significant effects emerged almost exclusively as interactions with IAF, Age, and Gender, rather than as direct group differences.
  • IAF Interaction: Significant group differences appeared primarily when using IAF-relative frequency bands combined with aperiodic-uncorrected power or the aperiodic signal itself.
  • Mechanism: The study suggests that apparent TBR elevations in ADHD are driven by the interaction between individual IAF and the slope of the aperiodic 1/f signal. Slower IAFs shift the "theta" band into lower frequencies where the 1/f slope is steeper, artificially inflating power estimates.
• Robustness: These interaction patterns replicated across both the HBN and validation samples and held true for both categorical diagnoses and dimensional symptom scores.
• Bootstrap Validation: Resampling to equal group sizes confirmed that the observed patterns were not artifacts of sample size imbalances.

5. Significance and Conclusion

• TBR is Not a Reliable Biomarker: The study provides strong evidence that TBR lacks the diagnostic reliability and discriminative validity required for clinical use as a standalone biomarker for ADHD. Previous positive findings are likely driven by specific, often unreported, methodological choices rather than genuine neurophysiological differences.
• Role of Aperiodic Activity: The findings highlight that the aperiodic 1/f slope and IAF are major confounds in spectral analysis. Failure to separate these from oscillatory activity leads to spurious TBR effects.
• Clinical Implications:
  • Clinicians and researchers should exercise extreme caution when interpreting TBR values.
  • Future biomarker development should prioritize individualized spectral features (like IAF) and explicitly model the aperiodic component to avoid artifacts.
  • The study underscores the necessity of multiverse approaches to evaluate candidate biomarkers in heterogeneous clinical populations, moving beyond single-pipeline analyses to ensure robustness.

In summary, the paper challenges the foundational assumption that TBR is a stable marker of ADHD, demonstrating that observed differences are largely methodological artifacts driven by the interaction of individual alpha frequency and aperiodic spectral slopes.