Higher Peak Heart Rate Zone Predicts Very Slightly Higher Sleep Duration for Population

Higher Peak Heart Rate Zone Predicts Very Slightly Higher Sleep Duration for Population

Contents

Variables

A
Peak Heart Rate Zone 425
A
Sleep Duration 3379

Categories

A
Physical Activity 1719
A
Sleep 111

Actions

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Your Data

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High Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 16.9% average increase in Sleep Duration following above average Peak Heart Rate Zone.

Abstract

Sleep Duration was generally 41% higher than average after a total of 118 seconds of Peak Heart Rate Zone Minutes over the previous 24 hours.

Aggregated data from 60 study participants suggests with a HIGH degree of confidence (p=0.139, 95% CI -1.021 to 1.108) that Peak Heart Rate Zone Minutes has a very weakly positive predictive relationship (R=0.0438) with Sleep Duration.

The highest quartile of Sleep Duration measurements were observed following an average 2 minutes Peak Heart Rate Zone Minutes per day.

The lowest quartile of Sleep Duration measurements were observed following an average 92 seconds of Peak Heart Rate Zone Minutes per day.

After an onset delay of 0 seconds, Sleep Duration is typically 0% lower than average over the 24 hours following around 92 seconds of Peak Heart Rate Zone Minutes Peak Heart Rate Zone Minutes.

Keywords: Peak Heart Rate Zone Minutes, Sleep Duration, N-of-1 trials, real-world evidence, causal inference, observational study

High Confidence: With 60 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 16,772 paired observations from 60 participants revealed a substantial improvement in Sleep Duration following above-average Peak Heart Rate Zone Minutes exposure.

+51.4%
Change from Baseline
Substantial effect on Sleep Duration
0.02
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
0.044
Correlation (r)
p = 0.354
Significance
z = 0.50
Effect Magnitude
φ = 0.93
Temporality

What This Means

When participants had above-average Peak Heart Rate Zone Minutes:

  • Sleep Duration increased by 51.4% on average
  • Temporal analysis supports Peak Heart Rate Zone Minutes as the predictor (not the outcome)

Interpreting the Predictor Impact Score

The Predictor Impact Score (PIS) integrates multiple Bradford Hill causal criteria into a single metric. Use this guide to interpret the score:

PIS Range Interpretation Recommended Action
≥ 0.5 Strong evidence High priority for RCT validation
0.3 - 0.5 Moderate evidence Consider for experimental investigation
0.1 - 0.3 Weak evidence Monitor for additional data
< 0.1 Insufficient evidence Low priority; may be noise

Note: PIS is a prioritization heuristic, not proof of causation. High scores indicate relationships worth investigating, not confirmed causal effects.

Optimal Daily Values (Precision Dosing)

Based on the observed relationship, we can estimate the predictor values associated with the best and worst outcomes. These values enable personalized dosing recommendations.

ℹ️ Moderate Confidence: Based on 60 participants. Values are reasonably reliable but may refine with additional data.

2.0 min
Value Predicting Higher Sleep Duration
Average Peak Heart Rate Zone Minutes when Sleep Duration exceeded its mean
1.0 min
Value Predicting Lower Sleep Duration
Average Peak Heart Rate Zone Minutes when Sleep Duration was below its mean

What This Suggests

Sleep Duration tended to be highest when Peak Heart Rate Zone Minutes was around 2.0 min.

Important: These values reflect correlations, not guaranteed causal effects. Individual responses may vary. Use as a starting point for personal experimentation, not as a definitive prescription. Consult healthcare providers before making treatment decisions.

Population Correlation

Peak Heart Rate Zone Minutes Distribution

Sleep Duration Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Peak Heart Rate Zone
Effect Variable Name Sleep Duration
Sinn Predictive Coefficient 0.021845715377869
Confidence Level HIGH
Confidence Interval 1.0645018943422
Forward Pearson Predictive Coefficient 0.0438
Critical T Value 1.6604166666667
Total Peak Heart Rate Zone Over Previous 24 hours Before ABOVE Average Sleep Duration 2 minutes
Total Peak Heart Rate Zone Over Previous 24 hours Before BELOW Average Sleep Duration 92 seconds
Duration of Action 24 hours
Effect Size very weakly positive
Number of Paired Measurements 16772
Optimal Pearson Product 0.022835186604772
P Value 0.13948663603229
Statistical Significance 0.3535
Strength of Relationship 1.0645018943422
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 60

Peak Heart Rate Zone Info

Property Value
Variable Name Peak Heart Rate Zone Minutes
Aggregation Method SUM
Analysis Performed At 2020-10-09
Duration of Action 24 hours
Filling Value 0
Kurtosis 121.79086276005
Maximum Allowed Value 7 days
Mean 67 seconds
Median 0 seconds
Minimum Allowed Value 0 seconds
Number of Aggregate Predictors 286
Number of Aggregate Outcomes 139
Number of Measurements 4724
Number of Measurements (including those generated by tagged, joined, or child variables) 1689
Public true
Onset Delay 0 seconds
Standard Deviation 3.7066913686037
Unit Minutes
User Variables 95
Variable Category Physical Activity
Variable ID 5211911
Variance 33.329542584477

Sleep Duration Info

Property Value
Variable Name Sleep Duration
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 7 days
Kurtosis 3.1431132810239
Maximum Allowed Value 16 hours
Mean 7 hours
Median 7 hours
Minimum Allowed Value 6 minutes
Number of Aggregate Predictors 3162
Number of Aggregate Outcomes 217
Number of Measurements 43055
Number of Measurements (including those generated by tagged, joined, or child variables) 16052
Public true
Onset Delay 0 seconds
Standard Deviation 1.2204190250991
Unit Hours
User Variables 404
UPC 067981966602
Variable Category Sleep
Variable ID 1867
Variance 2.1855287054824

Introduction

Background

Peak Heart Rate Zone Minutes (Physical Activity) and Sleep Duration (Sleep) are both important factors in understanding human health and well-being. This study investigates the relationship between these two variables using real-world observational data.

Traditional randomized controlled trials (RCTs), while the gold standard for causal inference, are often impractical, expensive, or unethical for studying many health relationships. Aggregated N-of-1 observational studies offer a complementary approach that leverages within-subject comparisons across large populations to identify meaningful patterns.

Research Question

Do Peak Heart Rate Zone Minutes affect Sleep Duration?

Additionally, we seek to determine:

  1. What is the direction and magnitude of any effect?
  2. How confident can we be in this relationship based on the available data?
  3. What are the optimal levels of Peak Heart Rate Zone Minutes for maximizing Sleep Duration?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Peak Heart Rate Zone Minutes and Sleep Duration. Additionally, we attempt to determine the Peak Heart Rate Zone Minutes values most likely to produce optimal Sleep Duration values.

Study Overview

This is a population-level observational study using aggregated N-of-1 methodology. By aggregating individual N-of-1 experiments, we can identify population-level patterns while accounting for the substantial individual variation that exists in most health relationships. Effect sizes are reported as percent change from baseline, enabling intuitive interpretation and comparison across different measures.

Full Methodology: Framework for Real-World Evidence-Based Pharmacovigilance: Aggregated N-of-1 Trials for Quantifying Treatment Effects

Discussion

Interpretation of Findings

Participants experienced a 51.4% improvement in Sleep Duration following above-average Peak Heart Rate Zone Minutes exposure. The Predictor Impact Score (PIS) of 0.02 indicates insufficient evidence for a causal relationship.

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Sleep Duration is statistically significant at a 95% confidence interval. The p-value of 0.3535 indicates there is less than a 35.35% probability that this result occurred by chance.

After treatment, a 16.9% increase (50 minutes) from the mean baseline 4 hours was observed. The relative standard deviation at baseline was 112.638%. The observed change was 0.504045 times the standard deviation.

A common rule of thumb considers a change greater than twice the baseline standard deviation on two separate pre-post experiments may be considered significant. This occurrence would have only a 5% likelihood of resulting from random fluctuation (a p-value < 0.05).

T-Test Details
Observed t-value: 2.584
Critical t-value: 1.660

Since t = 2.58 > 1.66, we reject the null hypothesis.

Biological Plausibility

A plausible bio-chemical mechanism between predictor and outcome is critical for interpreting observational findings. This is where human judgment excels beyond statistical analysis.

Community feedback on the biological plausibility of this relationship is still being collected. Consider the known mechanisms by which Peak Heart Rate Zone Minutes might influence Sleep Duration.

Bradford Hill Criteria Assessment

The Bradford Hill criteria provide a framework for assessing causality in observational studies. Our methodology operationalizes six of the nine criteria through the Predictor Impact Score (PIS):

Criterion How Addressed Metric
Strength Effect size magnitude Percent change from baseline (Δ%), z-score
Consistency Cross-participant replication Number of users (N), number of pairs (n)
Temporality Predictor precedes outcome Temporality factor (φ), onset delay (δ > 0)
Biological Gradient Dose-response relationship Gradient coefficient (φgradient)
Plausibility Biological mechanism assessment Community votes on mechanism plausibility
Specificity Category appropriateness Interest factor (finterest)

Predictor Impact Score (PIS)

The PIS integrates multiple Bradford Hill criteria into a composite metric quantifying how reliably a predictor affects an outcome. Higher scores indicate stronger evidence:

Population-Level PIS:

$$\text{PIS}_{\text{agg}} = |r_{\text{forward}}| \cdot w \cdot \phi_{\text{users}} \cdot \phi_{\text{pairs}} \cdot \phi_{\text{change}} \cdot \phi_{\text{gradient}}$$

Where φ-factors are saturation functions approaching 1 as evidence accumulates:

  • φusers = 1 - e-N/10 (user saturation)
  • φpairs = 1 - e-n/nsig (pair saturation)
  • φchange = 1 - e-Δspread/Δsig (effect spread saturation)
  • w = weighted average of plausibility votes

Temporality Assessment

We assess evidence for correct causal direction using the temporality factor:

$$\phi_{\text{temporal}} = \frac{|r_{\text{forward}}|}{|r_{\text{forward}}| + |r_{\text{reverse}}|}$$

Values approaching 1 indicate the predictor precedes the outcome (supporting causation); values near 0.5 suggest ambiguous directionality; values near 0 suggest reverse causation or confounding by indication.

Limitations

As with any observational study, correlation does not prove causation. Key limitations include:

  • Unmeasured confounders: Variables not tracked may influence results
  • Self-selection bias: Health trackers may differ from the general population
  • Measurement error: Self-reported data may contain recall bias
  • Confounding by indication: Sicker individuals may use more treatments

However, within-subject comparison and temporal precedence analysis partially mitigate these limitations. If the relationship is merely coincidental, as participants independently modify their Peak Heart Rate Zone Minutes values, the observed strength will decline over time. Spurious correlations naturally dissipate as more data is collected.

Future Directions

Future research should examine:

  • Subgroup analyses to identify individual differences in response
  • Potential confounders and mediators of the observed relationship
  • Optimal dosing and timing for Peak Heart Rate Zone Minutes
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

Above-average Peak Heart Rate Zone Minutes was associated with a 51.4% improvement in Sleep Duration—a substantial effect. The Predictor Impact Score of 0.02 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.02 and a 51.4% effect size, this relationship currently lacks sufficient evidence. Continue monitoring as more data becomes available.

These findings contribute to our understanding of how Peak Heart Rate Zone Minutes may influence Sleep Duration in real-world conditions. While preliminary, these results may inform future research directions.

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Methods

Study Design

This study is based on data donated by 60 participants. Thus, the study design is equivalent to the aggregation of 60 separate n=1 observational natural experiments.

This within-subject design is powerful because it controls for all stable individual characteristics (genetics, baseline health status, socioeconomic factors) that might otherwise confound the relationship between variables.

Data Analysis

Temporal Assumptions

The analysis incorporates temporal assumptions about the relationship between variables:

  • Onset Delay: It was assumed that 0 seconds would pass before a change in Peak Heart Rate Zone Minutes would produce an observable change in Sleep Duration.
  • Duration of Action: It was assumed that Peak Heart Rate Zone Minutes could produce an observable change in Sleep Duration for as much as 24 hours after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Peak Heart Rate Zone Minutes values and subsequent Sleep Duration values. Individual correlations were then aggregated using Fisher's z-transformation to produce a population-level estimate:

Individual Correlation:

$$r_i = \frac{\sum(x_{ij} - \bar{x}_i)(y_{ij} - \bar{y}_i)}{\sqrt{\sum(x_{ij} - \bar{x}_i)^2 \sum(y_{ij} - \bar{y}_i)^2}}$$

Fisher's Z-Transformation:

$$z_i = \frac{1}{2} \ln\left(\frac{1 + r_i}{1 - r_i}\right)$$

Aggregated Correlation:

$$\bar{r} = \tanh(\bar{z}) \quad \text{where} \quad \bar{z} = \frac{1}{N}\sum_{i=1}^{N} z_i$$

Effect Size Calculation

Effect sizes are reported as percent change from baseline. For each participant, we compare the outcome following above-average predictor values to the overall baseline outcome:

$$\Delta\%_{\text{baseline}} = \frac{\bar{O}_{\text{follow-up}} - \bar{O}_{\text{baseline}}}{\bar{O}_{\text{baseline}}} \times 100$$

Effect Magnitude (Z-Score)

To assess effect magnitude relative to natural variability, we calculate the z-score:

$$z = \frac{|\Delta\%_{\text{baseline}}|}{\text{RSD}_{\text{baseline}}}$$

where RSDbaseline is the relative standard deviation of outcome during baseline period

A z-score > 2 indicates statistical significance (p < 0.05), meaning the observed change exceeds typical baseline fluctuation and is unlikely due to random variation.

Statistical Significance

Correlation significance is assessed using a two-tailed t-test:

$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$

We reject the null hypothesis (ρ = 0) at α = 0.05 when |t| exceeds the critical value, providing statistical evidence that the observed relationship is not due to chance.

Data Sources

Peak Heart Rate Zone Minutes data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Sleep Duration data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Data Quality

Data quality measures were applied to ensure reliable results:

  • Minimum Data Requirement: Only participants with sufficient paired observations were included in the analysis.
  • Outlier Handling: Extreme values were winsorized to reduce the influence of measurement errors.
  • Missing Data: Days with missing values were handled using appropriate filling strategies based on the variable type.
  • Test User Exclusion: Test accounts and invalid users were excluded from all analyses.

Principal Investigator

Program & Methods

Mike P. Sinn
Sinn, M. P.

Designed and implemented data collection, aggregation, causal inference pipeline, and automated study generation framework. Developed the Predictor Impact Score methodology operationalizing Bradford Hill criteria for ranking causal relationships in observational data. When he tells people this at parties, they usually say they have to go check on their car.

Individual study outputs are automated, reproducible, and open to external audit. (Which I would seriously recommend.)

Contact

Cite This Study

APA Format
Sinn, M. P. (2026). Causal Analysis: Does Peak Heart Rate Zone Minutes Affect Sleep Duration?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5211911-effect-1867-population-study
BibTeX 
@misc{sinn_cause_5211911_effect_1867_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Peak Heart Rate Zone Minutes Affect Sleep Duration?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5211911-effect-1867-population-study},
  note = {Accessed: January 6, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Peak Heart Rate Zone Minutes Affect Sleep Duration?." The Journal of Citizen Science. Accessed January 6, 2026. https://studies.crowdsourcingcures.org/study/cause-5211911-effect-1867-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Peak Heart Rate Zone Minutes Affect Sleep Duration?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5211911-effect-1867-population-study [Accessed January 6, 2026].

Study Type: Aggregated N-of-1 Observational Mega-Study
Evidence Level: Level II (Real-World Evidence)
Methodology: Bradford Hill Criteria with Predictor Impact Score (PIS)

References

This framework was originally developed in 2013 based on the Bradford Hill criteria. Subsequent literature has independently validated similar approaches to causal inference from observational data:

  1. Hill, A.B. (1965). The environment and disease: association or causation? Proceedings of the Royal Society of Medicine, 58(5), 295-300. [Bradford Hill criteria]
  2. Lillie, E.O., et al. (2011). The n-of-1 clinical trial: the ultimate strategy for individualizing medicine? Personalized Medicine, 8(2), 161-173. [N-of-1 methodology]
  3. Pearl, J. (2009). Causality: Models, Reasoning, and Inference . Cambridge University Press. [Causal inference]
  4. Hernán, M.A., & Robins, J.M. (2020). Causal Inference: What If . Chapman & Hall/CRC. [Free textbook]
  5. FDA (2018). Framework for FDA's Real-World Evidence Program . U.S. Food and Drug Administration. [Regulatory context]
  6. Duan, N., et al. (2013). Single-patient (n-of-1) trials: a pragmatic clinical decision methodology . Journal of Clinical Epidemiology, 66(8), S21-S28.
  7. Platt, R., et al. (2018). The FDA Sentinel Initiative—an evolving national resource . New England Journal of Medicine, 379(22), 2091-2093.

This information is for research and educational purposes only, not medical advice. Consult a healthcare provider before making health decisions. Terms of Service

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