Higher Peak Heart Rate Zone Calories Out Predicts Very Slightly Lower Sleep Efficiency for Population

Higher Peak Heart Rate Zone Calories Out Predicts Very Slightly Lower Sleep Efficiency for Population

Contents

Variables

A
Peak Heart Rate Zone Calories Out 438
A
Sleep Efficiency 1854

Categories

A
Physical Activity 1719
A
Sleep 111

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High Confidence
Very Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 0.3% average decrease in Sleep Efficiency following above average Peak Heart Rate Zone Calories Out.

Abstract

Sleep Efficiency was generally 2% higher than average after a total of 170 calories of Peak Heart Rate Zone Calories Out over the previous 24 hours.

Aggregated data from 58 study participants suggests with a HIGH degree of confidence (p=0.25, 95% CI -5.77 to 5.749) that Peak Heart Rate Zone Calories Out has a very weakly negative predictive relationship (R=-0.0106) with Sleep Efficiency.

The highest quartile of Sleep Efficiency measurements were observed following an average 122 calories Peak Heart Rate Zone Calories Out per day.

The lowest quartile of Sleep Efficiency measurements were observed following an average 103 calories of Peak Heart Rate Zone Calories Out per day.

After an onset delay of 0 seconds, Sleep Efficiency is typically 2% lower than average over the 24 hours following around 103 calories of Peak Heart Rate Zone Calories Out Peak Heart Rate Zone Calories Out.

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

High Confidence: With 58 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 2,122 paired observations from 58 participants revealed a minimal improvement in Sleep Efficiency following above-average Peak Heart Rate Zone Calories Out exposure.

+0.1%
Change from Baseline
Minimal effect on Sleep Efficiency
0.01
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.011
Correlation (r)
p = 0.237
Significance
z = 0.62
Effect Magnitude
φ = 0.52
Temporality

What This Means

When participants had above-average Peak Heart Rate Zone Calories Out:

  • Sleep Efficiency increased by 0.1% on average

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 58 participants. Values are reasonably reliable but may refine with additional data.

169.5 cal
Value Predicting Higher Sleep Efficiency
Average Peak Heart Rate Zone Calories Out when Sleep Efficiency exceeded its mean
94.8 cal
Value Predicting Lower Sleep Efficiency
Average Peak Heart Rate Zone Calories Out when Sleep Efficiency was below its mean

What This Suggests

Sleep Efficiency tended to be lowest (best) when Peak Heart Rate Zone Calories Out was around 94.8 cal.

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 Calories Out Distribution

Sleep Efficiency Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Peak Heart Rate Zone Calories Out
Effect Variable Name Sleep Efficiency
Sinn Predictive Coefficient 0.0052839538046038
Confidence Level HIGH
Confidence Interval 5.7593917616428
Forward Pearson Predictive Coefficient -0.0106
Critical T Value 1.7904827586207
Total Peak Heart Rate Zone Calories Out Over Previous 24 hours Before ABOVE Average Sleep Efficiency 122 calories
Total Peak Heart Rate Zone Calories Out Over Previous 24 hours Before BELOW Average Sleep Efficiency 103 calories
Duration of Action 24 hours
Effect Size very weakly negative
Number of Paired Measurements 2122
Optimal Pearson Product 0.04015994262051
P Value 0.25049228270918
Statistical Significance 0.2371
Strength of Relationship 5.7593917616428
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 58

Peak Heart Rate Zone Calories Out Info

Property Value
Variable Name Peak Heart Rate Zone Calories Out
Aggregation Method SUM
Analysis Performed At 2020-10-11
Duration of Action 24 hours
Kurtosis 10.561204622351
Mean 83.758777567959 calories
Median 43.846630752688 calories
Number of Aggregate Predictors 330
Number of Aggregate Outcomes 108
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 115.47144568586
Unit Calories
User Variables 95
UPC 816137024037
Variable Category Physical Activity
Variable ID 5211901
Variance 42674.182004322

Sleep Efficiency Info

Property Value
Variable Name Sleep Efficiency
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 24 hours
Kurtosis 7.3216313398995
Mean 86.964972477359 percent
Median 87.801418439716 percent
Minimum Allowed Value 1 percent
Number of Aggregate Predictors 1698
Number of Aggregate Outcomes 156
Number of Measurements 22620
Number of Measurements (including those generated by tagged, joined, or child variables) 1914
Public true
Onset Delay 0 seconds
Standard Deviation 5.9209578901457
Unit Percent
User Variables 147
UPC 878881000699
Variable Category Sleep
Variable ID 5211811
Variance 75.785458915098

Introduction

Background

Peak Heart Rate Zone Calories Out (Physical Activity) and Sleep Efficiency (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

Does Peak Heart Rate Zone Calories Out affect Sleep Efficiency?

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 Calories Out for maximizing Sleep Efficiency?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Peak Heart Rate Zone Calories Out and Sleep Efficiency. Additionally, we attempt to determine the Peak Heart Rate Zone Calories Out values most likely to produce optimal Sleep Efficiency 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 0.1% improvement in Sleep Efficiency following above-average Peak Heart Rate Zone Calories Out exposure. The Predictor Impact Score (PIS) of 0.01 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 Efficiency is not statistically significant at a 95% confidence interval. This suggests that the Peak Heart Rate Zone Calories Out value may not have a significant influence on the Sleep Efficiency value, or that more data is needed to detect an effect.

After treatment, a 0.3% decrease (0.089 percent) from the mean baseline 88.2 percent was observed. The relative standard deviation at baseline was 6.00345%. The observed change was 0.61561 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: 1.167
Critical t-value: 1.790

Since t = 1.17 < 1.79, we cannot 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 Calories Out might influence Sleep Efficiency.

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 Calories Out 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 Calories Out
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

Above-average Peak Heart Rate Zone Calories Out was associated with a 0.1% improvement in Sleep Efficiency—a minimal effect. The Predictor Impact Score of 0.01 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.01 and a 0.1% 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 Calories Out may influence Sleep Efficiency 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 58 participants. Thus, the study design is equivalent to the aggregation of 58 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 Calories Out would produce an observable change in Sleep Efficiency.
  • Duration of Action: It was assumed that Peak Heart Rate Zone Calories Out could produce an observable change in Sleep Efficiency 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 Calories Out values and subsequent Sleep Efficiency 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 Calories Out data was primarily collected using Fitbit. Fitbit makes activity tracking easy and automatic.

Sleep Efficiency 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 Calories Out Affect Sleep Efficiency?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5211901-effect-5211811-population-study
BibTeX 
@misc{sinn_cause_5211901_effect_5211811_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Peak Heart Rate Zone Calories Out Affect Sleep Efficiency?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5211901-effect-5211811-population-study},
  note = {Accessed: January 8, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Peak Heart Rate Zone Calories Out Affect Sleep Efficiency?." The Journal of Citizen Science. Accessed January 8, 2026. https://studies.crowdsourcingcures.org/study/cause-5211901-effect-5211811-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Peak Heart Rate Zone Calories Out Affect Sleep Efficiency?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5211901-effect-5211811-population-study [Accessed January 8, 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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