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

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

Contents

Variables

A
Sleep Efficiency 1854
A
Peak Heart Rate Zone 425

Categories

A
Sleep 111
A
Physical Activity 1719

Actions

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A
Your Data

Tags

High Confidence
Very Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 9.4% average decrease in Peak Heart Rate Zone following above average Sleep Efficiency.

Abstract

Peak Heart Rate Zone was generally 54% higher than average after an average of 88.7 percent of Sleep Efficiency over the previous 24 hours.

Aggregated data from 57 study participants suggests with a HIGH degree of confidence (p=0.26, 95% CI -2.835 to 2.821) that Sleep Efficiency has a very weakly negative predictive relationship (R=-0.0071) with Peak Heart Rate Zone Minutes.

The highest quartile of Peak Heart Rate Zone Minutes measurements were observed following an average 90.6 percent Sleep Efficiency.

The lowest quartile of Peak Heart Rate Zone Minutes measurements were observed following an average 90.6 percent of Sleep Efficiency.

After an onset delay of 0 seconds, Peak Heart Rate Zone Minutes is typically 32% lower than average over the 24 hours following around 90.6 percent of Sleep Efficiency Sleep Efficiency.

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

High Confidence: With 57 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 10,706 paired observations from 57 participants revealed a substantial improvement in Peak Heart Rate Zone Minutes following above-average Sleep Efficiency exposure.

+276.6%
Change from Baseline
Substantial effect on Peak Heart Rate Zone Minutes
0.00
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.007
Correlation (r)
p = 0.467
Significance
z = 1.17
Effect Magnitude
Ļ† = 0.29
Temporality

What This Means

When participants had above-average Sleep Efficiency:

  • Peak Heart Rate Zone Minutes increased by 276.6% on average
  • Temporal analysis suggests possible reverse causationā€”interpret with caution

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
ā‰„ 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

No clear dose-response relationship detected. The Sleep Efficiency values associated with high and low Peak Heart Rate Zone Minutes are too similar to provide meaningful dosing guidance. This may indicate a threshold effect (any amount works equally well), no effect, or insufficient data variance.

Population Correlation

Sleep Efficiency Distribution

Peak Heart Rate Zone Minutes Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Sleep Efficiency
Effect Variable Name Peak Heart Rate Zone
Sinn Predictive Coefficient 0.0035381218456455
Confidence Level HIGH
Confidence Interval 2.8278989857546
Forward Pearson Predictive Coefficient -0.0071
Critical T Value 1.6665438596491
Average Sleep Efficiency Over Previous 24 hours Before ABOVE Average Peak Heart Rate Zone 90.6 percent
Average Sleep Efficiency Over Previous 24 hours Before BELOW Average Peak Heart Rate Zone 90.6 percent
Duration of Action 24 hours
Effect Size very weakly negative
Number of Paired Measurements 10706
Optimal Pearson Product 0.041311892799869
P Value 0.26041056942241
Statistical Significance 0.4668
Strength of Relationship 2.8278989857546
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 57

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

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

Introduction

Background

Sleep Efficiency (Sleep) and Peak Heart Rate Zone Minutes (Physical Activity) 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 Sleep Efficiency affect Peak Heart Rate Zone Minutes?

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 Sleep Efficiency for maximizing Peak Heart Rate Zone Minutes?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Sleep Efficiency and Peak Heart Rate Zone Minutes. Additionally, we attempt to determine the Sleep Efficiency values most likely to produce optimal Peak Heart Rate Zone Minutes 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 276.6% improvement in Peak Heart Rate Zone Minutes following above-average Sleep Efficiency exposure. The Predictor Impact Score (PIS) of 0.00 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 Peak Heart Rate Zone Minutes is not statistically significant at a 95% confidence interval. This suggests that the Sleep Efficiency value may not have a significant influence on the Peak Heart Rate Zone Minutes value, or that more data is needed to detect an effect.

After treatment, a 9.4% decrease (22 seconds) from the mean baseline 112 seconds was observed. The relative standard deviation at baseline was 348.502%. The observed change was 1.1654 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: 0.953
Critical t-value: 1.667

Since t = 0.95 < 1.67, 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 Sleep Efficiency might influence Peak Heart Rate Zone Minutes.

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 (Ī”%), z-score
Consistency Cross-participant replication Number of users (N), number of pairs (n)
Temporality Predictor precedes outcome Temporality factor (Ļ†), onset delay (Ī“ > 0)
Biological Gradient Dose-response relationship Gradient coefficient (Ļ†gradient)
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 Ļ†-factors are saturation functions approaching 1 as evidence accumulates:

  • Ļ†users = 1 - e-N/10 (user saturation)
  • Ļ†pairs = 1 - e-n/nsig (pair saturation)
  • Ļ†change = 1 - e-Ī”spread/Ī”sig (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 Sleep Efficiency 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 Sleep Efficiency
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

Above-average Sleep Efficiency was associated with a 276.6% improvement in Peak Heart Rate Zone Minutesā€”a substantial effect. The Predictor Impact Score of 0.00 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.00 and a 276.6% effect size, this relationship currently lacks sufficient evidence. Continue monitoring as more data becomes available.

These findings contribute to our understanding of how Sleep Efficiency may influence Peak Heart Rate Zone Minutes 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 57 participants. Thus, the study design is equivalent to the aggregation of 57 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 Sleep Efficiency would produce an observable change in Peak Heart Rate Zone Minutes.
  • Duration of Action: It was assumed that Sleep Efficiency could produce an observable change in Peak Heart Rate Zone Minutes for as much as 24 hours after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Sleep Efficiency values and subsequent Peak Heart Rate Zone Minutes 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 (Ļ = 0) at Ī± = 0.05 when |t| exceeds the critical value, providing statistical evidence that the observed relationship is not due to chance.

Data Sources

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

Peak Heart Rate Zone Minutes 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 Sleep Efficiency Affect Peak Heart Rate Zone Minutes?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5211811-effect-5211911-population-study
BibTeX 
@misc{sinn_cause_5211811_effect_5211911_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Sleep Efficiency Affect Peak Heart Rate Zone Minutes?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5211811-effect-5211911-population-study},
  note = {Accessed: January 8, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Sleep Efficiency Affect Peak Heart Rate Zone Minutes?." The Journal of Citizen Science. Accessed January 8, 2026. https://studies.crowdsourcingcures.org/study/cause-5211811-effect-5211911-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Sleep Efficiency Affect Peak Heart Rate Zone Minutes?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5211811-effect-5211911-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. HernƔn, 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 Initiativeā€”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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