Higher Protein Intake Predicts Very Slightly Higher Sleep Duration for Population

Higher Protein Intake Predicts Very Slightly Higher Sleep Duration for Population

Contents

Variables

A
Protein 355
A
Sleep Duration 3379

Categories

A
Nutrients 313
A
Sleep 111

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High Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 15.3% average increase in Sleep Duration following above average Protein Intake.

Abstract

Sleep Duration was generally 28% higher than average after a total of 194 grams of Protein over the previous 7 days.

Aggregated data from 47 study participants suggests with a HIGH degree of confidence (p=0.134, 95% CI -0.631 to 0.791) that Protein has a very weakly positive predictive relationship (R=0.0798) with Sleep Duration.

The highest quartile of Sleep Duration measurements were observed following an average 189 grams Protein per day.

The lowest quartile of Sleep Duration measurements were observed following an average 168 grams of Protein per day.

After an onset delay of 0 seconds, Sleep Duration is typically 17% lower than average over the 7 days following around 168 grams of Protein Protein.

Keywords: Protein, Sleep Duration, N-of-1 trials, real-world evidence, causal inference, observational study

High Confidence: With 47 participants, these findings have strong statistical power.

Results

Primary Findings

Analysis of 18,058 paired observations from 47 participants revealed a substantial improvement in Sleep Duration following above-average Protein exposure.

+50.4%
Change from Baseline
Substantial effect on Sleep Duration
0.53
Predictor Impact Score
Strong evidence for causal relationship

Supporting Statistics

High
Confidence
0.080
Correlation (r)
p = 0.705
Significance
z = 0.66
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Protein:

  • Sleep Duration increased by 50.4% on average
  • The Predictor Impact Score of 0.53 suggests this relationship warrants high priority for experimental validation
  • Temporal analysis supports Protein 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 47 participants. Values are reasonably reliable but may refine with additional data.

193.9 g
Value Predicting Higher Sleep Duration
Average Protein when Sleep Duration exceeded its mean
144.5 g
Value Predicting Lower Sleep Duration
Average Protein when Sleep Duration was below its mean

What This Suggests

Sleep Duration tended to be highest when Protein was around 193.9 g.

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

Protein Distribution

Sleep Duration Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Protein Intake
Effect Variable Name Sleep Duration
Sinn Predictive Coefficient 0.53498946102089
Confidence Level HIGH
Confidence Interval 0.71126119016809
Forward Pearson Predictive Coefficient 0.0798
Critical T Value 1.6552765957447
Total Protein Intake Over Previous 7 days Before ABOVE Average Sleep Duration 189 grams
Total Protein Intake Over Previous 7 days Before BELOW Average Sleep Duration 168 grams
Duration of Action 7 days
Effect Size very weakly positive
Number of Paired Measurements 18058
Optimal Pearson Product 0.124729286718
P Value 0.13433399316508
Statistical Significance 0.7047
Strength of Relationship 0.71126119016809
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 47

Protein Info

Property Value
Variable Name Protein
Aggregation Method SUM
Analysis Performed At 2022-11-18
Duration of Action 7 days
Filling Value 0
Kurtosis 23.194566921803
Maximum Allowed Value 7257 grams
Mean 13.129092081988 grams
Median 7.2463511695906 grams
Minimum Allowed Value 0 grams
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 355
Number of Measurements 5973
Number of Measurements (including those generated by tagged, joined, or child variables) 6790
Public true
Onset Delay 0 seconds
Standard Deviation 19.455904910566
Unit Grams
User Variables 224
UPC 885260235887
Variable Category Nutrients
Variable ID 1420
Variance 862.80013936942

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

Protein (Nutrients) 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

Does Protein 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 Protein for maximizing Sleep Duration?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Protein and Sleep Duration. Additionally, we attempt to determine the Protein 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 50.4% improvement in Sleep Duration following above-average Protein exposure. The Predictor Impact Score (PIS) of 0.53 indicates strong 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 0.7047 indicates there is less than a 70.47% probability that this result occurred by chance.

After treatment, a 15.3% increase (26 minutes) from the mean baseline 4 hours was observed. The relative standard deviation at baseline was 153.111%. The observed change was 0.661664 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: 2.871
Critical t-value: 1.655

Since t = 2.87 > 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.

Based on community responses so far, 1 person feels that there is a plausible mechanism of action and 0 feel that any relationship observed between Protein and Sleep Duration is coincidental.

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

Conclusion

Above-average Protein was associated with a 50.4% improvement in Sleep Duration—a substantial effect. The Predictor Impact Score of 0.53 indicates this relationship is high priority for experimental validation.

Bottom Line: Based on a PIS of 0.53 and a 50.4% effect size, this relationship shows strong evidence and should be prioritized for experimental validation through randomized controlled trials.

These findings contribute to our understanding of how Protein may influence Sleep Duration in real-world conditions. The combination of effect size, sample size, and temporal evidence supports this as a meaningful relationship worth investigating further.

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Methods

Study Design

This study is based on data donated by 47 participants. Thus, the study design is equivalent to the aggregation of 47 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 Protein would produce an observable change in Sleep Duration.
  • Duration of Action: It was assumed that Protein could produce an observable change in Sleep Duration for as much as 7 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Protein 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

Protein data was primarily collected using MyFitnessPal. Lose weight with MyFitnessPal, the fastest and easiest-to-use calorie counter for iPhone and iPad. With the largest food database of any iOS calorie counter (over 3,000,000 foods), and amazingly fast food and exercise entry.

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 Protein Affect Sleep Duration?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-1420-effect-1867-population-study
BibTeX 
@misc{sinn_cause_1420_effect_1867_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Protein Affect Sleep Duration?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-1420-effect-1867-population-study},
  note = {Accessed: January 6, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Protein Affect Sleep Duration?." The Journal of Citizen Science. Accessed January 6, 2026. https://studies.crowdsourcingcures.org/study/cause-1420-effect-1867-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Protein Affect Sleep Duration?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-1420-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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