Higher Deep Sleep Predicts Slightly Higher Resilience for Population

Higher Deep Sleep Predicts Slightly Higher Resilience for Population

Contents

Variables

A
Deep Sleep 177
A
Resilience 1180

Categories

A
Sleep 111
A
Emotions 2028

Tags

Low Confidence
Very Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 3.4% average increase in Resilience following above average Deep Sleep.

Abstract

Resilience was generally 1% higher than average after an average of 0.491 out of 1 of Deep Sleep over the previous 7 days.

Aggregated data from 2 study participants suggests with a LOW degree of confidence (p=0.328, 95% CI -0.016 to 0.285) that Deep Sleep has a weakly positive predictive relationship (R=0.135) with Resilience.

The highest quartile of Resilience measurements were observed following an average 0.539 out of 1 Deep Sleep.

The lowest quartile of Resilience measurements were observed following an average 0.494 out of 1 of Deep Sleep.

After an onset delay of 0 seconds, Resilience is typically 1% lower than average over the 7 days following around 0.494 out of 1 of Deep Sleep Deep Sleep.

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

Preliminary: Based on 2 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 91 paired observations from 2 participants revealed a minimal improvement in Resilience following above-average Deep Sleep exposure.

+1.6%
Change from Baseline
Minimal effect on Resilience
0.02
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Low
Confidence
0.135
Correlation (r)
p = 0.431
Significance
z = 0.19
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Deep Sleep:

  • Resilience increased by 1.6% on average
  • Temporal analysis supports Deep Sleep 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. With only 2 participants, these scores are preliminary and will become more reliable as additional data is collected.

Optimal Daily Values

No clear dose-response relationship detected. The Deep Sleep values associated with high and low Resilience 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. With more participants, a clearer pattern may emerge.

Population Correlation

Deep Sleep Distribution

Resilience Distribution

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Deep Sleep
Effect Variable Name Resilience
Sinn Predictive Coefficient 0.024416967612257
Confidence Level LOW
Confidence Interval 0.15044366215987
Forward Pearson Predictive Coefficient 0.1347
Critical T Value 1.7465
Average Deep Sleep Over Previous 7 days Before ABOVE Average Resilience 0.539 out of 1
Average Deep Sleep Over Previous 7 days Before BELOW Average Resilience 0.494 out of 1
Duration of Action 7 days
Effect Size weakly positive
Number of Paired Measurements 91
Optimal Pearson Product 0.032659344671146
P Value 0.32828375184007
Statistical Significance 0.4314
Strength of Relationship 0.15044366215987
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 2

Deep Sleep Info

Property Value
Variable Name Deep Sleep (/1)
Aggregation Method MEAN
Analysis Performed At 2020-10-09
Duration of Action 7 days
Kurtosis 4.480920546951
Maximum Allowed Value 1 out of 1
Mean 0.495378 out of 1
Median 0.48399 out of 1
Minimum Allowed Value 0 out of 1
Number of Aggregate Predictors 154
Number of Aggregate Outcomes 23
Number of Measurements 569
Number of Measurements (including those generated by tagged, joined, or child variables) 569
Public true
Onset Delay 0 seconds
Standard Deviation 0.1258535268134
Unit 0 to 1 Rating
User Variables 5
UPC 884904543333
Variable Category Sleep
Variable ID 5930076
Variance 0.016153310191236

Resilience Info

Property Value
Variable Name Resilience
Aggregation Method MEAN
Analysis Performed At 2020-10-11
Duration of Action 24 hours
Kurtosis 1.9334519243983
Maximum Allowed Value 5 out of 5
Mean 2.5113766833812 out of 5
Median 2.4890897325572 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 1070
Number of Aggregate Outcomes 110
Number of Measurements 25345
Number of Measurements (including those generated by tagged, joined, or child variables) 24386
Public true
Onset Delay 0 seconds
Standard Deviation 0.4900057068033
Unit 1 to 5 Rating
User Variables 1335
UPC 0
Variable Category Emotions
Variable ID 1436
Variance 0.52229282248446

Introduction

Background

Deep Sleep (Sleep) and Resilience (Emotions) 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 Deep Sleep affect Resilience?

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 Deep Sleep for maximizing Resilience?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Deep Sleep and Resilience. Additionally, we attempt to determine the Deep Sleep (/1) values most likely to produce optimal Resilience 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 1.6% improvement in Resilience following above-average Deep Sleep 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 Resilience is not statistically significant at a 95% confidence interval. This suggests that the Deep Sleep value may not have a significant influence on the Resilience value, or that more data is needed to detect an effect.

After treatment, a 3.4% increase (0.0438 out of 5) from the mean baseline 2.84 out of 5 was observed. The relative standard deviation at baseline was 8.65%. The observed change was 0.185058 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: 0.615
Critical t-value: 1.747

Since t = 0.61 < 1.75, 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 Deep Sleep might influence Resilience.

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

Conclusion

📊 Preliminary Findings: With 2 participants, these results are based on limited data. Effect sizes and confidence will improve as more participants contribute data. Consider these findings directional rather than definitive.

Above-average Deep Sleep was associated with a 1.6% improvement in Resilience—a minimal 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 1.6% effect size, this relationship currently lacks sufficient evidence. Continue monitoring as more data becomes available. Note: These conclusions may strengthen or change direction as more data is collected.

These findings contribute to our understanding of how Deep Sleep may influence Resilience in real-world conditions. While preliminary, these results may inform future research directions. As more participants contribute data, the reliability and precision of these findings will improve substantially.

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Methods

Study Design

This study is based on data donated by 2 participants. Thus, the study design is equivalent to the aggregation of 2 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 Deep Sleep would produce an observable change in Resilience.
  • Duration of Action: It was assumed that Deep Sleep could produce an observable change in Resilience for as much as 7 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Deep Sleep values and subsequent Resilience 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

Deep Sleep data was primarily collected using Sleep as Android. Smart alarm clock with sleep cycle tracking. Wakes you gently in optimal moment for pleasant mornings.

Resilience data was primarily collected using QuantiModo. QuantiModo allows you to easily track mood, symptoms, or any outcome you want to optimize in a fraction of a second. You can also import your data from over 30 other apps and devices. QuantiModo then analyzes your data to identify which hidden factors are most likely to be influencing your mood or symptoms.

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 Deep Sleep (/1) Affect Resilience?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1436-population-study
BibTeX 
@misc{sinn_cause_5930076_effect_1436_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Deep Sleep (/1) Affect Resilience?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1436-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Deep Sleep (/1) Affect Resilience?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1436-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Deep Sleep (/1) Affect Resilience?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5930076-effect-1436-population-study [Accessed January 10, 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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