Higher Outdoor Temperature Predicts Slightly Lower Leg Pain for Population

Higher Outdoor Temperature Predicts Slightly Lower Leg Pain for Population

Contents

Variables

A
Outdoor Temperature 454
A
Leg Pain 297

Categories

A
Environment 564
A
Symptoms 13336

Tags

Low Confidence
Very Weak Effect Size
Negative Relationship
Population Study
cause image gauge image effect image
Participants reported a 0.8% average increase in Leg Pain following above average Outdoor Temperature.

Abstract

Leg Pain was generally 15.725% lower than average after 13 degrees celsius of Outdoor Temperature per 7 days.

Aggregated data from 4 study participants suggests with a LOW degree of confidence (p=0.261, 95% CI -0.833 to 0.499) that Outdoor Temperature has a weakly negative predictive relationship (R=-0.167) with Leg Pain.

The highest quartile of Leg Pain measurements were observed following an average 9.09 degrees celsius Outdoor Temperature.

The lowest quartile of Leg Pain measurements were observed following an average 10.2 degrees celsius of Outdoor Temperature.

After an onset delay of 0 seconds, Leg Pain is typically 0% lower than average over the 7 days following around 10.2 degrees celsius of Outdoor Temperature Outdoor Temperature.

Keywords: Outdoor Temperature, Leg Pain, N-of-1 trials, real-world evidence, causal inference, observational study

Preliminary: Based on 4 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 48 paired observations from 4 participants revealed a moderate reduction in Leg Pain following above-average Outdoor Temperature exposure.

-15.7%
Change from Baseline
Moderate effect on Leg Pain
0.06
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

High
Confidence
-0.167
Correlation (r)
p = 0.008
Significance
z = 1.12
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Outdoor Temperature:

  • Leg Pain decreased by 15.7% on average
  • Temporal analysis supports Outdoor Temperature as the predictor (not the outcome)
  • This relationship is statistically significant (p = 0.008)

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 4 participants, these scores are preliminary and will become more reliable as additional data is collected.

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.

⚠️ Preliminary Data: With 4 participants and 48 observations, these optimal values are preliminary estimates. As more data is collected, precision will improve significantly.

10.0 C
Value Predicting Higher Leg Pain
Average Outdoor Temperature when Leg Pain exceeded its mean
13.0 C
Value Predicting Lower Leg Pain
Average Outdoor Temperature when Leg Pain was below its mean

What This Suggests

Leg Pain tended to be lowest (best) when Outdoor Temperature was around 13.0 C.

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

Outdoor Temperature Distribution

Leg Pain Distribution

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Outdoor Temperature
Effect Variable Name Leg Pain
Sinn Predictive Coefficient 0.055155456557624
Confidence Level LOW
Confidence Interval 0.66607416973874
Forward Pearson Predictive Coefficient -0.1673
Critical T Value 1.82425
Average Outdoor Temperature Over Previous 7 days Before ABOVE Average Leg Pain 9.09 degrees celsius
Average Outdoor Temperature Over Previous 7 days Before BELOW Average Leg Pain 10.2 degrees celsius
Duration of Action 7 days
Effect Size weakly negative
Number of Paired Measurements 48
Optimal Pearson Product 0.087125653353886
P Value 0.26093817929055
Statistical Significance 0.0079
Strength of Relationship 0.66607416973874
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 4

Outdoor Temperature Info

Property Value
Variable Name Outdoor Temperature
Aggregation Method MEAN
Analysis Performed At 2020-09-15
Duration of Action 7 days
Kurtosis 2.5869393546724
Maximum Allowed Value 101 degrees celsius
Mean 16.934805022738 degrees celsius
Median 16.806543406516 degrees celsius
Minimum Allowed Value -66 degrees celsius
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 454
Number of Measurements 312494
Number of Measurements (including those generated by tagged, joined, or child variables) 60483
Public true
Onset Delay 0 seconds
Standard Deviation 5.8976135603379
Unit Degrees Celsius
User Variables 927
UPC 0
Variable Category Environment
Variable ID 5954773
Variance 55.947734908476

Leg Pain Info

Property Value
Variable Name Leg Pain
Aggregation Method MEAN
Analysis Performed At 2020-12-19
Duration of Action 24 hours
Kurtosis 1.5715804739764
Maximum Allowed Value 5 out of 5
Mean 3.0246129032258 out of 5
Median 2.9573483870968 out of 5
Minimum Allowed Value 1 out of 5
Number of Aggregate Predictors 253
Number of Aggregate Outcomes 44
Number of Measurements 217
Number of Measurements (including those generated by tagged, joined, or child variables) 213
Public true
Onset Delay 0 seconds
Standard Deviation 0.62191487927359
Unit 1 to 5 Rating
User Variables 47
UPC 766239680184
Variable Category Symptoms
Variable ID 89409
Variance 0.68336728220125

Introduction

Background

Outdoor Temperature (Environment) and Leg Pain (Symptoms) 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 Outdoor Temperature affect Leg Pain?

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 Outdoor Temperature for maximizing Leg Pain?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Outdoor Temperature and Leg Pain. Additionally, we attempt to determine the Outdoor Temperature values most likely to produce optimal Leg Pain 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 15.7% reduction in Leg Pain following above-average Outdoor Temperature exposure. The Predictor Impact Score (PIS) of 0.06 indicates insufficient evidence for a causal relationship. This finding is statistically significant (p = 0.008).

Statistical Significance

Using a two-tailed t-test with alpha = 0.05, it was determined that the change in Leg Pain is not statistically significant at a 95% confidence interval. This suggests that the Outdoor Temperature value may not have a significant influence on the Leg Pain value, or that more data is needed to detect an effect.

After treatment, a 0.8% increase (-0.387 out of 5) from the mean baseline 3 out of 5 was observed. The relative standard deviation at baseline was 27.625%. The observed change was 1.1211 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: 0.914
Critical t-value: 1.824

Since t = 0.91 < 1.82, 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 Outdoor Temperature might influence Leg Pain.

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

Conclusion

📊 Preliminary Findings: With 4 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 Outdoor Temperature was associated with a 15.7% reduction in Leg Pain—a moderate effect. The Predictor Impact Score of 0.06 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.06 and a 15.7% 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 Outdoor Temperature may influence Leg Pain in real-world conditions. The within-subject design and temporal analysis provide confidence in these relationships, though observational limitations remain.

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Methods

Study Design

This study is based on data donated by 4 participants. Thus, the study design is equivalent to the aggregation of 4 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 Outdoor Temperature would produce an observable change in Leg Pain.
  • Duration of Action: It was assumed that Outdoor Temperature could produce an observable change in Leg Pain for as much as 7 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Outdoor Temperature values and subsequent Leg Pain 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

Outdoor Temperature data was primarily collected using Weather. Automatically import temperature, humidity, and ultraviolet light exposure.

Leg Pain 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 Outdoor Temperature Affect Leg Pain?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-5954773-effect-89409-population-study
BibTeX 
@misc{sinn_cause_5954773_effect_89409_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Outdoor Temperature Affect Leg Pain?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-5954773-effect-89409-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Outdoor Temperature Affect Leg Pain?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-5954773-effect-89409-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Outdoor Temperature Affect Leg Pain?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-5954773-effect-89409-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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