Higher Three Lac Probiotic Predicts Moderately Higher Resilience for Population

Higher Three Lac Probiotic Predicts Moderately Higher Resilience for Population

Contents

Variables

A
Three Lac Probiotic 48
A
Resilience 1180

Categories

A
Treatments 9356
A
Emotions 2028

Tags

Medium Confidence
Weak Effect Size
Positive Relationship
Population Study
cause image gauge image effect image
Participants reported a 18.8% average increase in Resilience following above average Three Lac Probiotic.

Abstract

Resilience was generally 17% higher than average after a total of 9 tablets of Three Lac Probiotic over the previous 21 days.

Aggregated data from 1 study participants suggests with a MEDIUM degree of confidence (p=0.0122, 95% CI 0.025 to 0.749) that Three Lac Probiotic has a moderately positive predictive relationship (R=0.387) with Resilience.

The highest quartile of Resilience measurements were observed following an average 4.02 tablets Three Lac Probiotic per day.

The lowest quartile of Resilience measurements were observed following an average 0.921 tablets of Three Lac Probiotic per day.

After an onset delay of 30 minutes, Resilience is typically 4% lower than average over the 21 days following around 0.921 tablets of Three Lac Probiotic Three Lac Probiotic.

Keywords: Three Lac Probiotic, Resilience, N-of-1 trials, real-world evidence, causal inference, observational study

Preliminary: Based on 1 participants. Results may change as more data is collected.

Results

Primary Findings

Analysis of 82 paired observations from 1 participants revealed a moderate improvement in Resilience following above-average Three Lac Probiotic exposure.

+21.6%
Change from Baseline
Moderate effect on Resilience
0.04
Predictor Impact Score
Insufficient evidence for causal relationship

Supporting Statistics

Low
Confidence
0.387
Correlation (r)
p = 0.358
Significance
z = 1.29
Effect Magnitude
φ = 1.00
Temporality

What This Means

When participants had above-average Three Lac Probiotic:

  • Resilience increased by 21.6% on average
  • Temporal analysis supports Three Lac Probiotic 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 1 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 1 participants and 82 observations, these optimal values are preliminary estimates. As more data is collected, precision will improve significantly.

9.0 tablets
Value Predicting Higher Resilience
Average Three Lac Probiotic when Resilience exceeded its mean
0.0 tablets
Value Predicting Lower Resilience
Average Three Lac Probiotic when Resilience was below its mean

What This Suggests

Resilience tended to be highest when Three Lac Probiotic was around 9.0 tablets.

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

Three Lac Probiotic Distribution

Resilience Distribution

Relationship Analysis

Statistical Summary

Relationship Statistics

Property Value
Cause Variable Name Three Lac Probiotic
Effect Variable Name Resilience
Sinn Predictive Coefficient 0.036827918698248
Confidence Level MEDIUM
Confidence Interval 0.36182752030412
Forward Pearson Predictive Coefficient 0.387
Critical T Value 1.66
Total Three Lac Probiotic Over Previous 21 days Before ABOVE Average Resilience 4.02 tablets
Total Three Lac Probiotic Over Previous 21 days Before BELOW Average Resilience 0.921 tablets
Duration of Action 21 days
Effect Size moderately positive
Number of Paired Measurements 82
Optimal Pearson Product 0.22210140086839
P Value 0.012188329774455
Statistical Significance 0.3581
Strength of Relationship 0.36182752030412
Study Type population
Analysis Performed At 2026-01-04
Number of Participants 1

Three Lac Probiotic Info

Property Value
Variable Name Three Lac Probiotic
Aggregation Method SUM
Analysis Performed At 2021-01-25
Duration of Action 21 days
Filling Value 0
Kurtosis 3.5431232195718
Maximum Allowed Value 20 tablets
Mean 0.31156 tablets
Median 0 tablets
Minimum Allowed Value 0 tablets
Number of Aggregate Predictors 0
Number of Aggregate Outcomes 48
Number of Measurements 112
Number of Measurements (including those generated by tagged, joined, or child variables) 112
Public true
Onset Delay 30 minutes
Standard Deviation 0.5059415519275
Unit Tablets
User Variables 2
UPC 816663007504
Variable Category Treatments
Variable ID 1563
Variance 0.2559768539668

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

Three Lac Probiotic (Treatments) 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 Three Lac Probiotic 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 Three Lac Probiotic for maximizing Resilience?

Study Objective

The objective of this study is to determine the nature of the relationship (if any) between Three Lac Probiotic and Resilience. Additionally, we attempt to determine the Three Lac Probiotic 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 21.6% improvement in Resilience following above-average Three Lac Probiotic exposure. The Predictor Impact Score (PIS) of 0.04 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 statistically significant at a 95% confidence interval. The p-value of 0.3581 indicates there is less than a 35.81% probability that this result occurred by chance.

After treatment, a 18.8% increase (0.576 out of 5) from the mean baseline 2.66 out of 5 was observed. The relative standard deviation at baseline was 16.8%. The observed change was 1.28806 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: 2.641
Critical t-value: 1.660

Since t = 2.64 > 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.

Community feedback on the biological plausibility of this relationship is still being collected. Consider the known mechanisms by which Three Lac Probiotic 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 Three Lac Probiotic 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 Three Lac Probiotic
  • Confirmation through prospective or randomized designs
  • Biological mechanisms underlying the observed effects

Conclusion

📊 Preliminary Findings: With 1 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 Three Lac Probiotic was associated with a 21.6% improvement in Resilience—a moderate effect. The Predictor Impact Score of 0.04 indicates this relationship is requiring additional data before conclusions.

Bottom Line: Based on a PIS of 0.04 and a 21.6% 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 Three Lac Probiotic 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 1 participants. Thus, the study design is equivalent to the aggregation of 1 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 30 minutes would pass before a change in Three Lac Probiotic would produce an observable change in Resilience.
  • Duration of Action: It was assumed that Three Lac Probiotic could produce an observable change in Resilience for as much as 21 days after the stimulus event.

Statistical Methods

For each participant, we calculated the Pearson correlation coefficient between Three Lac Probiotic 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

Three Lac Probiotic 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.

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 Three Lac Probiotic Affect Resilience?. The Journal of Citizen Science. https://studies.crowdsourcingcures.org/study/cause-1563-effect-1436-population-study
BibTeX 
@misc{sinn_cause_1563_effect_1436_population_study_2026,
  author = {Sinn, Mike P.},
  title = {Causal Analysis: Does Three Lac Probiotic Affect Resilience?},
  year = {2026},
  publisher = {The Journal of Citizen Science},
  url = {https://studies.crowdsourcingcures.org/study/cause-1563-effect-1436-population-study},
  note = {Accessed: January 10, 2026}
}
Chicago/Turabian
Sinn, Mike P. "Causal Analysis: Does Three Lac Probiotic Affect Resilience?." The Journal of Citizen Science. Accessed January 10, 2026. https://studies.crowdsourcingcures.org/study/cause-1563-effect-1436-population-study.
Harvard
Sinn, M.P., 2026. Causal Analysis: Does Three Lac Probiotic Affect Resilience?. [Aggregated N-of-1 Study] The Journal of Citizen Science. Available at: https://studies.crowdsourcingcures.org/study/cause-1563-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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