Biostatistics D Final Project

Reviewing and adressing Missing Data and Outliers in the Dataset

After thoroughly reviewing the dataset, we observed significant patterns of missing data, particularly in key variables such as “avg_pain” and “avg_stress,” which both exhibited 45.5% missing data. These variables play a critical role in our analysis, especially in testing hypotheses related to the effects of HRV-B training and mediation models. Given their importance, the decision was made to retain these variables in the analysis despite the substantial amount of missing data. However, caution will be exercised when interpreting results associated with these variables, considering the potential biases introduced by the missing data.

In addition to the missing data, we identified several problematic outliers. These include extreme values in “age_in_years” (values below 1 year), “height_in_cm” (values above 250 cm), “total_duration_in_min” (values exceeding 6000 minutes), and “avg_stress” (values above 10). These extreme values were deemed implausible and could distort the results of the analysis if left unaddressed. Consequently, these outliers were removed from the dataset to ensure more accurate modeling and to avoid skewing the findings.

With all missing values and outliers removed, the dataset is now prepared for further analysis. From this point forward, no missing or extreme values will affect the results, allowing us to focus on the key research questions with a more consistent and reliable dataset.

Descriptive Statistics of the Study Population

The descriptive statistics of the study population reveal key sociodemographic and anthropometric insights. As visualized in the charts, the age distribution of participants shows a predominance of individuals between 20 to 60 years, with a notable peak around the 30 to 40-year range. The range of ages spans from approximately 16 years to 93 years, with a fairly consistent distribution across both genders.

In terms of weight, the majority of the participants fall within the 60 to 90 kg range, with a few outliers indicating participants weighing either below 50 kg or over 120 kg. The weight distribution shows a higher density around the 70 kg mark, indicating a balanced distribution of weight in the study population.

The height distribution shows the majority of participants measuring between 160 cm and 180 cm, with a clear peak around 170 cm. A small number of participants were taller, with a few extreme cases above 200 cm, but these are rare. The spread in height appears to follow a relatively normal distribution.

The gender distribution, as shown in the bar plot, indicates a slightly higher number of female participants compared to males in the study. This pattern aligns with the overall demographic breakdown in the sample, where 56% of the participants were female and 44% male.

These charts provide a foundational overview of the population’s demographics, which will be crucial in interpreting the HRV-B training and its potential effects on pain and stress levels, as well as other variables.

Training and Week Index Distribution: Overview of Participation Trends

The bar plots illustrate the distribution of the number of records across the week index and the number of days of training in a week. The chart on the left shows a higher concentration of records at the start of the intervention (Week 0), followed by a more even distribution across subsequent weeks, with a slight increase around Week 7. This suggests a higher initial response rate in the early stages of the HRV-B training intervention, tapering off as the intervention progresses.

The chart on the right highlights the number of days participants trained per week. Most participants reported training between 3 to 5 days per week, with the highest concentration at 4 days. Fewer participants reported training 1 or 7 days a week, indicating that most participants engaged in moderate training frequency rather than extreme values. These insights provide a clearer understanding of participation trends during the HRV-B intervention, which may be relevant in modeling the effectiveness of the training on pain and stress outcomes.

Average Total Duration by Week Index and Days of Training The chart shows the average total training duration (in minutes) across the weeks of HRV-B training, grouped by the number of training days per week. Participants who trained 7 days a week (pink line) consistently recorded the highest training duration, with peaks over 3000 minutes, showing significant variability across weeks. Those training fewer days (1-2 days, red and yellow lines) maintained lower, more stable durations, below 500 minutes.

Overall, as the number of training days increases, the total training duration rises, with more frequent training leading to higher cumulative minutes. Week-to-week fluctuations are most pronounced for those training 7 days a week.

Average Total Duration by Week Index and Days of Training

Average Total Duration by Week Index and Days of Training The chart shows the average total training duration (in minutes) across the weeks of HRV-B training, grouped by the number of training days per week. Participants who trained 7 days a week (pink line) consistently recorded the highest training duration, with peaks over 3000 minutes, showing significant variability across weeks. Those training fewer days (1-2 days, red and yellow lines) maintained lower, more stable durations, below 500 minutes.

Overall, as the number of training days increases, the total training duration rises, with more frequent training leading to higher cumulative minutes. Week-to-week fluctuations are most pronounced for those training 7 days a week.

Stress and Pain Trends by Week Index and Days of Training

The graphs presented in this section analyze the fluctuations of stress and pain levels based on the week index and the number of days of training per week.

In the top left plot, we observe average stress levels by week index. The stress levels increased sharply in the early weeks, reaching a peak at around week 3, and then plateaued, maintaining relatively consistent levels from weeks 4 to 10. This indicates that the HRV-B training might have had a stabilizing effect on stress after the initial weeks of the intervention.

On the top right, we have the average stress by days of training per week. The data suggests that those training fewer days per week (2–3 days) had slightly lower stress levels. However, as the number of training days increased to 6 or 7, there was a noticeable rise in stress levels, which may suggest that higher frequency training is associated with increased stress, or it may point to a reverse effect where individuals experiencing higher stress tend to engage in more training.

On the bottom left, the average pain by week index shows a clear decline. Pain levels start at a higher point in the first week and decrease significantly by week 2, then maintain relatively lower values throughout the remaining weeks. This suggests that HRV-B training had a positive impact in reducing pain levels over time.

On the bottom right, the average pain by days of training per week shows an inverse relationship to stress. Participants who trained fewer days per week reported higher pain levels, while those who trained 6–7 days a week exhibited the lowest pain levels. This suggests that frequent training may be beneficial for pain reduction, as higher training frequency is associated with lower pain levels.

Correlation Between Stress, Pain, Week Index, and Days of Training

The table below presents the correlation matrix for the variables avg_stress, avg_pain, week_index, and days_training_in_week.

From this matrix, we can make the following observations:

Stress (avg_stress) has a slight positive correlation with week_index (0.28), suggesting that stress slightly increases over time during the intervention period. Pain (avg_pain) shows a moderate negative correlation with week_index (-0.34), supporting the findings from the chart that pain tends to decrease over time. The correlation between days_training_in_week and stress is weak (0.07), indicating minimal association between the number of training days and stress. Similarly, the correlation between days_training_in_week and pain is slightly negative (-0.08), suggesting that increased training frequency is associated with a small reduction in pain levels.

These insights from the correlation matrix complement the visual trends observed in the charts, emphasizing the complex interplay between stress, pain, and training frequency during the HRV-B intervention.

Pain Trajectory:

The “Trajectory of Average Pain over Week Index” shows a notable decline in pain levels, especially in the initial weeks, with pain stabilizing around week 4. This suggests that continuous HRV-B training may contribute to pain reduction over time. The “Trajectory of Average Pain over Days Training in Week” displays a decrease in pain levels with more training days per week. This trend reinforces the potential impact of frequent HRV-B training on reducing pain levels.

Stress Trajectory:

In the “Trajectory of Average Stress over Week Index”, there is an initial increase in stress levels, which then plateaus. This pattern might reflect participants’ adaptation to the HRV-B intervention, with stress stabilizing as they acclimate to the training.

The “Trajectory of Average Stress over Days Training in Week” chart shows a slight increase in stress as the number of training days rises. This could imply that while frequent training benefits pain management, it may contribute to mild stress elevation.

HRV-B Training Duration Trajectory:

The “Trajectory of HRV-B Duration over Week Index” reveals a gradual decrease in training duration over time, potentially indicating adaptation or increased efficiency in training. Conversely, the “Trajectory of HRV-B Duration over Days Training in Week” shows a steady increase with more training days, highlighting the importance of training frequency in sustaining HRV-B engagement.

Linear Model Summary for Training Days

The table below summarizes the linear models examining the relationship between days of training per week and each variable (pain, stress, HRV-B training duration):

Pain Model: The coefficient for days_training_in_week is negative and significant (β = -0.116, p < 0.001), indicating that increased training days are associated with a reduction in average pain levels.

Stress Model: For stress, the coefficient is positive (β = 0.095, p = 0.001), suggesting a slight increase in stress levels with more training days.

HRV-B Training Duration Model: The coefficient for days_training_in_week is positive and significant (β = 365.453, p < 0.001), demonstrating that more frequent training is associated with extended HRV-B duration.

Mixed Model Summary for Week Index

The table below summarizes the mixed-effects models that examine the relationship between week_index and each variable (pain, stress, HRV-B training duration), with random intercepts for individual participants. This approach allows us to assess how these variables change over time across different individuals in the study.

Pain Model: The coefficient for week_index is negative and significant (β = -0.219, p < 0.001), indicating that, on average, pain levels decrease as the weeks progress. This finding aligns with the expected effect of HRV-B training, which aims to reduce pain over time.

Stress Model: In the stress model, the coefficient for week_index is positive and significant (β = 0.176, p < 0.001), suggesting that average stress levels show a slight increase over time. This may indicate a cumulative or adaptive stress response over the intervention period, though the increase is modest.

HRV-B Training Duration Model: For HRV-B training duration, the coefficient for week_index is negative and significant (β = -46.163, p < 0.001), suggesting that training duration decreases slightly as the weeks advance. This could reflect participants becoming more efficient or protocol adjustments over time.

These results indicate distinct trajectories for pain, stress, and HRV-B duration throughout the intervention period. The pain reduction trend supports the intended therapeutic effect of HRV-B training, while the patterns for stress and HRV-B duration suggest areas for further exploration to understand individual and cumulative responses to the intervention.

Moderating Effects of Weight, Height, Age, and Gender

The table below summarizes the moderation analysis, which evaluates whether demographic factors—namely weight, height, age, and gender—moderate the relationship between HRV-B training duration (total_duration_in_min) and pain. This analysis was conducted to assess if the effect of HRV-B training on pain levels varies according to these demographic characteristics.

Moderation by Weight The interaction term between HRV-B training duration and weight (total_duration_in_min ) was not statistically significant (p = 0.451). This indicates that weight does not significantly moderate the relationship between HRV-B training and pain. In other words, the impact of HRV-B training on pain does not vary significantly based on the participants’ weight.

Moderation by Height The interaction between HRV-B training duration and height (total_duration_in_min ) was also found to be non-significant (p = 0.821). However, height itself was a significant predictor in the model (p = 0.002), suggesting that while height affects pain levels independently, it does not modify the effect of HRV-B training duration on pain.

Moderation by Age For age, the interaction term (total_duration_in_min ) did not reach statistical significance (p = 0.780), indicating that age does not moderate the relationship between HRV-B training duration and pain. Similar to height, age impacts pain independently but does not influence how HRV-B training duration affects pain.

Moderation by Gender The interaction between HRV-B training duration and gender (total_duration_in_min ) was also not statistically significant (p = 0.308). This result suggests that the effect of HRV-B training duration on pain does not vary significantly between males and females.

Summary Overall, the moderation analysis indicates that none of the demographic factors (weight, height, age, and gender) significantly moderate the effect of HRV-B training duration on pain. While some factors, such as height and age, independently affect pain levels, they do not alter the relationship between HRV-B training and pain. These findings suggest that the impact of HRV-B training on pain reduction is consistent across different demographic subgroups in this study.

Model Evaluation Metrics

RMSE (Root Mean Square Error) is 2.270, suggesting an average deviation of the predicted pain levels from the actual values.

MAE (Mean Absolute Error) is 1.767, representing the average magnitude of prediction errors without regard to direction.

R-squared value is 0.132, indicating that approximately 13.2% of the variability in pain levels is explained by the model.

The relatively low R-squared suggests that while some predictors are significant.

The scatter plot below compares predicted pain levels to actual pain levels across participants. The linear trend line shows a generally positive relationship, suggesting that the model captures the directional trend of pain levels but with noticeable deviations. Despite some alignment along the trend line, the spread of points indicates variability in predictions, reflecting the relatively low R-squared value (0.132) observed in the model evaluation metrics.

Linear Regression Model Summary for Predicting Stress

The regression model summary for predicting stress includes various predictors such as weight, height, age, gender, training days per week, stress and HRV-B duration variables, and week index. Notable findings from this model include:

Weight: There is a small but significant negative association between weight and stress levels (β = -0.008, p = 0.037), suggesting that higher weight is associated with slightly lower reported stress.

Age: Age shows a positive association with stress (β = 0.009, p = 0.010), indicating that older participants report higher stress levels.

Gender: Gender also has a significant negative coefficient (β = -0.404, p = 0.003), with male participants (assuming male is the reference group) showing lower stress levels compared to females.

Days of Training per Week: The days_training_in_week variable has a positive effect on stress levels (β = 0.106, p = 0.009), implying that an increase in training days correlates with higher stress levels.

Week Index: A significant positive association with stress levels is observed for the week_index variable (β = 0.188, p < 0.001), suggesting that stress levels increase as the intervention period progresses.

Other predictors, such as height, no-stress and stress duration in minutes, and total HRV-B duration, did not demonstrate statistically significant effects on stress levels in this model.

Model Evaluation Metrics

RMSE (Root Mean Square Error): The RMSE is 2.264, indicating the average deviation of the predicted stress levels from the actual values.

MAE (Mean Absolute Error): The MAE is 1.808, showing the average magnitude of errors in the predictions.

R-squared: The R-squared value is 0.102, suggesting that around 10.2% of the variability in stress levels is explained by this model.

The low R-squared value implies that, while certain predictors are significant, the model explains only a modest portion of the variance in stress levels.

The scatter plot above illustrates the comparison between predicted and actual stress levels across participants. The linear trend line indicates a generally positive relationship, showing that the model follows the overall trend of stress levels. However, there are notable deviations from the trend line, as evidenced by the dispersion of points. This spread reflects the model’s relatively low R-squared value (0.102), indicating that, while the model captures some trend, a significant portion of the variability in stress levels remains unexplained.