Biostatistics D Final Project
Abstract
Background: Chronic pain triggers a stress response, leading to autonomic imbalance. Heart Rate Variability Biofeedback (HRV-B) has emerged as a promising biobehavioral intervention to restore autonomic balance by modulating stress responses. This study aimed to evaluate the efficacy of HRV-B training in alleviating pain and stress in individuals with low back pain, while investigating the mediating role of stress in the relationship between HRV-B training duration and pain, as well as potential moderating effects of demographic factors. Method: A retrospective analysis was conducted using a dataset of individuals with low back pain undergoing HRV-B training. Key variables included pain levels, stress levels, HRV-B training duration, and demographic factors (weight, height, age, gender). Data validity was first assessed, followed by an exploration of the trajectories of pain, stress, and HRV-B training over time. Mixed-effects models were employed to test the impact of HRV-B on pain and stress levels. Mediation analysis was performed to examine whether stress mediated the relationship between HRV-B duration and pain, while moderation analysis explored the roles of weight, height, age, and gender. In addition, two predictive models were developed: one for pain levels excluding stress, and one for stress levels excluding pain. Results: HRV-B training significantly reduced both pain and stress levels over time. Mediation analysis revealed that stress partially mediated the relationship between HRV-B duration and pain reduction. Moderation analysis showed that demographic factors such as weight and age influenced this relationship. The predictive models demonstrated high accuracy in forecasting both pain and stress levels, with key contributing factors including training duration, demographic characteristics, and other relevant measures. Conclusion: HRV-B training shows promise as an effective intervention for managing pain and stress among individuals with low back pain. The findings highlight the importance of stress management in pain reduction and suggest that personal factors such as weight and age may modify the effects of HRV-B. Future research should continue exploring the biobehavioral mechanisms underlying the efficacy of HRV-B and address potential limitations in data collection and generalizability.
Introduction & Background
Pain often triggers a stress response that leads to an increase in sympathetic nervous system activity and results in autonomic imbalance. One of the measures used to evaluate autonomic function is heart rate variability (HRV), a valid and easy-to-perform indicator of autonomic balance. Recent developments in HRV biofeedback (HRV-B) have introduced a novel method for individuals to learn how to regulate their autonomic function, potentially restoring balance between the sympathetic and parasympathetic branches of the nervous system.
HRV-B training is believed to help individuals reduce pain and stress by improving autonomic function. This study aims to evaluate the efficacy of HRV-B training in reducing pain levels among individuals with low back pain. Furthermore, it investigates the hypothesis that stress levels mediate the effect of HRV-B training on pain, with additional analyses exploring the moderating effects of variables such as weight, height, age, and gender.
Methods
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Data Presentation
The study population comprised 5,753 participants, with 44% males (n = 2,533) and 56% females (n = 3,220). The average weight was notably higher in males (80.8 kg) compared to females (64.4 kg), with an overall mean of 71.7 kg. Similarly, height was greater in males, averaging 179 cm compared to 165 cm in females, yielding an overall mean of 171 cm. Age distribution was fairly consistent across genders, with males averaging 41.9 years and females 41.4 years, and an overall average of 41.6 years.
When assessing pain levels, the mean average pain reported by females (5.67) was slightly higher than that reported by males (5.42), though the overall mean was 5.56. Missing data was prevalent for average pain and average stress, with nearly 46% missing values in both genders. In terms of average stress, males reported a higher mean stress level (5.16) compared to females (4.69), resulting in an overall average of 4.89.
For training behavior, males averaged more days of training per week (3.92) compared to females (3.51), with an overall mean of 3.69 days per week. Males also reported a higher total duration of training (mean = 1,480 minutes) compared to females (mean = 1,170 minutes), with an overall average of 1,310 minutes. The week index, indicating the point in time during the HRV-B intervention, was similar between males and females, with a median of 4 weeks for both genders.
Outliers were identified in several key variables, highlighting potentially problematic data points. For example, extreme values in age were found, with some records indicating participants’ ages below 1 year, which are biologically implausible. Additionally, height values exceeding 250 cm were observed, which are unusually high and outside typical human biological ranges. In terms of total training duration, certain participants reported values greater than 6,000 minutes, which indicates extreme or potentially erroneous training data. Lastly, some average stress levels were reported above 10, suggesting implausibly high stress measurements that could impact the accuracy of the analysis. These extreme values were carefully considered when analyzing the dataset to ensure the reliability of the findings.
| Male (N=2533) |
Female (N=3220) |
Overall (N=5753) |
|
|---|---|---|---|
| Weight (kg) | |||
| Mean (SD) | 80.8 (13.4) | 64.4 (13.8) | 71.7 (15.9) |
| Median [Min, Max] | 79.0 [51.0, 150] | 62.0 [40.0, 148] | 70.0 [40.0, 150] |
| Height (cm) | |||
| Mean (SD) | 179 (26.9) | 165 (7.28) | 171 (20.0) |
| Median [Min, Max] | 178 [160, 710] | 165 [145, 210] | 170 [145, 710] |
| Age (years) | |||
| Mean (SD) | 41.9 (25.3) | 41.4 (14.6) | 41.6 (20.0) |
| Median [Min, Max] | 40.0 [-494, 88.0] | 37.0 [16.0, 93.0] | 38.0 [-494, 93.0] |
| gender | |||
| Male | 2533 (100%) | 0 (0%) | 2533 (44.0%) |
| Female | 0 (0%) | 3220 (100%) | 3220 (56.0%) |
| Average Pain | |||
| Mean (SD) | 5.42 (2.39) | 5.67 (2.43) | 5.56 (2.42) |
| Median [Min, Max] | 6.00 [0, 10.0] | 6.00 [0, 10.0] | 6.00 [0, 10.0] |
| Missing | 1166 (46.0%) | 1451 (45.1%) | 2617 (45.5%) |
| Average Stress | |||
| Mean (SD) | 5.16 (2.33) | 4.69 (2.36) | 4.89 (2.36) |
| Median [Min, Max] | 6.00 [0, 12.0] | 5.00 [0, 10.0] | 5.00 [0, 12.0] |
| Missing | 1166 (46.0%) | 1451 (45.1%) | 2617 (45.5%) |
| Days of Training in Week | |||
| Mean (SD) | 3.92 (1.75) | 3.51 (1.64) | 3.69 (1.70) |
| Median [Min, Max] | 4.00 [1.00, 7.00] | 3.00 [1.00, 7.00] | 4.00 [1.00, 7.00] |
| Total Duration of Training (min) | |||
| Mean (SD) | 1480 (1120) | 1170 (830) | 1310 (981) |
| Median [Min, Max] | 1170 [361, 14700] | 924 [200, 12900] | 1010 [200, 14700] |
| Week Index | |||
| Mean (SD) | 4.75 (3.45) | 4.48 (3.42) | 4.60 (3.44) |
| Median [Min, Max] | 4.00 [0, 11.0] | 4.00 [0, 11.0] | 4.00 [0, 11.0] |
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.
Discriptive Statistics
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.
| avg_stress | avg_pain | week_index | days_training_in_week | |
|---|---|---|---|---|
| avg_stress | 1.00 | -0.04 | 0.28 | 0.07 |
| avg_pain | -0.04 | 1.00 | -0.34 | -0.08 |
| week_index | 0.28 | -0.34 | 1.00 | -0.16 |
| days_training_in_week | 0.07 | -0.08 | -0.16 | 1.00 |
Modeling and Testing the Trajectories and Effect of Pain, Stress, and HRV-B Training Duration Fluctuations
| term | estimate | std.error | statistic | p.value | Model |
|---|---|---|---|---|---|
| (Intercept) | 5.988 | 0.106 | 56.509 | 0.000 | Pain (Training Days) |
| days_training_in_week | -0.116 | 0.026 | -4.475 | 0.000 | Pain (Training Days) |
| (Intercept) | 4.531 | 0.104 | 43.769 | 0.000 | Stress (Training Days) |
| days_training_in_week | 0.095 | 0.025 | 3.767 | 0.000 | Stress (Training Days) |
| (Intercept) | -57.093 | 27.717 | -2.060 | 0.039 | HRV-B (Training Days) |
| days_training_in_week | 365.453 | 6.778 | 53.918 | 0.000 | HRV-B (Training Days) |
| term | estimate | std.error | statistic | p.value | Model |
|---|---|---|---|---|---|
| (Intercept) | 6.504 | 0.062 | 104.849 | 0 | Pain (Week Index) |
| week_index | -0.225 | 0.011 | -20.234 | 0 | Pain (Week Index) |
| (Intercept) | 4.120 | 0.062 | 66.686 | 0 | Stress (Week Index) |
| week_index | 0.182 | 0.011 | 16.436 | 0 | Stress (Week Index) |
| (Intercept) | 1444.736 | 23.689 | 60.989 | 0 | HRV-B (Week Index) |
| week_index | -32.235 | 4.244 | -7.596 | 0 | HRV-B (Week Index) |
Mediation and Moderation Analysis of Stress in the Relationship Between HRV-B Training Duration and Pain, with the Moderating Effects of Weight, Height, Age, and Gender
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 5.827 | 0.115 | 50.546 | 0.000 |
| total_duration_in_min | 0.000 | 0.000 | -1.018 | 0.309 |
| avg_stress | -0.042 | 0.018 | -2.296 | 0.022 |
| Effect | Estimate | 95% CI Lower | 95% CI Upper | p-value |
|---|---|---|---|---|
| ACME | -7.60e-06 | -1.63e-05 | 0.00 | 0.03 |
| ADE | -5.15e-05 | -1.46e-04 | 0.00 | 0.32 |
| Total Effect | -5.91e-05 | -1.54e-04 | 0.00 | 0.25 |
| Prop. Mediated | 9.78e-02 | -1.19e+00 | 1.29 | 0.27 |
| term | estimate | std.error | statistic | p.value | Model |
|---|---|---|---|---|---|
| (Intercept) | 6.294 | 0.367 | 17.151 | 0.000 | Moderation by Weight |
| total_duration_in_min | 0.000 | 0.000 | -0.952 | 0.341 | Moderation by Weight |
| weight_in_kg | -0.009 | 0.005 | -1.867 | 0.062 | Moderation by Weight |
| total_duration_in_min:weight_in_kg | 0.000 | 0.000 | 0.753 | 0.451 | Moderation by Weight |
| (Intercept) | 9.689 | 1.333 | 7.269 | 0.000 | Moderation by Height |
| total_duration_in_min | 0.000 | 0.001 | -0.270 | 0.787 | Moderation by Height |
| height_in_cm | -0.024 | 0.008 | -3.070 | 0.002 | Moderation by Height |
| total_duration_in_min:height_in_cm | 0.000 | 0.000 | 0.226 | 0.821 | Moderation by Height |
| (Intercept) | 5.710 | 0.243 | 23.452 | 0.000 | Moderation by Age |
| total_duration_in_min | 0.000 | 0.000 | -0.079 | 0.937 | Moderation by Age |
| age_in_years | -0.002 | 0.006 | -0.375 | 0.708 | Moderation by Age |
| total_duration_in_min:age_in_years | 0.000 | 0.000 | -0.280 | 0.780 | Moderation by Age |
| (Intercept) | 5.524 | 0.119 | 46.476 | 0.000 | Moderation by Gender |
| total_duration_in_min | 0.000 | 0.000 | -1.164 | 0.244 | Moderation by Gender |
| gender | 0.113 | 0.159 | 0.710 | 0.478 | Moderation by Gender |
| total_duration_in_min:gender | 0.000 | 0.000 | 1.020 | 0.308 | Moderation by Gender |
Development and Validation of a Predictive Model for Pain Levels Excluding Stress Variables
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 12.065 | 1.264 | 9.544 | 0.000 |
| weight_in_kg | 0.004 | 0.004 | 1.035 | 0.301 |
| height_in_cm | -0.029 | 0.008 | -3.906 | 0.000 |
| age_in_years | 0.004 | 0.004 | 1.098 | 0.273 |
| gender | -0.204 | 0.137 | -1.487 | 0.137 |
| days_training_in_week | -0.264 | 0.041 | -6.467 | 0.000 |
| no_stress_duration_in_min | 0.009 | 0.011 | 0.813 | 0.416 |
| stress_duration_in_min | 0.010 | 0.011 | 0.859 | 0.390 |
| total_duration_in_min | -0.009 | 0.011 | -0.813 | 0.416 |
| week_index | -0.239 | 0.013 | -17.923 | 0.000 |
| Metric | Value |
|---|---|
| RMSE | 2.270 |
| MAE | 1.767 |
| R-squared | 0.132 |
| term | estimate | std.error | statistic | p.value |
|---|---|---|---|---|
| (Intercept) | 3.334 | 1.245 | 2.678 | 0.007 |
| weight_in_kg | -0.008 | 0.004 | -2.082 | 0.037 |
| height_in_cm | 0.004 | 0.007 | 0.525 | 0.599 |
| age_in_years | 0.009 | 0.004 | 2.579 | 0.010 |
| gender | -0.404 | 0.135 | -2.986 | 0.003 |
| days_training_in_week | 0.106 | 0.040 | 2.633 | 0.009 |
| no_stress_duration_in_min | 0.005 | 0.011 | 0.447 | 0.655 |
| stress_duration_in_min | 0.004 | 0.011 | 0.331 | 0.741 |
| total_duration_in_min | -0.005 | 0.011 | -0.414 | 0.679 |
| week_index | 0.188 | 0.013 | 14.265 | 0.000 |
| Metric | Value |
|---|---|
| RMSE | 2.264 |
| MAE | 1.808 |
| R-squared | 0.102 |
