Biostatistics D Final Project

Data Exploration and Identification of Issues in Blood Glucose (BG) and Blood Pressure (BP) Data

The dataset contains various variables related to blood glucose (BG) and blood pressure (BP) measurements. As part of the initial data exploration, several issues related to data quality were identified, including missing values, unqualified values (e.g., values that do not represent realistic measurements), and incorrect data types. These issues were addressed systematically to ensure the data’s reliability for further analysis.

Changes Applied

Analysis of Missing Data Patterns in BP and BG Variables

Missing Values in BP Variables - Bar Chart

Missing Values in BG Variables - Bar Chart

Combining Levels “pen” and “pump” in Insulin Treatment and Handling Missing Values

In the data, the “insulin_treatment” variable was modified by combining the “pen” and “pump” levels into a single category called “pump_plus_pen.” Additionally, any instances where the “insulin_treatment” value was recorded as “0” were converted to missing values (NA). This adjustment ensures that the data accurately reflects the insulin treatment modalities used by patients and removes non-informative entries.

Defining Baseline Measurement of Blood Glucose (BG)

The baseline BG measurement for each subject was determined by identifying the first available monthly BG measurement. This baseline value serves as a reference point for subsequent BG measurements, allowing for the assessment of changes over time.

Description of the Sample Based on Clinical and Socio-Demographic Information

Socio-Demographic Variables Summary

Categorical Variables Distribution

Category	Distribution
Smoking Status
Alcohol Consumption
Ethnicity Distribution
Gender Distribution
Activity Level
Stress Level

Group Comparisons Based on Baseline

The balance between groups based on the baseline measurement was assessed by comparing clinical and socio-demographic variables across different baseline categories.

Summary and Implications

The sample exhibits variability in both clinical and socio-demographic characteristics across different baseline groups. Notably, there is a significant age difference and variation in the prevalence of hypertension and high blood lipids across groups. The socio-demographic variables show less variability, with gender distribution being fairly consistent across groups. This analysis suggests that the sample is diverse in terms of health status and socio-economic factors, which should be considered when interpreting the results of further analyses or when planning interventions.

Model Interpretation

Intercept: The estimated average BG level at the baseline time (when baseline = 0) after starting BP monitoring is approximately 145.61.

before_after_bp Before BP Monitoring

There is a slight, non-significant decrease in the average BG level before BP monitoring compared to after BP monitoring (p = 0.0517), with an estimate of -3.85. This suggests that, on average, the BG levels were slightly lower before BP monitoring started, but this difference is not statistically significant at the 0.05 level.

baseline

The coefficient for baseline is -0.60, indicating that for each unit increase in baseline (time), the average BG decreases by approximately 0.60 units (p = 0.0132). This is a statistically significant finding, suggesting a trend of decreasing BG levels over time.

Interaction (before_after_bp:baseline)

The interaction term is not defined in the model summary due to singularity. This means that the interaction between before_after_bp and baseline is not contributing uniquely to the model, possibly because of collinearity or a lack of variation.

Summary

Model Fitting and Statistical Findings

To evaluate whether systolic blood pressure (BP) changes over time as a result of BP monitoring, a linear regression model was fitted using the baseline time variable as the predictor for average systolic BP. The key statistics from the model are presented in the table below:

Interpretation of the Results

Intercept: The intercept of 135.60 mmHg represents the estimated average systolic BP at the baseline time (when baseline = 0). This is the starting point before considering any changes over time.

Baseline Coefficient: The baseline coefficient of -0.32 suggests that, on average, systolic BP decreases by 0.32 mmHg for each unit increase in time since BP monitoring began. This negative coefficient, coupled with a p-value of 0.01, indicates that the decrease in systolic BP over time is statistically significant.

Residual Standard Error: The standard deviation of the residuals is 12.50 mmHg, which shows the average deviation of observed BP values from the predicted values. This value reflects the variability in systolic BP not explained by the model.

R-squared: The R-squared value of 0.01 indicates that only 1% of the variance in systolic BP is explained by time since baseline. This low R-squared value suggests that, while the trend is statistically significant, the practical significance or the proportion of variation in BP explained by time is minimal.

Graphical Presentation

The graph below visualizes the trend of average systolic BP over time. The blue line represents the average systolic BP at each time point, with black points indicating specific averages. The overall trend suggests a slight downward trajectory in systolic BP as time progresses.

Limitations

Low R-squared Value: The very low R-squared value (0.01) indicates that the model explains only a small fraction of the variation in systolic BP. Although the downward trend is statistically significant, the model’s ability to predict changes in BP over time is limited, and other factors likely play a more substantial role in BP variation.

Residual Variability: The residual standard error of 12.50 mmHg suggests substantial variability in BP measurements not accounted for by time. This highlights the possibility that other unmeasured variables may be influencing BP.

Potential Confounders: The model does not account for other potential factors that might influence BP changes over time, such as medication adjustments, dietary changes, exercise, or adherence to treatment protocols. Without considering these factors, the conclusions drawn from this analysis are limited.

Temporal Resolution: The use of the baseline variable as a linear time indicator assumes a simple, linear relationship between time and BP. However, BP changes could be non-linear or influenced by more complex patterns, which this model does not capture.

Conclusion

The analysis indicates a statistically significant, though modest, decrease in systolic BP over time following the initiation of BP monitoring. However, due to the low R-squared value and unaccounted variability, the practical significance of this finding is limited. Further research incorporating additional variables and more sophisticated modeling techniques could provide a more comprehensive understanding of BP changes over time.

Model Summary

A linear regression model was fitted to assess the association between average blood glucose (BG) levels and systolic blood pressure (BP). The model aimed to determine whether changes in systolic BP are associated with variations in BG levels.

Key Findings

Intercept: The model estimates an intercept of 81.59, representing the expected BG level when systolic BP is zero. While necessary for the model, this value has limited clinical significance, as a systolic BP of zero is not realistic.

BP Coefficient: The coefficient for systolic BP (0.44) indicates that for each unit increase in systolic BP, the average BG level is expected to increase by approximately 0.44 units. This positive association suggests that higher systolic BP may be linked to slightly higher BG levels.

Residual Standard Error: The residual standard error is 29.80, suggesting that on average, the model’s predictions deviate from the actual BG levels by approximately 29.80 units. This value reflects the variation in BG levels not accounted for by systolic BP.

R-squared: The R-squared value is 0.03, indicating that systolic BP explains only 3% of the variation in BG levels. This low R-squared value suggests that while there is a statistically significant association, systolic BP alone is not a strong predictor of BG levels.

P-value (BP): The p-value for systolic BP is 0.00, indicating that the association between systolic BP and BG levels is statistically significant at the conventional 0.05 level. This finding implies that the observed association is unlikely to be due to random chance.

Graphical Findings

The scatter plot with the regression line visually represents the association between BG and systolic BP. While there is a slight upward trend, the plot shows considerable scatter around the regression line, reflecting the low R-squared value and indicating that other factors may influence BG levels.

Limitations

Low R-squared: The low R-squared value suggests that systolic BP accounts for only a small fraction of the variance in BG levels. Other factors not included in the model may play a more substantial role in determining BG levels.

Observational Data: The analysis is based on observational data, meaning that causality cannot be established. The association between BP and BG might be influenced by confounding factors, such as medication use, dietary habits, or physical activity.

Potential Biases: The model does not account for potential measurement errors or biases in data collection, which could affect the accuracy of the findings.

Clinical Relevance: Although the association is statistically significant, the small effect size (0.44 increase in BG per unit increase in BP) may not be clinically meaningful. Further research is needed to explore the clinical implications of this association.

Overview

This analysis aimed to explore the mediation effect of blood pressure (BP) on the relationship between stress level and blood glucose (BG) levels. Additionally, we examined whether the association between stress level and BP is moderated by several factors including gender, centered time, hypertension, age, depression, comorbidities, and smoking status.

Mediation Analysis

The mediation analysis tested whether the effect of stress level on BG is mediated by BP. The following key metrics were obtained from the mediation model:

Findings

The mediation analysis shows that the effect of stress level on blood glucose is not significantly mediated by blood pressure. The ACME (Average Causal Mediation Effect) is small (0.16) and not statistically significant (p = 0.96). The ADE (Average Direct Effect) suggests that there is a small negative direct effect of stress level on blood glucose, but this is also not statistically significant (p = 0.78). Overall, the total effect of stress level on blood glucose is not significant, and the proportion of the effect mediated by blood pressure is minimal and non-significant.

Moderation Analysis

The moderation analysis examined whether the relationship between stress level and blood pressure (BP) is moderated by gender, centered time, hypertension, age, depression, comorbidities, and smoking status. The following statistics summarize the findings:

Significant Findings

The overall model is statistically significant (p = 0.00), with an R-squared value of 0.39, indicating that 39% of the variance in BP is explained by the predictors in the model. Despite the model’s significance, none of the interaction terms (Stress Level * Gender, Stress Level * Centered Time, Stress Level * Hypertension, Stress Level * Age, Stress Level * Depression, Stress Level * None Comorb, and Stress Level * Smoke) were statistically significant in moderating the relationship between stress level and BP. This is evident as all these coefficients returned NA values, indicating they were not included in the final model, likely due to multicollinearity or lack of statistical significance.

Statistical Report

The mediation model tested whether blood pressure mediates the relationship between stress level and blood glucose. However, neither the mediation effect (ACME) nor the direct effect (ADE) was statistically significant. The total effect of stress level on blood glucose was also non-significant. The moderation model aimed to test if certain factors moderate the stress level’s impact on BP. While the overall model was significant, none of the specific interactions between stress level and the moderators (gender, centered time, hypertension, age, depression, none comorb, and smoking) were statistically significant.

Conclusion

There is no significant evidence to suggest that blood pressure mediates the relationship between stress level and blood glucose levels. Additionally, there is no significant evidence that the relationship between stress level and blood pressure is moderated by gender, centered time, hypertension, age, depression, comorbidities, or smoking status. The findings suggest that while stress level, blood pressure, and blood glucose levels are related, the complexities of these relationships require further investigation, possibly with different or more refined variables.

Model Performance Summary

Confusion Matrix Results

Accuracy: The model’s accuracy is 91.3%, meaning it correctly predicts 91.3% of the cases. This high accuracy suggests that the model performs well overall, but it’s important to consider this metric in the context of class imbalance. Sensitivity: The model has a very high sensitivity of 97.62%, indicating that it correctly identifies 97.62% of true positives (cases where BG is below the cutoff). This is crucial in clinical settings where missing a positive case could have serious consequences. Specificity: The specificity is 25%, meaning the model correctly identifies only 25% of true negatives (cases where BG is above the cutoff). This low specificity suggests that the model often predicts BG to be below the cutoff when it is actually above, which could lead to missed alerts for high BG levels. Positive Predictive Value (PPV): The PPV is 93.18%, meaning that when the model predicts a BG below the cutoff, it is correct 93.18% of the time. This high PPV indicates confidence in the positive predictions. Negative Predictive Value (NPV): The NPV is 50%, indicating that when the model predicts a BG above the cutoff, it is correct only 50% of the time. This suggests uncertainty in the model’s ability to correctly predict high BG levels. Balanced Accuracy: The balanced accuracy is 61.31%, which provides a more balanced view of the model’s performance by averaging sensitivity and specificity. This metric is particularly useful when dealing with imbalanced datasets.

ROC Curve and AUC

AUC-ROC: The Area Under the Curve (AUC) is 0.6131. This value is slightly above 0.5, indicating that the model is only marginally better than random guessing. The ROC curve shows that while the model has high sensitivity, its ability to distinguish between true positives and true negatives is limited.

Interpretation

The model shows excellent sensitivity but low specificity. This means that while the model is very good at identifying when BG levels are below the cutoff, it struggles to correctly identify cases where BG levels are above the cutoff. This trade-off may reflect the importance of catching low BG events (high sensitivity) at the expense of more false positives (low specificity). The AUC-ROC score of 0.6131 suggests that the model’s ability to discriminate between the two classes (BG peaks above or below the cutoff) is modest. This indicates that the model’s overall discriminatory power could be improved, particularly in distinguishing between true negatives and false positives. The low specificity and balanced accuracy highlight a potential area for improvement. The model may benefit from further refinement, such as better feature selection, model tuning, or exploring alternative modeling techniques.

Conclusion

The current model provides a good starting point for predicting BG peaks, particularly with its high sensitivity. However, there is significant room for improvement in specificity and overall discriminatory ability, as indicated by the AUC-ROC score. Further work, including model tuning and exploration of more advanced modeling techniques, is necessary before this model can be confidently used in a clinical setting.

Data Cleaning and Preprocessing

Missing data was addressed by converting string representations of missing values (“NA”, “N/A”) to actual NA values. Unqualified values, such as zeros in non-meaningful fields, were converted to NA. Date fields were corrected and converted to appropriate formats.

Statistical Methods:

Descriptive statistics were used to summarize clinical and sociodemographic variables. Linear regression models were employed to assess the relationship between BP and BG, with adjustments for potential confounders. Mediation analysis was conducted to explore the role of BP in the stress-BG relationship, with moderation analysis to identify significant interactions.

Modeling Details

The predictive model for BG peaks was developed using logistic regression. The model’s performance was evaluated using accuracy, sensitivity, specificity, and AUC-ROC metrics. The model for time-related BG fluctuations was based on linear regression, considering before and after BP monitoring as key time points.

Graphs and Figures

Figures illustrating BG and BP trends over time, as well as ROC curves for model performance, are included to visually support the statistical findings. This appendix provides the necessary details for replicating the study’s analysis and understanding the methodological decisions made throughout the project.