Time Series Regression Analysis in Biostatistics: Evaluating PM2.5, Temperature, and Intervention Effects on Asthma Cases

 Introduction

Time series regression is a powerful statistical tool used in biostatistics and environmental health to analyze data collected at regular intervals over time. It enables researchers to identify the influence of various time-varying predictors, such as pollution levels or weather, on biological or health-related outcomes.

In this study, we investigate how PM2.5 concentration, temperature, lagged PM2.5, and a policy intervention influence asthma-related hospital admissions over time using a multiple linear regression model with time series data.

Time Series Regression Model Summary

The following model was fitted:

$$\text{Asthma Cases} = \beta_0 + \beta_1(\text{PM2.5}) + \beta_2(\text{Lag\_PM2.5}) + \beta_3(\text{Temperature}) + \beta_4(\text{Intervention}) + \epsilon$$

Regression Output Table

Predictor	Estimate	Std. Error	t-value	p-value	Significance
Intercept	41.262	16.565	2.491	0.0471	*
PM2.5	2.4629	0.1861	13.236	1.15e-05	***
Lag_PM2.5	0.1570	0.2110	0.744	0.4848
Temperature	-0.6875	0.3320	-2.071	0.0838	.
Intervention	1.9952	1.8669	1.069	0.3263

Significance codes: *** = p < 0.001, ** = p < 0.01, * = p < 0.05, . = p < 0.1

Interpretation of Results

1. Intercept (41.26)

The baseline number of asthma cases, when all predictors are zero, is estimated at 41.26. Although not directly meaningful alone, it anchors the regression line.

2. PM2.5 (2.46, p < 0.001)

The most statistically significant variable. A 1 µg/m³ increase in PM2.5 is associated with an increase of approximately 2.46 asthma cases, holding other variables constant. This confirms the strong health impact of air pollution.

3. Lagged PM2.5 (0.16, p = 0.48)

The lagged PM2.5 concentration (from the previous month) was not statistically significant, suggesting that the current month’s pollution is more influential on asthma hospitalizations.

4. Temperature (-0.69, p = 0.08)

Temperature showed a negative association with asthma cases. A 1°C rise in temperature is associated with a 0.69 decrease in asthma cases, which is marginally significant (p = 0.08). Warmer months may correspond to lower respiratory distress.

5. Intervention (1.99, p = 0.33)

The policy intervention did not have a statistically significant effect. However, the positive estimate implies it may have coincided with rising asthma cases — this result needs further contextual validation.

Model Fit and Residuals

• Multiple R-squared: 0.9929 — the model explains ~99% of the variation in asthma cases.
• Adjusted R-squared: 0.9881 — still very high after accounting for the number of predictors.
• Residual Std. Error: 2.295 — relatively small, indicating a good model fit.
• F-statistic: 209.4, p-value = 1.43e-06 — overall model is highly significant.

Time Series Regression

Graph Interpretation 

1. Asthma Cases Over Time

The top panel displays monthly asthma-related hospital admissions, which peak in March and reach their lowest point in July. This U-shaped trend suggests a potential seasonal effect, possibly moderated by environmental conditions such as temperature and air quality.

2. PM2.5 and Lag PM2.5 Over Time

• PM2.5 (red line): The current month's particulate matter concentration drops from February to June, then rises again through December.

• Lag PM2.5 (orange line): Tracks similarly but lags by one month, supporting its use in the regression model.
• The strong upward trend after June may correlate with the post-lockdown increase in pollution sources, coinciding with the later rise in asthma cases.

This visual supports the significant positive regression coefficient for PM2.5, reinforcing its impact on respiratory health.

3. Temperature Over Time

Temperature follows a parabolic curve, peaking in July (~27°C) and gradually declining. The inverse relationship between temperature and asthma cases is visually apparent — as temperature rises, asthma admissions fall. This matches the negative coefficient found for temperature in the regression model.

Conclusion

This time series regression analysis shows a strong positive relationship between PM2.5 levels and asthma cases, highlighting the critical public health implications of air pollution. While temperature appears to reduce asthma admissions, the intervention policy did not yield statistically significant effects in this short observation window.

🔗 Implications:

• Pollution control is key for respiratory health.
• Continuous monitoring and longer timeframes may improve the detection of policy effects.
• Models like this should be integrated into early warning systems.