Underestimation of standard errors in multi-site time series studies.

Area of Science:

• Environmental Epidemiology
• Biostatistics

Background:

• Multi-site time series studies are crucial for estimating short-term air pollution effects on health.
• Hierarchical models are standard for pooling site-specific data, accounting for uncertainty and heterogeneity.
• Modeling all uncertainty sources in time series data presents challenges, potentially leading to variance underestimation.

Purpose of the Study:

• To investigate the impact of statistical variance underestimation on pooled relative rate estimates in air pollution health studies.
• To assess the sensitivity of hierarchical models to underestimation of site-specific variances.

Main Methods:

• Focused on two-stage normal-normal hierarchical models.
• Utilized mathematical derivations and simulation studies to evaluate variance underestimation effects.
• Examined the National Morbidity, Mortality and Air Pollution (NMMAPS) study data.

Main Results:

• Variance underestimation generally had a minor effect on the pooled relative rate estimate.
• Pooled estimates showed some sensitivity when the number of sites was small and variance underestimation was severe.
• Variance underestimation up to 40% had minimal impact on the NMMAPS national average estimate.

Conclusions:

• The findings suggest that variance underestimation is not a major concern for pooled estimates in most hierarchical air pollution studies.
• Results are applicable to two-stage normal-normal hierarchical models and meta-analyses.
• Care should be taken with small numbers of sites and severe variance underestimation.