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A simulation study of confounding in generalized linear models for air pollution epidemiology
C Chen1, D P Chock, S L Winkler
1Ford Research Laboratory, Dearborn, MI 48121 USA.
Environmental Health Perspectives
|March 4, 1999
Summary
Model overfitting in air pollution epidemiology does not bias coefficients but reduces significance. Underfitting or misfit leads to erroneous coefficients and false confidence in their significance.
Area of Science:
- Environmental Epidemiology
- Statistical Modeling
- Public Health
Background:
- Confounding between model covariates and causal variables is a known issue in regression models for air pollution epidemiology.
- This problem is often acknowledged but rarely investigated, particularly within generalized linear models.
Purpose of the Study:
- To investigate the impact of model overfit, underfit, and misfit on estimated coefficients and their confidence levels in Poisson regression models.
- To examine how these effects vary with covariate ranges and sample size.
Main Methods:
- Utilized synthetic datasets to simulate scenarios of correlated causal variables within a Poisson regression framework.
- Analyzed the effects of including non-causal variables (overfit), excluding causal variables (underfit), and including only non-causal variables (misfit).
Main Results:
- Overfitting covariates did not bias coefficients but decreased their statistical significance.
- Model underfit or misfit resulted in biased coefficients and inflated confidence (large t-values), suggesting false significance.
- Results showed qualitative agreement with large-sample limit expressions for ordinary linear models.
Conclusions:
- Models using limited air quality variables (e.g., PM10, SO2) may be unreliable due to potential underfit or misfit.
- Investigating models with multiple correlated air quality variables is crucial to mitigate underfit/misfit issues and improve epidemiological findings.