### Abstract

In this article a time-varying coefficient model is developed to examine the relationship between adverse health and short-term (acute) exposure to air pollution. This model allows the relative risk to evolve over time, which may be due to an interaction with temperature, or from a change in the composition of pollutants, such as particulate matter, over time. The model produces a smooth estimate of these time-varying effects, which are not constrained to follow a fixed parametric form set by the investigator. Instead, the shape is estimated from the data using penalized natural cubic splines. Poisson regression models, using both quasi-likelihood and Bayesian techniques, are developed, with estimation performed using an iteratively re-weighted least squares procedure and Markov chain Monte Carlo simulation, respectively. The efficacy of the methods to estimate different types of time-varying effects are assessed via a simulation study, and the models are then applied to data from four cities that were part of the National Morbidity, Mortality, and Air Pollution Study.

Original language | English |
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Pages (from-to) | 1253-1261 |

Number of pages | 9 |

Journal | Biometrics |

Volume | 63 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2007 |

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## Cite this

Lee, D., & Shaddick, G. (2007). Time-varying coefficient models for the analysis of air pollution and health outcome data.

*Biometrics*,*63*(4), 1253-1261. https://doi.org/10.1111/j.1541-0420.2007.00776.x