Lee Duncan, Shaddick Gavin
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK.
Biometrics. 2007 Dec;63(4):1253-61. doi: 10.1111/j.1541-0420.2007.00776.x. Epub 2007 Apr 9.
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.
在本文中，我们开发了一种时变系数模型，以研究不良健康状况与短期（急性）空气污染暴露之间的关系。该模型允许相对风险随时间演变，这可能是由于与温度的相互作用，或者是由于污染物组成（如颗粒物）随时间的变化。该模型对这些时变效应进行了平滑估计，这些估计不受研究者设定的固定参数形式的限制。相反，其形状是使用惩罚自然立方样条从数据中估计出来的。我们开发了使用拟似然和贝叶斯技术的泊松回归模型，分别使用迭代加权最小二乘法和马尔可夫链蒙特卡罗模拟进行估计。通过模拟研究评估了估计不同类型时变效应方法的有效性，然后将这些模型应用于来自四个城市的数据，这些城市是国家发病率、死亡率和空气污染研究的一部分。
