On inferences about lag effects using lag models in air pollution time-series studies

The choice of lag length is a matter of uncertainty in air pollution time-series studies. Lag models and model selections are widely used for inferences about lag effects, but there is lack of discussion on the integration of the two. We aimed to provide theoretical discussion on the performance of lag models, and the impact of model selections on inferences about lag effects. Bias and model selections based upon information criteria, statistical significance, effect size, and model averaging were discussed in the context of lag analysis. A simulation with eight of PM_2.5-mortality relation scenarios was also conducted in order to explore the performances of lag models and to compare the model selections. The application of lag models with an insufficient lag interval taken into account (i.e. insufficient lag models) provides biased estimates. We provided features of the model selections and showed their pitfalls in lag analysis of air pollution time-series studies. We also discussed limitations of meta-analysis which fails to consider the application of different lag models in individual studies. To foster exploration on air pollution-lag-response relations with relevant tools, we encourage researchers to compare different lag models in terms of effect estimates and variance estimates, and to report their favored models and competing models together based upon scientific knowledge supporting lag-response relations.