Modeling Time-varying Dispersion to Improve Estimation of the Short-term Health Effect of Environmental Exposure in a Time-series Design.

Background: Time-series models for count outcomes are routinely used to estimate short-term health effects of environmental exposures. The dispersion parameter is universally assumed to be constant over the study period.

Objective: The aim is to examine whether dispersion depends on time-varying covariates in a case study of emergency department visits in Atlanta during 1999-2009 and to evaluate approaches for addressing time-varying dispersion.

Methods: Using the double generalized linear model framework, we jointly modeled the Poisson log-linear mean and dispersion to estimate associations between emergency department visits for respiratory diseases and daily ozone concentrations. We conducted a simulation study to evaluate the impact of time-varying overdispersion on health effect estimation when constant overdispersion is assumed and developed an analytic code for implementing double generalized linear model using R.

Results: We found dispersion to depend on calendar date and meteorology. Assuming constant dispersion, the relative risk (RR) per interquartile range increase in 3-day moving ozone exposure was 1.037 (95% confidence interval: 1.024, 1.050). In the multivariable dispersion model, the RR was reduced to 1.029 (95% confidence interval: 1.020, 1.039), but with a large (26%) reduction in log RR standard error. The positive associations for ozone were robust against different dispersion model specifications. Simulation study results also demonstrated that when time-varying dispersion is present, it can lead to a larger standard error assuming constant dispersion.

Conclusion: When the outcome exhibits large dispersion in a time-series analysis, allowing for covariate-dependent time-varying dispersion can improve inference, particularly by increasing estimation precision.