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.