Time series models of environmental exposures: Good predictions or good understanding

Time series data are popular in environmental epidemiology as they make use of the natural experiment of how changes in exposure over time might impact on disease. Many published time series papers have used parameter-heavy models that fully explained the second order patterns in disease to give residuals that have no short-term autocorrelation or seasonality. This is often achieved by including predictors of past disease counts (autoregression) or seasonal splines with many degrees of freedom. These approaches give great residuals, but add little to our understanding of cause and effect. We argue that modelling approaches should rely more on good epidemiology and less on statistical tests. This includes thinking about causal pathways, making potential confounders explicit, fitting a limited number of models, and not over-fitting at the cost of under-estimating the true association between exposure and disease.