Selection bias and confounding in case-crossover analyses of environmental time-series data

The case-crossover study design is a popular analytic tool for estimating the effects of triggers of acute outcomes by environmental exposures. Although this approach controls for time-invariant confounders by design, it may allow for selection bias and confounding by time-varying factors. We conducted a simulation study of the sensitivity of the symmetric bidirectional case-crossover design to time-varying patterns in exposure and outcome. We identified the effects of selection bias and confounding on symmetric bidirectional case-crossover results and offer strategies to eliminate or reduce these biases. Selection bias results when exposure in the reference periods is not identically representative of exposure in the hazard periods, even when the distribution of exposure is stationary. This bias can be estimated and removed. Selection bias also occurs when the distribution of exposure is nonstationary, but the adjusted symmetric bidirectional case-crossover methodology substantially controls for this. Confounding results from a common temporal pattern in the exposure and the outcome time series, but can also be the result of patterns in exposure and outcome that, although asymptotically uncorrelated, are correlated at finite series lengths. All three biases are reduced by choosing shorter referent-spacing lengths. This effect is illustrated using data on air pollution and daily deaths in Chicago.