Bidirectional case-crossover studies of air pollution: bias from skewed and incomplete waves

The case-crossover design compares exposures during the period of time of failure with one or more periods when failure did not occur and evaluates the potential excess risk using conditional logistic regression. In this simulation study, we applied several control sampling approaches to control for confounding by various temporal patterns of an exposure variable and evaluated the usefulness of symmetric bidirectional control strategies. We simulated true relative risks (RRs; true ss = 0.001) of deaths of 1.051 per 50-ppb increase of sulfur dioxide and included confounding by right- or left-skewed seasonal waves, linear long-term time trends, or a combination of both. The range of the estimated RRs from symmetric bidirectional control sampling approaches was 1.044 approximately 1. 056 at either a long-term trend or any skewed seasonal wave of SO(2) levels, which indicated the bidirectional control sampling methods would successfully control confounding by design. The simulations with bidirectional sampling, however, show that biases may occur if waves are incomplete (20-43% underestimated RRs). In conclusion, our simulations show that the symmetric bidirectional case-crossover design can substantially control for confounding by linear long-term trends and/or seasonality of an exposure variable by design as well. However, unidirectional control sampling would fail to control confounding by those variations of air pollution. Simulation results also show that even the bidirectional case-crossover design can be biased in a situation where the exposure variable shows incomplete cyclic waves, and therefore it cannot completely control for temporal confounding.