Bidirectional Case-Crossover Studies of Air Pollution: Bias from Skewed and Incomplete Waves
Lee, Jong-Tae, Kim, Ho, Schwartz, Joel, Environmental Health Perspectives
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 [Beta] = 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 1.044-1.056 at either a long-term trend or any skewed seasonal wave of [SO.sub.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. Key words: air pollution, case--crossover designs, control sampling strategy, epidemiologic methods. Environ Health Perspect 108:1107-1111 (2000) [Online 1 November 2000].
Two recently published case--crossover studies on air pollution epidemiology by Neas et al. (1) and Lee and Schwartz (2) present an attractive alternative approach to analyzing the mortality effects of short-term exposure to ambient air pollution. Instead of using time-series analysis, the case--crossover study design developed by Maclure (3) was applied to evaluate the association between daily death counts and air pollution. This approach compares exposures during the period of time of death (case period) with one or more periods when death did not occur (control periods) and evaluates the potential excess risk using conditional logistic regression.
The study design requires no additional control subjects to be sampled and can control individual susceptibility by making comparisons within a subject. Therefore, this design can control for all measured and unmeasured time-invariant potential confounders. As Pope (4) described, this approach controls for potential confounding variables such as day of the week, seasonality, long-term time trends, and changes in population size and composition by design rather than by statistical modeling.
Various case--crossover designs have been proposed, involving different strategies for selecting control information. In a case--crossover study, there are two main reasons for applying different control sampling schemes. One is to improve the relative efficiency described by Mittleman et al. (5), who showed that the empirical relative efficiency increased as the number of control periods sampled increased. The other reason is to control for exposures with temporal patterns such as long-term time trends and seasonal waves in exposure, outcome, or both (1,2,6,2). The latter problem is related to the validity of the case--crossover estimator. If the estimator were not valid, then the estimation of efficiency would not be meaningful. Navidi (6) demonstrated that the existence of systematic seasonal patterns in exposure could introduce bias into the estimates if air pollution exposure is the only source of the seasonal pattern in the outcome. …