Case-Crossover Analysis of Air Pollution Health Effects: A Systematic Review of Methodology and Application

The first epidemiologic studies on the impact of air pollution on health were undertaken as a consequence of the extreme pollution episodes that took place in the decades from 1930 to 1960. The association between air pollution and certain health variables was made clear by simple graphic representations or by comparisons of mortality rates for these time periods (Firket 1931; Logan 1953). Since that time, air pollution levels have fallen substantially, such that, to evaluate their effects on health, longer time series are required. To this end, epidemiologists began to use dynamic regression models in the 1970s that consisted of models in which the relationship between the dependent and explanatory variables were distributed over time, rather than being expected to occur simultaneously. Moreover, investigators were able to control for residual autocorrelation, with the error being specified by means of autoregressive integrated moving-average models (ARIMA). The problem with these types of models is that they assume that the dependent variable is distributed normally, which, in fact, is extremely rare in the daily outcome count variables of morbidity and mortality events (Saez et al. 1999). The early 1990s saw the appearance of linear models based on Poisson regression, in which a parametric approach was used to control for trend and seasonality because the event counts more typically have a Poisson distribution. These models use the variable “time” and its transforms, quadratic and sinusoidal functions (sine or cosine) of different frequency and amplitude, to control for the effect on the dependent variable (mortality or morbidity) of unmeasured variables that may vary seasonally, such as in pollen concentration, meteorological variables, and influenza outbreaks, or that may have a trend, such as changes in a city’s population distribution, in order to ascertain the effect of such variables on the dependent variable (Saez et al. 1999). Insofar as changes in a city’s population pyramid are concerned, Poisson regression is particularly useful only when cases, rather than the entire population, can be enumerated, because this form of regression analysis does not require knowledge of the denominator as long as population flux is in steady state (Loomis et al 2005). Nevertheless, Poisson regression poses the problem that, if any of these unmeasured variables follows a cyclical component of varying frequency and width (as might be the case of pollen concentration or influenza), the parametric functions of time or of its sinusoidal transforms cannot be easily “adapted” to such changes. These limitations led to the development of nonparametric Poisson regression with the application of generalized additive models (GAMs) that use nonparametric functions of the variable “time” (Kelsall et al. 1997), which adapt flexibly to the irregular cyclic components of unmeasured variables and allow for flexible fits for important variables, such as temperature, barometric pressure, and relative humidity, thus reducing any potential confounding due to these factors. One difficulty with this method is that the number of degrees of freedom of the smoothed nonparametric function must be specified by the researcher, with discrepancies arising as to the most appropriate way to calculate this. Because inappropriate determination of the number of degrees of freedom can lead to bias in the estimates of nonparametric Poisson designs, epidmiologists focused on the case-crossover (CCO) design that purported to control time trends. The CCO design was proposed by Maclure (1991) to identify risk factors of acute events; it is characterized by the fact that each subject serves as his or her own control by assessing referent exposure at a point in time prior to the event. By virtue of its design, this type of study controls for the influence of confounding variables that remain constant in the subject at both dates, that of the event and that of the referent time, such as sex, smoking history, occupational history, and genetics. This design was initially used to assess the effect of exposures measured at an individual level (telephone calls and traffic accidents, physical or sexual activity, and acute myocardial infarction) and was not applicable to exposures with a time trend, such as air pollution. Thus, if an investigator selected exposure control dates before the effect, and there was a trend, prior exposures would be systematically higher or lower than at the date of the effect. To circumvent this bias, Navidi (1998) developed a variant of this design, bidirectional CCO, which is conceptually characterized by having control time periods before and after the event, something that made it possible to control for the effect of long-term trend and seasonality on the variable “exposure.” This design was already appropriate for ecologic-type exposures, such as air pollution, because the existence of registries means that the values of such exposure can be ascertained even after the event. In addition, pollution values are not affected by the presence of prior morbidity and mortality events. In the CCO design, the referent time periods represent the counterfactual exposure experience of the individual, had he or she not become sick; because in air pollution pre- and postevent exposure values are independent of the hazard-period exposure, those that are postevent referent can be appropriate. One advantage of CCO design over Poisson regression is its ability to assess potential effect modification (i.e., statistical interaction) at the individual level rather than at the group level (Figueiras et al. 2005). As an alternative analytic methodology to Poisson regression, the CCO approach allows for direct modeling of interaction terms, rather than depending on multiple subgroup analyses (Figueiras et al. 2005). We conducted a systematic review of the CCO design used to study the relationship between air pollution and morbidity and mortality, from both a methodologic and an applied standpoint.