Biostatistics Advance Access originally published online on June 29, 2006
Biostatistics 2007 8(2):337-344; doi:10.1093/biostatistics/kxl013
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On the equivalence of case-crossover and time series methods in environmental epidemiology
Department of Biostatistics, Johns Hopkins Bloomberg School of Public health, 615 North Wolfe Street, Baltimore, MD 21205-2179, USA ylu{at}jhsph.edu
Department of Biostatistics, Johns Hopkins Bloomberg School of Public health, 615 North Wolfe Street, Baltimore, MD 21205-2179, USA
* To whom correspondence should be addressed.
The case-crossover design was introduced in epidemiology 15 years ago as a method for studying the effects of a risk factor on a health event using only cases. The idea is to compare a case's exposure immediately prior to or during the case-defining event with that same person's exposure at otherwise similar "reference" times. An alternative approach to the analysis of daily exposure and case-only data is time series analysis. Here, log-linear regression models express the expected total number of events on each day as a function of the exposure level and potential confounding variables. In time series analyses of air pollution, smooth functions of time and weather are the main confounders. Time series and case-crossover methods are often viewed as competing methods. In this paper, we show that case-crossover using conditional logistic regression is a special case of time series analysis when there is a common exposure such as in air pollution studies. This equivalence provides computational convenience for case-crossover analyses and a better understanding of time series models. Time series log-linear regression accounts for overdispersion of the Poisson variance, while case-crossover analyses typically do not. This equivalence also permits model checking for case-crossover data using standard log-linear model diagnostics.
Keywords: Air pollution; Case-crossover design; Environmental epidemiology; Log-linear model; Overdispersion; Poisson regression; Time series
Received March 11, 2006; revised May 31, 2006; revised June 15, 2006; revised June 21, 2006; accepted for publication June 27, 2006.
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