Time series and case-crossover methods are often viewed as competing alternatives in environmental epidemiologic studies. Several recent studies have compared the time series and case-crossover 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 over-dispersion 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.
Lu, Yun and Zeger, Scott L., "ON THE EQUIVALENCE OF CASE-CROSSOVER AND TIME SERIES METHODS IN ENVIRONMENTAL EPIDEMIOLOGY" (March 2006). Johns Hopkins University, Dept. of Biostatistics Working Papers. Working Paper 101.