title: Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis.
abstract: BACKGROUND
  The time stratified case cross-over approach is a popular alternative to conventional time series regression for analysing associations between time series of environmental exposures (air pollution, weather) and counts of health outcomes. These are almost always analyzed using conditional logistic regression on data expanded to case-control (case crossover) format, but this has some limitations. In particular adjusting for overdispersion and auto-correlation in the counts is not possible. It has been established that a Poisson model for counts with stratum indicators gives identical estimates to those from conditional logistic regression and does not have these limitations, but it is little used, probably because of the overheads in estimating many stratum parameters.
  
  
  METHODS
  The conditional Poisson model avoids estimating stratum parameters by conditioning on the total event count in each stratum, thus simplifying the computing and increasing the number of strata for which fitting is feasible compared with the standard unconditional Poisson model. Unlike the conditional logistic model, the conditional Poisson model does not require expanding the data, and can adjust for overdispersion and auto-correlation. It is available in Stata, R, and other packages.
  
  
  RESULTS
  By applying to some real data and using simulations, we demonstrate that conditional Poisson models were simpler to code and shorter to run than are conditional logistic analyses and can be fitted to larger data sets than possible with standard Poisson models. Allowing for overdispersion or autocorrelation was possible with the conditional Poisson model but when not required this model gave identical estimates to those from conditional logistic regression.
  
  
  CONCLUSIONS
  Conditional Poisson regression models provide an alternative to case crossover analysis of stratified time series data with some advantages. The conditional Poisson model can also be used in other contexts in which primary control for confounding is by fine stratification.
authors.affiliation: Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine (LSHTM), 15-17 Tavistock Place, London WC1H 9SH, UK. Ben.Armstrong@lshtm.ac.uk.
authors.forename: Ben G
authors.initials: BG
authors.lastname: Armstrong
authors.forename: Antonio
authors.initials: A
authors.lastname: Gasparrini
authors.forename: Aurelio
authors.initials: A
authors.lastname: Tobias
mesh_terms: D000397:Air Pollution; D016022:Case-Control Studies; D018592:Cross-Over Studies; D004781:Environmental Exposure; D006801:Humans; D015233:Models, Statistical; D016012:Poisson Distribution; D012621:Seasons; D016896:Treatment Outcome