Abstract
BackgroundThe 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.MethodsThe 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.ResultsBy 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.ConclusionsConditional 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.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2288-14-122) contains supplementary material, which is available to authorized users.
Highlights
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 and counts of health outcomes
* Correspondence: Ben.Armstrong@lshtm.ac.uk 1Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine (LSHTM), 15-17 Tavistock Place, London WC1H 9SH, UK Full list of author information is available at the end of the article those which we focus on here, pollution measurements are available only for a city or at least district, so are not unique to each individual
The standard analysis of case crossover studies is by conditional logistic regression on an expanded data set, in which for every death occurring on a day with at least one death, the day of death is entered as a “case” and other days in the same stratum as “controls” [1]
Summary
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. The standard analysis of case crossover studies is by conditional logistic regression on an expanded data set, in which for every death occurring on a day with at least one death, the day of death is entered as a “case” and other days in the same stratum as “controls” [1] This is somewhat computationally intensive, and cannot allow for overdispersion or auto-correlation in the original counts, which can distort estimates. It has been established that a Poisson model for counts with stratum indicators gives identical estimates and can allow for these phenomena [2], but it is little used, probably because of the overheads in estimating many stratum parameters
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