The online version of this article (doi:10.1186/1471-2288-14-122) contains supplementary material, which is available to authorized users.
The authors declare that they have no competing interests.
BA drafted the manuscript. AG and AT contributed by discussion and comments on drafts and helped develop the R and Stata code respectively. All authors read and approved the final manuscript.
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.
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.
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.
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.
Additional file 1: R and Stata code for conditional Poission analysis. This is a pdf document. (DOCX 27 KB)
Additional file 2: London 2002–6 daily mortality data set for use in illustrative analyses. This is a Stata dataset (.dta). (ZIP 23 KB)
Hausman JA, Hall BH, Griliches Z: Econometric models for count data with an application to the patents-R&D relationship. Book Econometric Models for Count Data With an Application to the Patents-R&D Relationship. 1984, Mass., USA: National Bureau of Economic Research Cambridge CrossRef
Whitaker HJ, Hocine MN, Farrington C: On case‒crossover methods for environmental time series data. Environmetrics. 2007, 18: 157-171. 10.1002/env.809. CrossRef
Preston D, Lubin J, Pierce D, McConney M: Epicure Release 2.10. 1998, Seattle: HiroSoft International
Xu S, Gargiullo P, Mullooly J, McClure D, Hambidge SJ, Glanz J: Fitting parametric and semi-parametric conditional Poisson regression models with Cox’s partial likelihood in self-controlled case series and matched cohort studies. J Data Sci. 2010, 8: 349-360.
McCullagh P, Nelder JA: Generalized Linear Models (Monographs on Statistics and Applied Probability 37). 1989, London: Chapman Hall
Brumback B, Ryan L, Schwartz J, Neas L, Stark P, Burge H: Transitional regression models, with application to environmental time series. J Am Statist Ass. 2000, 95: 16-27. 10.1080/01621459.2000.10473895. CrossRef
Hausman J, Hall B, Griliches Z: Econometric models for count data with an application to the patents-R & D relationship. Econometrica. 1984, 52: 909-938. 10.2307/1911191. CrossRef
Bennett JE, Blangiardo M, Fecht D, Elliott P, Ezzati M: Vulnerability to the mortality effects of warm temperature in the districts of England and Wales. Nat Clim Change. 2014, 4: 269-273. 10.1038/nclimate2123. CrossRef
Tonne C, Beevers S, Kelly F, Jarup L, Wilkinson P, Armstrong BG: An approach for estimating the health effects of changes over time in air pollution: an illustration using cardio-respiratory hospital admissions in London. Occup Environ Med. 2010, 67: 422-427. 10.1136/oem.2009.048702. CrossRefPubMedPubMedCentral
- Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis
Ben G Armstrong
- BioMed Central
Neu im Fachgebiet AINS
Meistgelesene Bücher aus dem Fachgebiet AINS
Mail Icon II