Conditional Poisson models: a flexible alternative to conditional logistic case cross-over analysis

BMC Medical Research Methodology

Aurelio Tobias²  Antonio Gasparrini¹  Ben G Armstrong³ 

[1] Department of Medical Statistics, London School of Hygiene and Tropical Medicine (LSHTM), Keppel Street, London WC1E 7HT, UK;Institute of Environmental Assessment and Water Research (IDAEA), Spanish Council for Scientific Research (CSIC), C/Jordi Girona 18-26, 08031 Barcelona, Spain;Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine (LSHTM), 15-17 Tavistock Place, London WC1H 9SH, UK

关键词: Environment;    Time series regression;    Poisson regression;    Conditional distributions;    Statistics;   

Others  :  1090539
DOI  :  10.1186/1471-2288-14-122

 received in 2014-09-22, accepted in 2014-11-13,  发布年份 2014

【 摘 要 】

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.

【 授权许可】

   
2014 Armstrong et al.; licensee BioMed Central Ltd.

【 参考文献 】

• [1]Janes H, Sheppard L, Lumley T: Case-crossover analyses of air pollution exposure data: referent selection strategies and their implications for bias. Epidemiology 2005, 16:717-726.
• [2]Lu Y, Zeger SL: On the equivalence of case-crossover and time series methods in environmental epidemiology. Biostatistics 2007, 8:337-344.
• [3]Bhaskaran K, Gasparrini A, Hajat S, Smeeth L, Armstrong B: Time series regression studies in environmental epidemiology. Int J Epidemiol 2013, 42:1187-1195.
• [4]Levy D, Lumley T, Sheppard L, Kaufman J, Checkoway H: Referent selection in case-crossover analyses of acute health effects of air pollution. Epidemiology 2001, 12:186-192.
• [5]Hausman JA, Hall BH, Griliches Z: Econometric models for count data with an application to the patents-R&D relationship. In Book Econometric Models for Count Data With an Application to the Patents-R&D Relationship. Mass., USA: National Bureau of Economic Research Cambridge; 1984.
• [6]Farrington C: Relative incidence estimation from case series for vaccine safety evaluation. Biometrics 1995, 51:228-235.
• [7]Weldeselassie Y, Whitaker H, Farrington C: Use of the self-controlled case-series method in vaccine safety studies: review and recommendations for best practice. Epidemiol Infect 2011, 139:1805-1817.
• [8]Whitaker HJ, Paddy Farrington C, Spiessens B, Musonda P: Tutorial in biostatistics: the self‒controlled case series method. Stat Med 2006, 25:1768-1797.
• [9]Whitaker HJ, Hocine MN, Farrington C: On case‒crossover methods for environmental time series data. Environmetrics 2007, 18:157-171.
• [10]Preston D, Lubin J, Pierce D, McConney M: Epicure Release 2.10. Seattle: HiroSoft International; 1998.
• [11]Richardson DB, Langholz B: Background stratified Poisson regression analysis of cohort data. Radiat Environ Biophys 2012, 51:15-22.
• [12]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.
• [13]McCullagh P, Nelder JA: Generalized Linear Models (Monographs on Statistics and Applied Probability 37). London: Chapman Hall; 1989.
• [14]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.
• [15]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.
• [16]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.
• [17]Hondula DM, Barnett AG: Heat-related morbidity in Brisbane, Australia: spatial variation and area-level predictors. Environ Health Perspect 2014, 122(8):831-836.
• [18]Cummings P, McKnight B, Greenland S: Matched cohort methods for injury research. Epidemiol Rev 2003, 25:43.
• [19]Grundy C, Steinbach R, Edwards P, Green J, Armstrong B, Wilkinson P: Effect of 20 mph traffic speed zones on road injuries in London, 1986–2006: controlled interrupted time series analysis. BMJ 2009, 339:b4469.
• [20]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.
• [21]Whitaker HJ, Hocine MN, Farrington CP: The methodology of self-controlled case series studies. Stat Methods Med Res 2009, 18:7-26.