Poisson regression model (created 1999-09-21).

Dear Professor Mean, I have just received feedback on a manuscript under review in which one reviewer recommended use of Poisson regression. I am not familiar with this technique--when it is appropriate and/or recommended, what assumptions the data must meet, whether the procedure in SAS? SPSS? I would appreciate a reference and/or citation to article(s) in which it has been used. Thanks! -- Denied Denise

Dear Denied,

I always distrust reviewers who insist on a specific statistical method. It's probably that they used this technique for their dissertation and they think that everyone else should follow their pioneering lead. This is not unlike the saying that when your only tool is a hammer, everything looks like a nail to you.

Is your data a nail or not? Well, Poisson regression assumes that your data follows a Poisson distribution, a distribution that we frequently encounter when we are counting a number of events. The distribution was first used to characterize deaths by horse kicks in the Prussian army. Let's hope that your application is not as unpleasant.

Further reading

Exact confidence interval for Poisson count. Tomas Aragon and Travis Porco. Accessed on October 29, 2002. http://www.medepi.org/epitools/rfunctions/cipois.html

Confidence Intervals for the Mean of a Poisson Distribution. P.D. M. Macdonald. Accessed on October 29, 2002. http://www.math.mcmaster.ca/peter/s743/poissonalpha.html

Summary

Denied Denise had a manuscript rejected. The reviewers suggested that she use Poisson regression. Professor Mean explains that you should consider using Poisson regression when you are trying to predict a count or a rate.

Resources

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Exact confidence interval for Poisson count. Tomas Aragon, Travis Porco. Accessed on 2002-11-27. www.medepi.org/epitools/rfunctions/cipois.html

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Maximum (Max) and Mid-P Confidence Intervals and p Values for the Standardized Mortality and Incidence Ratios. Pandurang M. Kulkarni, Ram C. Tripathi, Joel E. Michalek. American Journal of Epidemiology 1998: 147(1); 83-86. [Medline]

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The application of poisson random-effects regression models to the analyses of adolescents; current level of smoking. Ohidul Siddiqui. Preventive Medicine 1999: 2992-101. [Medline]

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Linear and nonlinear techniques for the deconvolution of hormone time-series. G. De Nicolao, D. Liberati. IEEE Trans Biomed Eng 1993: 40(5); 440-55.

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A more powerful test for comparing two Poisson means. K. Krishnamoorthy, Jessica Thomson, University of Louisiana at Lafayette. Accessed on 2003-02-10. www.mathpreprints.com/math/Preprint/krishna/20021020/1/?=&coll=Selection

Power in comparing Poisson means: I. One-sample test. LS Nelson. Journal of Quality Technology 1991: 23(1); 68-70.

Power in comparing Poisson means: II. Two-sample test. LS Nelson. Journal of Quality Technology 1991: 23(2); 163-66.

Sample size for Poisson regression. DF Signorini. Biometrika 1991: 78(2); 446-50.

Application of sample survey methods for modelling ratios to incidence densities. L. M. Lavange, L. L. Keyes, G. G. Koch, P. A. Margolis. Stat Med 1994: 13(4); 343-55.

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