Why is it more common for logistic regression (with odds ratios) to be used in cohort studies with binary outcomes, as opposed to Poisson regression (with relative risks)?
Undergraduate and graduate statistics and epidemiology courses, in my experience, generally teach that logistic regression should be used for modelling data with binary outcomes, with risk estimates reported as odds ratios.
However, Poisson regression (and related: quasi-Poisson, negative binomial, etc.) can also be used to model data with binary outcomes and, with appropriate methods (e.g. robust sandwich variance estimator), it provides valid risk estimates and confidence levels. E.g.,
- Greenland S., Model-based estimation of relative risks and other epidemiologic measures in studies of common outcomes and in case-control studies, Am J Epidemiol. 2004 Aug 15;160(4):301-5.
- Zou G., A modified Poisson regression approach to prospective studies with binary data, Am J Epidemiol. 2004 Apr 1;159(7):702-6.
- Zou G.Y. and Donner A., Extension of the modified Poisson regression model to prospective studies with correlated binary data, Stat Methods Med Res. 2011 Nov 8.
From Poisson regression, relative risks can be reported, which some have argued are easier to interpret compared with odds ratios, especially for frequent outcomes, and especially by individuals without a strong background in statistics. See Zhang J. and Yu K.F., What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes, JAMA. 1998 Nov 18;280(19):1690-1.
From reading the medical literature, among cohort studies with binary outcomes it seems that it is still far more common to report odds ratios from logistic regressions rather than relative risks from Poisson regressions.
For cohort studies with binary outcomes:
- Is there good reason to report odds ratios from logistic regressions rather than relative risks from Poisson regressions?
- If not, can the infrequency of Poisson regressions with relative risks in the medical literature be attributed mostly to a lag between methodological theory and practice among scientists, clinicians, statisticians, and epidemiologists?
- Should intermediate statistics and epidemiology courses include more discussion of Poisson regression for binary outcomes?
- Should I be encouraging students and colleagues to consider Poisson regression over logistic regression when appropriate?
exp(beta_M1) =/= 1/exp(beta_M2)). That disturbs me quite a bit. $\endgroup$