Poisson regression uses counts of events during a sertain time interval. If I observe 500 subjects, half men, half women, for lets say one year, between January 1 and December 31 and counting all events (for example fractures) during that time, this would be easy to analyze (dependent: 50 fractures, continous covariate: 1 year, categorical: gender)
But lets say I have two groups (A and B) with 500 subjects in each, that are included in the study at different times during year 1 and followed for two more years. The event I'm counting is death. Each subject contributes with their own individual amount of person days, depending on when included, and if and when they died or not. Death is by nature an event that happens only once to each person, and is relatively rare so one day might have only one event occuring that day.
How do I arrange the analysis when subjects within the same group might have contributed with a wide array of person days. lets say that two subjects remained in the study for 300 days (died) and 750 days (survivor) repectively?
Categorical :Group A and B
Dependent: 70 in group A, 40 in group B during the study duration.
Continous Covariate: Person-days/months/year? Calendar-years from 1:st subject included? Other definition of time?
In your case person-days is called an exposure variable, and most statistical packages allow you to declare this as person-days as an exposure variable, and then handle it correctly.
The exposure is often called an offset and is ie natural log of time that is included on the right hand side of the model - you need to check exactly what your preferred software requires. Essentially this is an another predictor variable in the model but the associated coefficient is constrained to be 1 and is not estimated from the data.
see for example
http://stats.stackexchange.com/questions/11182/when-to-use-an-offset-in-a-poisson-regression
r code would like
glm(y ~ offset(log(exposure)) + x, family=poisson(link=log) )
Hi Ulf!
There's also a quite good (introductory) explanation on this wikipedia page: https://en.wikipedia.org/wiki/Poisson_regression. Further, in this PDF the author discusses Poisson regression and offsets in a bit more detail: http://www.stat.umn.edu/geyer/5931/mle/seed2.pdf.
Generally, since Adrian made it clear that the person-time is an exposure variable, finding a host of documents on Google is quite easy.
Cheers,
Ben
All answers put nicely what is needed to do.
Perhaps you want share the name of software and more specific help could come.
Thank you for your replies to my question, this was really helpful. Still one question remains. When I've logged person-days to use as offset, will this need to be considered when interpreting the output, in the same way as you do with logged variables in other types of regression analyses?
I use SPSS v.23
Thanks again for your help.
/Ulf
No - once you have declared the person-days variable as an exposure or offset variable, then it can be ignored, and the exponential of the regression coefficients represent incidence rate ratios
The log of the offset is simple taking account of differential exposure and its coefficient is constrained to the value 1.
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