Poisson regression uses counts of events during a certain 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).
In my dataset (using SPSS), i have 7000 different patients with a different follow up time (max 5 years) and i want to count the times they come with a certain symptom (f.e. coughing) between 3 categories of people.
I already used ln(follow_up_time_years) as my offset variable, but since the chances of someone coming with this symptom are not very big, my parameter estimates are very small and not really expressive.
An idea would be to express these estimates in 1000 patient years, but I do not know how to put this in my poisson regression. I already calculated that the total no of patient years in my dataset is 32.707,01.
Is there an easy way to put this information in my regression model?
Thanks in advance
An interesting question, Maria.
It seems to me that presenting "patient-years" would be a useful approach for presenting your results. Not for your analysis but for presenting results. Patient-years would be more tangible, and meaningful, for your reader than some coefficient that comes out of your stats package. But it really is just an algebraic transformation of the coefficients, and so will be subject to the same caveats as the coefficients. That is, for example, if your exponentiated Beta suggests that males are 20% more likely to suffer a broken arm than females, and the 95% confidence range is between 1.05 and 1.35 then your confidence range for "Patient-years" should reflect that too.
- Other approaches to your problem...
- In addition to your Poisson Regression, consider Survival analysis. Given that you probably have "censored" data (your observations include events before or after your measured time range), in SPSS you would choose Kaplan-Meier. This link should get you started:
- https://statistics.laerd.com/spss-tutorials/kaplan-meier-using-spss-statistics.php
- If you're comfortable moving out of SPSS into the R Statistical Programming Language, then consider the types of analysis that actuaries use for Extreme Value modelling. This link gives you a sizeable list of options:
- https://cran.r-project.org/web/views/ExtremeValue.html
- (R can be a steep learning curve, but worth it if you're going to be doing a lot of these sorts of analyses. If your task is a one-off then ignore this suggestion)
Maybe I got it wrong, but shouldn't it be meaningful just to multiply the estimates? If, for instance, your model estimates 0.001 events per patient and year, this is the same as estimating 1 event per 1000 patient-years.
If I understand the question correctly, then your concern is simply that the estimated rates in each group are numerically quite small.
If so, this isn't really a problem, as it's just a function of what units you use in your data. If you prefer you can re-scale your variables or scale your coefficients (e.g. change your time unit from 1 to 1000 years, or equivalently rescale your event rate by 1000) .
What is of more interest is the relative rate of events between groups. That's why it is common to express the results of poisson regression as an incidence rate ratio (irr). This will be the same regardless of what time units you use.
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