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In epidemiology, exponentiated coefficients are often reported as odds ratios, relative risks/ incidence rate ratios or hazard ratios. In the analysis of cross-sectional data using Poisson/negative binomial models if we have an exposure time, the exponentiated coefficients may be called relative risks/incidence rate ratios. However, when analyzing cross-sectional data using Poisson/negative binomial models without a defined exposure time, what may we call the exponentiated coefficients?

Ayalew A.
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    With those models you model a count. A count always happen within a time/space frame, even if you don't explicitly specify it. The fact that you did not specify the time/space frame probably means that the time/space frame is equal across observations. So I would go back and consider how the data was collected and think about what the time/space frame is. – Maarten Buis Nov 18 '14 at 13:18
  • Thank you Maarten Buis. We collected data on the number of health complaints/disease symptoms people had in the 30 days time preceding our study. Though we asked the question for the past 30 days, the complaint/symptom might have started before 30 days and persisted to the time frame of our interest. In that case, I have doubt whether we could call the exponentiated coefficients 'incidence rate ratios' since in the epidemiological sense 'incidence' refers to the occurrence of 'new cases/events/etc' in the specified time frame. – Ayalew A. Nov 18 '14 at 14:18

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In a cross-sectional study, you are almost always getting prevalence data, so as a first step, you could consider these prevalence ratios.

But, it sounds like you are modeling the number of symptoms as your outcome based on some covariates, using Poisson or negative binomial models. So you have something like this model: $log(Symptom Count|Gender) =\beta_{0} +\beta_{1}*Gender$. If we want to compare men (gender = 1, say) and women (gender = 0, say), we might be interested in the ratio: $log(Symptom Count|Male) / log(Symptom Count|Female) = (\beta_{0} +\beta_{1}*1)/(\beta_{0} +\beta_{1}*0)$.

When we exponentiate this comparison, the left-hand-side is the ratio of the count of symptoms in men to the count of symptoms in women, and the right-hand-side is $e^{\beta{1}}$. Which is what you want to know the interpretation of. This is the ratio of the Average Symptom Count in men to the Average Symptom Count in women (and if there are other covariates, it is the adjusted Symptom Count ratio). Say you had a value like 1.2. You could interpret that as "on average, men in our study reported 20% more symptoms in the past 30 days than women, adjusting for ".

Ellie
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It depends who your intended audience is and how strongly they respond to terminology. In principle you can redefine a word to mean whatever you want it mean, as long as you are clear about it. So in some situation you would be fine with using the term incidence rate ratio and add a footnote describing the difference between the way you used the term and the way others used that term. Some fiels react very strongly to terminology, and in those fiels it would strategically bad to do so. In that case you can create a new term (say rate ratio) and define that in your text to fit your data and model.

Maarten Buis
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Better to name as RM (ratio of means) given the outcome is count. It may still be possible to use Poisson model for a binary outcome and this time, the effect estimate may be called PR (prevalence ratio).

Eskindir Loha
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