Adjusted incidence rate using margins after Poisson regression

[Jeff He]

Hi all,

In my project, I would like to calculate the adjusted (for age, education, etc) incidence rates of the outcome for smoking and non-smoking groups and the difference in adjusted incidence rates between two groups. I have individual-level data (rather than aggregated data like dollhill3).

I learnt a lot from a discussion about the calculation using Poisson regression at https://www.statalist.org/forums/for...-after-poisson

Two approaches were mentioned in that thread:

A:

webuse dollhill3, clear
poisson deaths i.smokes agecat, irr exp(pyears)
margins smokes, predict(ir)

B:

webuse dollhill3, clear
poisson deaths i.smokes agecat, irr exp(pyears)
egen sm_spec_pyears = mean(pyears), by(smokes)
margins, over(smokes) exp(predict(n)/sm_spec_pyears)

I still have a few questions about the methods:

Q1. The two approaches give quite different results (although both of them can be called 'adjusted incidence rate'). In your opinion, which approach is more commonly used or more practical in epidemiology studies?

Q2. No matter which approach I use, I need to describe the methods. Are the following descriptions appropriate and sufficient for an epidemiology journal?

For approach A
Adjusted incidence rates for smokers or non-smoker were calculated based on observed data on covariates using Poisson regression, assuming all participants were smokers or non-smoker, respectively.

For approach B
Adjusted incidence rates for smokers or non-smoker were calculated by dividing the total predicted number of the outcome by the total person-years in smoking or non-smoking group, respectively, after a Poisson regression was fit.

Q3. Can I use the -pwcompare- option in the -margins- command to get the 'incidence rate difference' between the two groups and claim this is an 'adjusted incidence rate difference'?

Thank you very much.

[Clyde Schechter]

I would incline towards approach A. I think your description of the approach would sound confusing to some readers. I would say it as "Incidence rates for smokers and non-smokers were adjusted using Poisson regression and standardizing to the observed distribution of all covariates."

Yes, you can use the -pwcompare- option in the -margins- command to get the incidence rate difference, and it would be reasonable to call that an adjusted incidence rate difference.

[Jeff He]

Thank you very much for your reply Dr Schechter!