Poisson regression using mid-year population estimates (census data)

[Dil Singh]

Dear all

I am reasonably familiar with using Poisson regression as part of "stset" when I have dates individuals entering observation, dates they leave or the event happens and whether or not an event happens. Calculating rates, rate ratios etc and regressing based on another variables seems relatively straightforward.

However, the project I am doing is using cross-sectional data of hospital admissions over a 5 year period and seeing what number of individuals are admitted with the disease of interest (an "event"). Whilst calculating ratios using all admissions that year as a denoninator is ok, I have been advised to try and calculate a crude incidence rate based on mid-year population estimates from the hospital catchment area.

I have done this by dividing the number of "events" over the mid-year population estimate and obtaining a rate in 100,000 person-years. Is this correct? Additionally, how would I examine for trends over time using a rate with these data since "strate" commands won't work here.

Many thanks in advance.

Regards, D

[Clyde Schechter]

Your calculation of a crude incidence rate sounds correct.

However, if you want to fit a Poisson model to the incidence process, you would not use those rates to do it. Rather, you would use a Poisson regression in which the numerator of those rates (# of events) is the dependent variable, and the denominator, is the exposure() variable. So if you have a data set with variables year, n_cases, and mid_year_population, and you wanted to see if there is a linear time trend in the rate, you would do:

poisson n_cases year, exposure(mid_year_population)

If you wanted to adjust the analysis, you can add other covariates to the regression equation. The model you are fitting here is:

n_cases ~ Poisson(mu), where mu = exp(b0 + b1*year + ln(mid_year_population)). For more details, and some worked examples, see the -poisson- chapter of the [R] manual.

The coefficients you get in the output are then the adjusted logarithms of the adjusted incidence rate ratios associated with a unit increase in the corresponding covariate. See also the -margins- command for calculating other interesting statistics from the Poisson model output.

[Dil Singh]

Thanks so much for that! That worked perfectly.

As you can tell, I'm a bit of newbie when it comes to Stata.

Thanks again.