Comparing rates of hospital episodes in different groups

Hi there,

I'm trying to compare the rates of hospital admissions in different groups. For example:

200,000 people live in the local area, and they had 1,000 admissions over the year (500/100k).

1,000,000 people live in the wider area, and they had 5,500 admissions over the year (550/100k).

My first thought was to compare proportions with a z-test (i.e. comparing 0.50% with 0.55%). However, admissions are not really a proportion of the population, and individuals have multiple admissions, so we can't say that 0.50% of people in the local area were admitted to hospital.

So I'm looking for a test of the significance of the difference between the two rates. Is a z-test valid, or do I need something else?

Many thanks!
I don't know the number of unique patients with admissions. It may be possible to find that out, but it would be a lot of work. There definitely are multiple admissions - but what I'm mainly interested in is the rate of admissions for the population (rather than the number of individuals who have been admitted).


Omega Contributor
The z-test was a reasonable idea. However, I will stress one last time, that proceeding with it can result in a biased interpretation of the truth. The issue is you don't have a clear understanding of the numerator or situation context. Population A may be much older and a majority of visits are made up from readmissions or chronic use of just a few people, while Pop B is younger and a larger proportion of the population uses the hospital, but they only have one unique encounter or very few per person.

I am not sure if this breaks an assumption of the test or not, since the standard errors are calculated maybe on the assumption of independence on observation in the sample. I am uncertain on this, though.


Omega Contributor
I was also just thinking that given your scenario, there is a rare possibility that the numerator could be greater than the denominator, if there were more visits than people. So if you had to put it in words, what is the ratio you are actually calculating?


TS Contributor
My first thought was to compare proportions with a z-test (i.e. comparing 0.50% with 0.55%).
Does it play any theoretical role whether this difference is significant
or not? Moreover, as hlsmith explained, the results are nearly
uninterpretable without an idea of how utilization patterns differ
between loca area and wider area.

Just my 2pence

hlsmith - It is theoretically possible that the numerator is greater than the denominator. In this case, members of the population would on average visit hospital more than once per year. The rate is the number of admissions per member of the population.

Your points around the possible reasons for different rates are very valid. In this case, the populations are similar, demographically speaking, but more investigation of their characteristics and reasons for differences would be needed.

I spoke to a couple of statisticians and they felt that chi-square is the best test, treating each episode as a separate person. This allows a contingency table of 'local area / wider area' vs. 'admitted / not admitted'. They felt this was valid given the assumption that the pattern of multiple admissions is similar in each group. Obviously in the extreme scenario that the number of admissions exceeds the number of people, this would not be possible...

Thanks for the help.