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!