We are trying to establish if a significantly higher proportion of obstetric patients in our hospital are being admitted to intensive care than previously. We have nearly three years of historic data on the number of patients coming through the obstetric department and the number that subsequently end up on our ICU.

2012 - 5195 patients, 13 ICU admissions
2013 - 5917 patients, 18 ICU admissions
2014 - 3829 patients, 18 ICU admissions (8 months data)

I think the answer is to use a 2 x 3 contingency table and run a chi square test (which I've done - p = 0.18). If I project to 2014 data (5744 patients, 28 admissions) my p value improves to 0.09. Is this a reasonable approach to take? It feels overly simple.