T-test or Z-test of two proportions?

Question

We did an intervention to reduce the frequency of use of a certain type of treatment and now I want to compare the data pre vs post intervention.

For each month I have the number of treatments per 1000 patient visits (because the monthly number of visits fluctuates). I have 6 months of pre-intervention data and 6 months of post-intervention data. Sample sizes are about 800 visits per month.

My first question: Is it better to

• A. do a t-test comparing the means of the monthly rate per 1000 patient visits, or
• B. take the raw data and calculate the rate per 1000 patient visits for the entire pre-intervention period, then do the same for the post-intervention period, and use the z-test of two proportions?

My second question: There are actually 3 subtypes of treatment. If I want to say "subtype A accounted for 50% of the total treatments given in the pre-intervention period but only accounted for 20% in the post-intervention period" what test would be best?

Answer 1

I would prefer to use (B) in a statistical test for the equability of treatment frequencies prior and posterior to the intervention. This is because you want to choose the statistic with lowest variance, and it is not difficult to show that alternative (A) has a greater variance than (B).

Regarding your second question the first thing that popped in my mind was why would you care for a change in relative proportion? Wouldn't it be more appropriate to test if the occurrence of, for example, treatment (1) had a significant increase or decrease after intervention? For me the difficult of adopting the comparison of relative proportions is the formulation of a set of statistical hypothesis. How would you formulate the null hypothesis of no change in relative proportions?