Since the outcome is count (for instance number of positives) you could either use poisson regression (if variances ~ mean) or negative binomial regression (if var > mean). Logistic regressions work as well if you use ratios. But If you feel extra spicy you could try a difference-in-difference (DID) regression, where

Y (outcome variable, proportion of positives) = β0 + β1(post) + β2(intervention) + β3(postxintervention) + ε

where post is coded for instance as 0 for pre-period and 1 after the intervention, intervention for instance 0 for control centers and 1 for treated.

Using this you can estimate the causal impact of the intervention while controlling for baseline differences, very easy to do in R

library(dplyr)

did

Marius Ole Johansen Thanks for your insightful comment! My data shows over dispersion, so I think using negative binomial regression would be the better choice.

If you have the counts for both the positive and negative results, logistic regression would be the better approach. The model is slightly complicated because you have multiple centers (locations) within each treatment group, and two time periods.

You could probably do an initial, more simple, analysis by pooling the centers within each treatment, and just looking at the proportions. Maybe just plot the proportions with confidence intervals about the proportions. A plot like this may tell the whole story.