Hi Heidi,
I appreciate the details and explanations for your proposed study design. I think you are correct that the 5% change is meaningful, and may require large sample size (500-1000 depending on the trends). I think it would be incredibly helpful in your case to obtain the monthly c-section rate and plot it out x 24 months… then you can get very precise about how many months you will need to follow forward after your intervention.
Another analytical idea was to think about a design that compares cross-sectionally the c-section rate when doula services are actively available vs. not available… i don't know if you will have 24/7 availability, or if you expect some natural gaps. If you expect gaps, then that could serve as a control group possibly...