I didn't know the comparative death rates, but I took it for granted that hospital births were not a random sample, and that they included more cases where problems were diagnosed during pregnancy.I don't know whether that claim is true, but I would imagine that in cases where a planned home birth runs into complications, an ambulance would be called and the woman would be taken to the hospital. High risk pregnancies are probably also more likely to be hospital births. What we do know is that for the infants, the rate of death is higher for home deliveries:
https://www.nytimes.com/2015/12/31/...n-us-a-new-study-examines-the-risks.html?_r=0