Very interesting - thanks for posting!

My knowledge was pre-Delta, and this study (in its current prepring form) suggests that for Delta, we have infection + mRNA vaccine > infection > mRNA vaccine.

Upon quick screening the authors do not discuss survivorship bias - which I would have expected.

Regarding what we discussed earlier the authors note:

"The advantageous protection afforded by natural immunity that this analysis demonstrates could be explained by the more extensive immune response to the SARS-CoV-2 proteins than that generated by the anti-spike protein immune activation conferred by the vaccine. However, as a correlate of protection is yet to be proven, including the role of B-Cell and T-cell immunity, this remains a hypothesis."

One thing that stands out is that the group that has been previously infected (both unvaccinated and single-jabbed post-infection) has been selected for survival already. I personally wouldn't draw the conclusion they propose from that population.