I'm sorry, are you asking for some sort of paper that shows one thing or another? Most of my conclusions about this are based on consultations with the epidemiologists and disease scientists at my employer (a pharma company that vends COVID tests and treatments, among other things). I trust their verbal communications a lot more than what gets published in the literature now.

My point is that none of the analysis being done now controls for anything and there are a ton of different reporting systems which are being compared and people are pointing at one country or another as "having done the right thing". We simply don't have the epistemic certaintly to declare that specific techniques worked or didn't. That sort of certainty comes only after decades of people working the data over and over to identify and correct for a lot of stuff missed in the heat of the pandemic.