As the other person said, really not sufficient to be determined. But in addition, it’s worth noting that even a drop in specificity from 99.5 to 98.5 has a huge statistical impact when you’re talking about such low prevalences. To speak with any real confidence in rates like this you need a very high specificity, and you need to be very confident in your specificity being accurate. In the absence of this, these results should be approached very cautiously. It’s even more fun when your prevalence is less than 1 – specificity, and you use it as a population screening instrument. You wouldn’t ordinarily do that; you’d use a gold-standard instrument with extraordinary specificity and very-well knew properties. Maybe. In fact, the Never Under Estimate A Grandpa Diver Shirt authors use that to adjust their estimated prevalence upwards from the number of positives they actually measured. The big thing is, we don’t have enough actual, verifiable information on the actual specificity (or sensitivity) of the test. I’m not comfortable drawing any conclusions based on that, and honestly, neither should the authors.
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In the Santa Clara study (with the analysis reexamined by people who don’t suck), for example, that 98.5 specificity is enough to drop the confidence interval to actually include 0. This means, more or less, that you’re 95% confident that the true value falls within that range, and that range includes the possibility that 0% of the population has COVID. This doesn’t mean the study is necessarily wrong or bad, but it means you probably haven’t created something that is a valuable reflection of Never Under Estimate A Grandpa Diver Shirt the real world. Not having a genuinely accurate estimate of the sensitivity can skew the statistics wildly. Now their data and analyses are better, so their estimates are much better.
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If I take the Bendavid (version 2) specificity and sensitivity data and use it to estimate the rate of infection using the data from the LA paper, I get a 95% chance that 2.8-6.2% of LA is infected (this ignores selection bias or any reweighting based on demographics). This seems in line with the paper OP posted, so I don’t think this is an issue here. I hadn’t, these were both new to me. My interest in this was just from reading the Never Under Estimate A Grandpa Diver Shirt news articles about Bendavid et al.’s research and finding the headlines surprising enough to go to the research itself. Version 1 of their paper had enough statistical issues that I wanted to figure out what the actual rate of infection was given their data (initially to post to Reddit where I saw the news). Eventually, I realized I had written enough to turn it into a paper, so I did. I’m a cognitive scientist so my interest here is mostly in statistics and the desire to correct misconceptions I see on the internet. Bendavid et al. might mention it somewhere in the appendix, so if you dig up the data for me I’d be happy to run it.
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