In both cases linearity is not an unreasonable assumption (your criticism 1), although one should be cautious that * 'a' may not be stable wrt time, as testing regimes change (to allow different dates to be compared, cumulative hospitalisations might be better)
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* 'p' might reflect proportion of an 'effective' actively mixing population, rather than the whole population * there could be several other confounding factors systematically relating the two variables But it's not an unreasonable relation to investigate.
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Replying to @heald_j
But that's not true. They do not calculate either R or R0, they calculate a completely different metric from case numbers and called it R which tbh is another serious problem with the paper
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Replying to @GidMK
Look more closely, and you'll find that they have constructed R_ADIR as an estimate of R(t)
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Replying to @heald_j
That's certainly what they argue, but it is at best an extremely vague estimate and definitely not a realistic calculation
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Replying to @GidMK
See their definition of R_ADIR It's not a very sophisticated estimator; & its associated date should be shifted to account for date of test usually being sometime after the date of end of incubation. But I can't see why it should be grossly off, even if Fig 2 doesn't look righ
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Replying to @heald_j
At best, it's a remarkably crude estimate that disregards any uncertainty and uses the input of another model as an assumption. And to your earlier point, the prediction is not of proportion resistant - at best, it is proportion INFECTED which is obviously not the same
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Ideally, you'd want a more sophisticated estimate of R and some attempt at an SIR model, which any infectious disease epi could've done for them
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Just come back to this and realized that it's actually wrong - the R(ADIR) in the paper isn't in any way an estimate of R(eff). They've confused infectious period with serial interval, which I suspect has driven some of the bad calculations
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Replying to @GidMK
Agree to some extent - I don't think their derivation is good - but I think the actual calculation may not be that far off. Better might be 7-day rolling avg of new cases divided by previous 7-day rolling avg, all raised to the power of (6.5/7) if 6.5 days is the serial interval.
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Let me put it this way - if they've arrived at the right number using an incorrect calculation, then it's pretty unimpressive
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