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Poisson designs and minimum detectable effects
Ian Adam’s posted a working paper the other day on power analysis for analyzing counts, Power Simulations of Rare Event Counts and Introduction to the ‘Power Lift’ Metric (Adams, 2024). I have a fe…
If we say we think best case the intervention had a 20% reduction in CED usage, we would then need exp(-se*2) = 0.8. log(0.8) ~ -0.22, so we need a standard error of se = 0.11 to meet this minimum detectable effect. When you have a fixed background count, in either in a treated or control arm, that pretty much puts a lower bound on the standard error. This approach relies on very similar Poisson models to what Ian is showing here, you just monitor the process over time and draw the error intervals as you go.
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