What is a public health test? A thread on population-level vs. individual-level optimal criteria (this is for a thread to be linked elsewhere so is probably quite incoherent)
From a clinical perspective we want a test that is optimal for helping the individual being treated. So we want to be as sure as possible that the result leads us to the right diagnosis and treatment
To achieve this, we might favour sensitivity and specificity above all else – those are the important metrics for treating our patient. We are probably happy to use a battery of expensive and time-consuming tests because we want to do the right thing for the person in front of us
But for a population, the optimal criteria may be quite different, because we are considering the outcome summed across many patients, not just one. Maybe we don’t have the resources to use the whole battery of tests on everyone...
... either we can use 3 tests on 10 people or 1 test on 30 people. Which is better from the perspective of the patient and which is better from the perspective of the population?
A toy example: say we are rolling many dice of different shapes. We have two strategies: either rolling 60x6-sided dice, or a 600x20-sided dice. Each person is a die, and the number of trials is our tested population. We get a “win” when we roll the highest number – a 6 or a 20.
If we take the perspective of an individual die (the individual-level metric), then we are better off being a 6-sided die. *I* only get 1 roll and *I* want it to be 6. *I* have a 1/6 chance of getting the max score vs. 1/20. That is the “individual-level optimal test”.
But across all dice, rolling a 6-sided dice 60 times *we* expect to get only 10 "wins". If instead *we* want to maximize the number of "wins" overall (either 6s or 20s), then rolling a 20-sided dice 600 times is a better choice, because we expect 30 “wins”.
A key additional factor for a communicable disease is that averting/treating infections is not only beneficial to the individual, but there is the knock-on effect benefiting everyone who is not yet, but COULD be infected. So we must factor that into our calculation.
To use the dice example, maybe we are allowed to roll an extra dice for each “win” we get. The 600x20 strategy becomes even better to maximize the number of wins overall – that is the “public health test”.
So the individual-level optimal approach is to use a 6-sided die. But the population-level optimal approach is to use many 20-sided dice.
I agree that the term "Public Health Test" is new without a rigorous textbook definition yet (AFAIK). But I think it's a useful framework, particularly in the context of an epidemic or pandemic. The term "Public Health Test" has a clear use and is distinct from a "Clinical Test".
Actually with these numbers the 6-sided strategy gives us slightly more "indirect wins", but you get the idea.
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