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I've historical data about different types of interventions my nurses work on. Think about it this way: if a customer has diabetes and the nurse decides to intervene, then the nurse achieves a return $x on her effort with probability px. Aggregate data (at intervention type level) looks like:

interve_type  average_success average_return_on_success_cases tot_volume
A             0.23            $2000                           3000
B             0.07            $10000                          500
C             0.65            $700                            2500

If I set the total number of intervention (volume) I can do in a given time frame how do I find the optimal order of interventions? Is this as easy as deriving the expected return per intervention type and sorting on that?

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Assuming each intervention takes the same time (resources), then simply sorting on highest expected return and working your way down will do the trick.

For your data:

  1. $E[A] = 0.23*2000 = 460$
  2. $E[B] = .07 * 10000 = 700$
  3. $E[C] = .65*700 = 455$

So, given that you have a large volume of cases, the financial prioritization would be $B>A>C$.

However, using a purely financial approach can lead to perverse behavior. I'm sure there are other considerations, like keeping the most people alive/good prognosis. Intervention $B$ has a very low success rate, so I presume it means most people leave uncured. If you only have, say, 500 units of nursing time, then you're only going to treat people who come in needing $B$ and turn away all others (since they have negative opportunity cost). The end result will be that $0.07 * 500 = 35$ people will be helped and the rest of the people coming into the facility will either be untreated or not helped, giving your facility a very dismal satisfaction and outcomes rating!

So, word of caution -- medicine is more than just money (or it should be!)

Ok...stepping off soapbox.

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