Solving previous problem

If we analyze the previous problem, we could consider that there are three decisions that the decision maker could take:

1. No treatment
   
2. Treatment with aspirin
   
3. Treatment with warfarin

So, we should draw a decision three with these three decisions at first branch of tree.
There are three different uncertainties that could appear for treatments. Tow of these three is applied also for no treatment.
If we draw the decision three it should looks like the following pictures. (I just provide two pictures, because the tree for treatment with warfarin is the same as the aspirin, just different valuse)






If we calculate the Expected Value (EV, which clarifies the best decision that we could make) it will be clear that patients should be treated with warfarin.

A decision tree of the problem is given at the end of this document.
No treatment & CVA & affected = ‐158,000 SEK
No treatment & CVA & unaffected = ‐76,600 SEK
No treatment & No CVA = 0
Aspirin/Warfarin & side‐effect & CVA & affected = ‐(15,000+158,000) = ‐173,000 SEK
Aspirin/Warfarin & side‐effect & CVA & unaffected = ‐(15,000+76,600) = ‐91,600 SEK
Aspirin/Warfarin & side‐effect & haemorrhage = ‐(15,000+32,000) = ‐47,000 SEK
Aspirin/Warfarin & no side‐effect & CVA & affected = ‐(15,000+158,000) = ‐173,000 SEK
Aspirin/Warfarin & no side‐effect & CVA & unaffected = ‐(15,000+76,600) = ‐91,600 SEK
Aspirin/Warfarin & no side‐effect & No CVA = ‐15,000 SEK
Folding back the tree:
EMV(no treatment) =( 0.25*(‐158,000) + 0.75*(‐76,600))*0.8 = ‐77,560
EMV(aspirin treatment) =(((( 0.25*(‐173,000)+0.75*(‐91,600))*0.644)+0.356*(‐47,000))*0.048) + (((0.25*(‐173,000)+0.75*(‐91,600))*0.5)+0.5*(‐15,000))*0.952 = ‐64,692
EMV(warfarin treatment) = (((0.25*(‐173,000)+0.75*(‐91,600))*0.5)+0.5*(‐47,000))*0.072 + (((0.25*(‐173,000)+0.75*(‐91,600))*0.1)+0.9*(‐15,000))*0.928 = ‐28,639
Thus, if we merely look at the costs for the hospital, patients should be treated with warfarin.

These kind of analysis are called subjective analysis. If you are interested to deal with these kind of problem, I recommend the Making Hard Decisions: An Introduction to Decision Analysis book by Robert T. Clemen.