Problem 3 Consider two hospitals A and B that have the data relating to patient
ID: 2922218 • Letter: P
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Problem 3 Consider two hospitals A and B that have the data relating to patient condition before admission and survival outcomes after being admitted for treatment Outcome Condition Hospital A Hospital B Good Bad Good 10 40 800 200 Died 295 1000 SurvivedBad (a)Compare the two hospitals' overall percentage of deaths. If you needed surgery, would you prefer Hospital A or Hospital B? (b) If you needed surgery and your condition was rated as good, which hospital would you prefer'? (c) If you needed surgery and your condition was rated as bad, which hospital would you prefer? (d) Do your answers from (b) and (c) contradict your answer in (a)? What is this phenomenon called? Which hospital do you ultimately decide to be better?Explanation / Answer
ANSWER :-
(a)
Total percentage of deaths in Hospital A = 300 / 3300 = 9.09 %
Total percentage of deaths in Hospital B = 50/ 1050 = 4.76%
If you need surgery , Hospital B is more preferable as it has less percentage of deaths.
(b)
Probability of survival in hospital A with condition rated as good = 1000/1005 = 0.995
Probability of survival in hospital B with condition rated as good = 800 / 810 = 0.988
So Hospital A would be preferable.
(c)
Probability of survival in Hospital A with condition was rated as bad = 2000 / 2295 = 0.871
Probability of survival in Hospital B with condition was rated as bad = 200 / 240 = 0.833
So Hospital A would be preferable.
(d)
NO. The answers in (b) and (c) do not contradict in (a).
people who survived in good condition in Hospital A = 1000 / (5 + 295 + 1000 + 2000) = 1000 / 3300 = 0.303
people who survived in good condition in Hospital B = 800 / ( 10+ 40 + 800 + 200 ) = 0.761
So Hospital B is better.
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