A family member can go to one of two local hospitals for heart surgery. Checking

Question

A family member can go to one of two local hospitals for heart surgery. Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived. Based on the numbers presented, which hospital do you think is superior in cardiac surgery? Surely hospital A is better, right? Now, let’s look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the number of survivors from surgery (in percent) for the two local hospitals. Patient Entering Condition Hospital A Hospital B Fair 700 100 Serious 200 200 Critical 100 700 Total 1000 1000 Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Explanation / Answer

Hospital B is definitely superior in cardiac surgery.

Because as the data presents, Hospital A saves 50% of 200 "serious" patients i.e the probability is 0.5 while Hospital B saves 75% of 200 "serious" patients i.e the probability is 0.75

Similarly Hospital A saves 10% of 100 "critical" patients i.e the probability is 0.1 and Hospital B saves 43% of 700 "critical" patients.

Thus, in either case the probability of survival of patients in Hospital B is greater than that of Hospital A.

So Hospital B is superior.

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