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 survival rate from surgery (in percent) for the two local hospitals.

Patient Entering Condition

Hospital A

Hospital B

Survivors from A (# and percent)

Survivors from B (# and percent)

Fair

700

100

600 or 86%

90 or 90%

Serious

200

200

100 or 50%

150 or 75%

Critical

100

700

10 or 10%

300 or 43%

Total

1000

1000

710 or 71%

540 or 54%

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

In the example, two parameters were used to determine which Hospital is superior in cardiac surgery, -

1. Success rate in all three categories of patients

2. Overall survival rate

For the first parameter, Hospital B has a higher success rate in all three categories of patients. So, Hospital B is superior in Cardiac surgery as per the first parameter.

For the second parameter, Hospital A has a higher overall success rate. So, Hospital A is superior in Cardiac surgery as per the second parameter. But looking at the percentage of critical patients entering in Hospital A = 100/1000 = 10% is lower than in Hospital B is 700/1000 = 70%. We assume that the chance of sucess in critical cardiac surgery is very low. (as can be seen 10 % for hospital A and 43% for hospital B), so the overall success rate of B is low. If we normalize the data and same percentage of patients with different conditions enter the hospital A and B, and calculate number of survivors based on their past performance, we get the overall success rate as

So, Hospital B has higher overall survival rate of (69.33%).

So, we determined that Hospital B has a higher success rate in all three categories of patients and also has higher overall survival rate c.ompared with Hospital A So, Hospital B is superior in Cardiac surgery

Patient entering condition Hospital A Hospital B Survivors from A (# and percent) Survivors from B (# and percent) Fair 100 100 86 (or 86%) 90 (or 90%) Serious 100 100 50 (or 50%) 75 (or 75%) Critical 100 100 10 (or 10%) 43 (or 43%) Total 300 300 146 (or 48.67%) 208 (or 69.33%)

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