Question 2.101

2.101 Patients in “poor” or “good” condition

Not all surgery cases are equally serious, however. Patients are classified as being in either “poor” or “good” condition before surgery. Here are the data broken down by patient condition. Check that the entries in the original two-way table are just the sums of the “poor” and “good” entries in this pair of tables.

Good Condition
Hospital A Hospital B
Died 6 8
Survived 594 592
Total 600 600
Poor Condition
Hospital A Hospital B
Died 57 8
Survived 1443 192
Total 1500 200
  1. Find the percent of Hospital A patients who died who were classified as “poor” before surgery. Do the same for Hospital B. In which hospital do “poor” patients fare better?
  2. Repeat part (a) for patients classified as “good” before surgery.
  3. What is your recommendation to someone facing surgery and choosing between these two hospitals?
  4. How can Hospital A do better in both groups, yet do worse overall? Look at the data and carefully explain how this can happen.

2.101

(a) For patients in poor condition, 3.8% of Hospital A's patients died, and 4% of Hospital B's patients died. (b) For patients in good condition, 1% of Hospital A's patients died, while 1.33% of Hospital B's patients died. (c) The percentage of deaths for both conditions is lower for Hospital A, so recommend Hospital A. (d) Because Hospital A had so many more patients in poor condition (1500) compared to good condition patients (600), its overall percentage is mostly representing poor condition patients, who have a high death rate. Similarly, Hospital B had very few patients in poor condition (200) compared to good condition patients (600), so its overall percentage is mostly representing good condition patients, who have a low death rate, making their overall percentage lower.

hosp