Question

Story:

Your 10 year old son has had right lower abdominal pain and tenderness, with nausea and vomiting for the past 6 hours. He ate at a fast food restaurant earlier today. A CT scan of the abdomen with contrast can help identify appendicitis, but there is not one available in your town. The physician approaches you with a decision to do surgery now (assuming it is appendicitis) or wait and see what happens. You must make the decision.

Possible Outcome	Probability
Dies from surgery	0.010
Survives surgery	0.990
Appendicitis after waiting	0.5
Appendix ruptures	0.25
Remains the same	0.75
Nonspecific abdominal pain after waiting	0.5
Dies from surgery after appendix ruptures	0.040
Survives surgery after appendix ruptures	0.96
Dies from surgery after no rupture	0.002
Survives surgery after no rupture	0.998

Having surgery is a less desirable outcome than having no surgery.  

Possible Outcome	Utility
Dies	0.00
Survives surgery	0.95
No surgery	1.00

Decision node	Possible outcomes
Treatment decision	Surgery or wait and see
Surgery	Survives or dies
Wait and See	Appendicitis or nonspecific abdominal pain
Appendicitis	Ruptures or remains the same
Ruptures	Survives or dies from surgery
Remains the same	Survives or dies from surgery

Construct a decision tree and find the expected value for the surgery or wait and see decision.

Answer 1

Based on the expected values obtained below, it is always better to wait