cs156_cancer.py

# This short script ues some hypothetical numbers to calculate whether or not
# to operate on a possibly-cancerous lump, given the results of a screening test


u = {
     "healthy":100.0,
     "late-stage cancer":-10000.0,
     "surgery": -50.0,
    }

p = {
     "FP": 0.05,  # False Positive
     "TP": 0.01,  # True Positive
     "FN": 0.001,  # False Negative
     "TN": 0.939,  # True Negative
     }

assert 1.0 == p["FP"]+p["TP"]+p["FN"]+p["TN"]

# Given the various outcomes of the test, we can infer stats on the test:
p["positive"] = p["TP"] + p["FP"]
p["negative"] = p["TN"] + p["FN"]

print("The probability of a positive test result is: %0.3f"%p["positive"])
print("The probability of a negative test result is: %0.3f"%p["negative"])


# Calculate the expected utility of ignoring a positive test:
expected_positive_ignore_utility = p["FP"] * u["healthy"] + p["TP"]*u["late-stage cancer"]

# Calculate the expected utility of operating (given a positive test)
# Also we assume that the surgery is 100% reliable:
expected_positive_operate_utility = u["surgery"]

if expected_positive_ignore_utility > expected_positive_operate_utility:
    print("It is better to ignore the positive test result!")
else:
    print("It is better to operate with a positive test result!")
expected_positive = max(expected_positive_ignore_utility, expected_positive_operate_utility)

expected_negative_ignore_utility = p["FN"] * u["late-stage cancer"] + p["TN"]*u["healthy"]

# Calculate the expected utility of operating (given a negative test)
# Also we assume that the surgery is 100% reliable:
expected_negative_operate_utility = u["surgery"]

if expected_negative_ignore_utility > expected_negative_operate_utility:
    print("It is better to ignore the negative test result!")
else:
    print("It is better to operate with a negative test result!")

expected_negative = max(expected_negative_ignore_utility, expected_negative_operate_utility)

expected_test_utility = p["positive"]*expected_positive + p["negative"]*expected_negative
print("The expected utility of the test is: %f" % expected_test_utility)