Question

Research has shown that specific biochemical markers are found exclusively in the breath of patients with lung cancer. However, no lab test can currently distinguish the breath of lung cancer patients from that of other subjects. Could dogs be trained to identify these markers in specimens of human breath, as they can be to detect illegal substances or to follow a person's scent? An experiment trained dogs to distinguish breath specimens of lung cancer patients from breath specimens of control individuals by using a food‑reward training method. After the training was complete, the dogs were tested on new breath specimens without any reward or clue using a double‑blind, completely randomized design. The results for a random sample of 1290 breath specimens.

Note: The numerical values in this problem have been modified for testing purposes.

	Breath specimen from A
Dog test result	Control subject	Cancer subject	Total
Negative	703	11	714
Positive	5	571	576
Total	708	582	1290

(a) The sensitivity of a diagnostic test is its ability to correctly give a positive result when a person tested has the disease, or ? (positive test | disease)P (positive test | disease) .

Find the sensitivity of the dog cancer‑detection test for lung cancer. (Enter your answer rounded to four decimal places.)

? (positive test | disease)=P (positive test | disease)=

(b) The specificity of a diagnostic test is the conditional probability that the subject tested doesn't have the disease, given that the test has come up negative.

Find the specificity of the dog cancer‑detection test for lung cancer. (Enter your answer rounded to four decimal places.)

? (no disease | negative)=P (no disease | negative)=

Question Source: Moore, The Basic Practice Of Statistics, 8e|Publisher: W.H. Freeman

Answer 1

Given that

Total = 1290

a)

The sensitivity of a diagnostic test is its ability to correctly give a positive result when a person tested has the disease

P(positive test | disease) = P(positive test and disease) / P(disease)

= (571/1290) / (582/1290)

= 0.9810

b)

The specificity of a diagnostic test is the conditional probability that the subject tested doesn't have the disease, given that the test has come up negative

? (no disease | negative) = P(no disease and negative) / P(negative)

= (703/1290) / (714/1290)

= 0.9846