Research has shown that specific biochemical markers are found exclusively in th

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. Here are the results for a random sample of 1287 breath specimens BREATH SPECIMEN FROMA DOG TEST CONTROL RESULT Negative Positive Total CANCER SUBJECT SUBJECT TOTAL 720 567 1287 707 7 714 13 560 573 (a) The sensitivity of a diagnostic test is its ability to correctly give a positive result when a person tested has the disease, or P(positive test | disease). Find the sensitivity of the dog cancer-detection test for lung cancer. (Round your answer to four decimal places.) 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. (Round your answer to four decimal places.) P(no disease | negative) -

Explanation / Answer

A)P(positive test)=567/1287

P(disease)=573/1287

P(positive test n disease)=560/1287

P(positive test |disease)=

= p(positive test n disease)/p(disease)

=(560/1287)/(573/1287)

=560/573

=0.9773

B)p(nodisease) =714/1287

P(negative)=720/1287

P(nodisease n negative) = 707/1287

P(no disease| negative)=p(nodisease n negative)/p(negative)

= (707/1287)/(720/1287)

= 707/720

=0.9819

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