Questions: (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. Give your answer to four decimal places. P(positive test disease) = 0.9810 Correct Answer (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. Give your answer to four decimal places. P(no disease negative) =

(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. Give your answer to four decimal places. P(positive test disease) = 0.9810 Correct Answer (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. Give your answer to four decimal places. P(no disease negative) =
Transcript text: (a) The sensitivity of a diagnostic test is its ability to correctly give a positive result when a person tested has the disease, or $\boldsymbol{P}$ (positive test | disease). Find the sensitivity of the dog cancer-detection test for lung cancer. Give your answer to four decimal places. \[ P(\text { positive test } \mid \text { disease })=\begin{array}{l} 0.9810 \\ \text { Correct Answer } \end{array} \] (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. Give your answer to four decimal places. \[ P(\text { no disease } \mid \text { negative })= \]
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Solution

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Solution Steps

To solve the given problem, we need to calculate the sensitivity and specificity of the diagnostic test using the provided data.

(a) Sensitivity is the probability that the test is positive given that the subject has the disease. This is calculated as the number of true positives divided by the total number of subjects with the disease.

(b) Specificity is the probability that the test is negative given that the subject does not have the disease. This is calculated as the number of true negatives divided by the total number of subjects without the disease.

Step 1: Calculate Sensitivity

The sensitivity of a diagnostic test is the probability that the test is positive given that the subject has the disease. It is calculated using the formula:

\[ \text{Sensitivity} = \frac{\text{True Positives}}{\text{Total with Disease}} \]

Given:

  • True Positives (cancer_positive) = 571
  • Total with Disease (total_disease) = 582

Substituting the values:

\[ \text{Sensitivity} = \frac{571}{582} \approx 0.9811 \]

Step 2: Calculate Specificity

The specificity of a diagnostic test is the probability that the test is negative given that the subject does not have the disease. It is calculated using the formula:

\[ \text{Specificity} = \frac{\text{True Negatives}}{\text{Total without Disease}} \]

Given:

  • True Negatives (control_negative) = 703
  • Total without Disease (total_no_disease) = 708

Substituting the values:

\[ \text{Specificity} = \frac{703}{708} \approx 0.9929 \]

Final Answer

\(\boxed{0.9929}\)

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