# Sensitivity

This is the probability of a positive test result from patients with disease a/a+c. Sensitivity of a test gives values from 0 to 1 (0-100%) and tells us how the test captures the presence of the reference condition in the body.

\begin{align} \text{sensitivity} & = \frac{\text{number of true positives}}{\text{number of true positives} + \text{number of false negatives}} \\ \\ & = \text{probability of a positive test given that the patient is ill} \end{align}

For example, if he had a mammography screening test for breast cancer with 100% sensitivity, it would mean that all women who had breast cancer, the tumour was actually detected. We have a group of 4 women - Lucy, Jane, Cathie and Lenka. Lucy has breast cancer. All women undergo the screening mammography. It detects Lucy and Jane as positive. Lucy is really positive. Jane is a false positive. Cathie and Lenka are actually negative. Nobody is falsely negative. When you enter the values into the formula above, we find that the test showed 100% sensitivity.

 Test Disease + Healthy- Total + a b a+b - c d c+d Total a+c b+d n