Understanding and Use of Sensitivity, Specificity, and Predictive Values

T. Dhasaratharaman*

Statistician, Kauvery Hospitals, India

*Correspondence: tel: +91 90037 84310 Email: dhasa.cst@kauveryhospital.com

Background

We shall discuss the basic knowledge to calculate Sensitivity, Specificity, Positive Predictive Value (PPV) and Negative Predictive Value (NPV). We shall also discuss the advantage and limitations of these measures and how we should use these measures in our day-to-day clinical practice. I illustrate below how to calculate sensitivity and specificity, combining two tests and how to apply these results to our day-to-day practice.

Interpretation

Think of any screening test for a disease. For each patient:

  • the disease itself may be present or absent
  • the test result may be positive or negative

Table 1 shows 2 × 2 (two-by-two) table

Table 1. Venue time-based notion management in diabetic foot

Disease vs Test result Present Absent
Positive A (True Positive) B (False Positive)
Negative C (False Negative) D (True Negative)

Sensitivity

If a patient has the disease, we need to know how often the test will be positive, i.e., “positive in disease”.

This is calculated from:

S=TP/TP + FN or A/(A+C)

This is the rate of pick-up of the disease in a test, and is called the Sensitivity.

Specificity

If the patient is in fact healthy, we want to know how often the test will be negative, i.e., “negative in health”.

This is given by

S=TN/TN + FP or D/(B+D)

This is the rate at which a test can exclude the possibility of the disease, and is known as the Specificity.

Positive Predictive Value

If the test result is positive, what is the likelihood that the patient will have the condition?

Look at:

PPV=TP/TP + FP or A/(A+B)

This is known as the Positive Predictive Value (PPV).

Negative Predictive Value

If the test result is negative, what is the likelihood that the patient will be healthy?

Here we use:

NPV=TN/TN + FN or D/(C+D)

This is known as the Negative Predictive Value (NPV).

In a perfect test, the sensitivity, specificity, PPV and NPV would each have a value of 1. The lower the value (the nearer to zero), the less useful the test is in that respect.

Example 1

Imagine a blood test for gastric cancer, tried out on 100 patients admitted with haematemesis. The actual presence or absence of gastric cancers was diagnosed from endoscopic findings and biopsy. The results are shown

Disease vs Test result Present Absent
Positive A (True Positive) 20 B (False Positive) 30
Negative C (False Negative) 5 D (True Negative) 45

Sensitivity = 20/(20+5) = 20/25 = 0.8

If the gastric cancer is present, there is an 80% (0.8) chance of the test picking it up.

Specificity = 45/ (30+45) = 45/75 = 0.6

If there is no gastric cancer, there is a 60% (0.6) chance of the test being negative – but 40% will have a false positive result.

PPV = 20/ (20+30) = 20/50 =0.4

There is a 40% (0.4) chance, if the test is positive, that the patient actually has gastric cancer.

NPV = 45/ (45+5) = 45/50 = 0.9

There is a 90% (0.9) chance, if the test is negative, that the patient does not have gastric cancer. However, there is still a 10% chance of a false negative, i.e. that the patient does have gastric cancer.

Caution

The “Likelihood Ratio” (LR) is the likelihood that the test result would be expected in a patient with the condition compared to the likelihood that that same result would be expected in a patient without the condition.

To calculate the LR, divide the sensitivity by (1 – specificity).

Try using the example above to calculate the LR for a positive result.

LR = Sensitivity/(1-Specificity) = 0.8/(1 – 0.6) = 0.8/0.4 = 2

In this example, LR for a positive result = 2. This means that if the test is positive in a patient, that patient is twice as likely to have gastric cancer than not have it.

One thing you may notice is that in a rare condition, even a diagnostic test with a very high sensitivity may result in a low PPV.

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