Calculating Negative Likelihood Ratio

What is a Likelihood Ratio?

The likelihood ratio (LR) is calculated by dividing the probability of a test result in people with the condition by the probability of the same test result in people without the condition. It helps clinicians assess the diagnostic accuracy of a test.

There are four types of likelihood ratios:

• Positive LR: When a test result is more likely in people with the condition than without it (LR > 1)
• Negative LR: When a test result is less likely in people with the condition than without it (LR < 1)
• Positive predictive value (PPV): The probability that a person has the condition given a positive test result
• Negative predictive value (NPV): The probability that a person does not have the condition given a negative test result

Negative Likelihood Ratio

A negative likelihood ratio (LR < 1) indicates that a test result is less likely to occur in people with the condition than in those without the condition. This means the test result provides little or no diagnostic value for confirming the presence of the condition.

Negative likelihood ratios are common in screening tests where the test is more likely to be positive in healthy individuals than in those with the condition. For example, a test with a high false positive rate might have a negative likelihood ratio.

How to Calculate a Negative Likelihood Ratio

To calculate a negative likelihood ratio, you need the following information:

1. The probability of the test result in people with the condition (sensitivity)
2. The probability of the test result in people without the condition (specificity)

Here's the step-by-step calculation:

1. Identify the test result you're evaluating (positive or negative)
2. Find the sensitivity (probability of test result in people with condition)
3. Find the specificity (probability of test result in people without condition)
4. Divide the sensitivity by the specificity to get the likelihood ratio

Interpreting Negative Likelihood Ratios

Interpreting a negative likelihood ratio involves understanding what the value means in the context of the test and condition being evaluated. Here are some key points:

• A negative likelihood ratio (LR < 1) indicates the test result is less likely in people with the condition than without it
• The closer the ratio is to 1, the less useful the test is for diagnosing the condition
• Values between 0.1 and 0.9 suggest the test has limited diagnostic value
• Values below 0.1 suggest the test is not useful for diagnosing the condition

Worked Example

Let's calculate a negative likelihood ratio for a hypothetical test:

Calculating the negative likelihood ratio for a negative test result:

1. Probability of negative test in people with condition: 80/100 = 0.8
2. Probability of negative test in people without condition: 30/100 = 0.3
3. Negative LR = 0.8 / 0.3 ≈ 2.67

In this example, the negative likelihood ratio is 2.67, which is actually positive. For a true negative likelihood ratio, we would need a scenario where the probability of the test result is higher in people without the condition than with it.