False Negative Error Rate Calculation

What is False Negative Error Rate?

False Negative Error Rate (FNER) is the probability that a test result will be negative when the condition being tested for is actually present. In other words, it measures how often a test misses a true positive case.

FNER is particularly important in medical testing, where missing a positive case could have serious consequences. For example, in cancer screening, a false negative means a patient with cancer might be told they are healthy, leading to delayed treatment.

False Negative Error Rate Formula

The False Negative Error Rate can be calculated using the following formula:

Where:

• Number of False Negatives - The count of cases where the test result was negative but the condition was actually present.
• Number of Actual Positives - The total count of cases where the condition was actually present.

The result is typically expressed as a decimal or percentage. A lower FNER indicates better test performance.

How to Calculate FNER

To calculate FNER, follow these steps:

1. Determine the number of false negatives in your test results.
2. Determine the total number of actual positive cases.
3. Divide the number of false negatives by the number of actual positives.
4. Multiply the result by 100 to convert it to a percentage if desired.

For example, if a cancer screening test has 10 false negatives and there are 100 actual positive cases, the FNER would be 10%.

Example Calculation

Let's work through a practical example to illustrate how to calculate FNER.

Scenario

A new diagnostic test for a rare disease is evaluated on 500 patients. The results are as follows:

• True Positives (TP): 450
• False Positives (FP): 20
• True Negatives (TN): 20
• False Negatives (FN): 50

Calculation

First, identify the number of false negatives (FN) and the number of actual positives (TP + FN).

In this example, the FNER is 10%, meaning the test misses 10% of actual positive cases.

Interpreting the Result

Interpreting FNER requires understanding the context of the test and the consequences of false negatives. Here are some guidelines:

• Low FNER (e.g., <5%) - Indicates a highly accurate test with few missed positive cases.
• Moderate FNER (e.g., 5-15%) - Suggests the test may miss some positive cases, requiring further evaluation.
• High FNER (e.g., >15%) - Indicates the test is unreliable for identifying positive cases and may need improvement.

It's important to consider FNER in conjunction with other metrics like False Positive Rate (FPR) and overall accuracy to get a complete picture of test performance.