In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

 and diagnostic testing, the negative predictive value (NPV) is a summary statistic used to describe the performance of a diagnostic testing procedure. It is defined as the proportion of subjects with a negative test result who are correctly diagnosed. A high NPV means that when the test yields a negative result, it is most likely correct in its assessment. In the familiar context of medical testing, a high NPV means that the test only rarely misclassifies a sick person as being healthy. Note that this says nothing about the tendency of the test to mistakenly classify a healthy person as being sick.

Definition

The Negative Predictive Value is defined as:

where a "true negative" is the event that the test makes a negative prediction, and the subject has a negative result under the gold standard, and a "false negative" is the event that the test makes a negative prediction, and the subject has a positive result under the gold standard.

The following diagram illustrates how the positive predictive value

Positive predictive value

In statistics and diagnostic testing, the positive predictive value, or precision rate is the proportion of subjects with positive test results who are correctly diagnosed. It is a critical measure of the performance of a diagnostic method, as it reflects the probability that a positive test...

, negative predictive value, sensitivity

Sensitivity

Stimulus|Sensitivity may refer to:* Sensitivity , the ability to react to a stimulus* Sensitivity , the strength of physical or emotional reaction in people* Sensitivity , variations in process dynamics and control systems...

, and specificity

Specificity

Specificity may refer to:* Being specific * Specificity , the proportion of negatives in a binary classification test which are correctly identified...

 are related.
Note that the positive and negative predictive values can only be estimated using data from a cross-sectional study

Cross-sectional study

Cross-sectional studies form a class of research methods that involve observation of all of a population, or a representative subset, at one specific point in time...

 or other population-based study in which valid prevalence

Prevalence

In epidemiology, the prevalence of a health-related state in a statistical population is defined as the total number of cases of the risk factor in the population at a given time, or the total number of cases in the population, divided by the number of individuals in the population...

 estimates may be obtained. In contrast, the sensitivity and specificity can be estimated from case-control studies.

If the prevalence, sensitivity, and specificity are known, the negative predictive value can be obtained from the following identity:

Worked example

Suppose that a fecal occult blood

Fecal occult blood

Fecal occult blood refers to blood in the feces that is not visibly apparent. A fecal occult blood test checks for hidden blood in the stool...

 (FOB) screen test is used in 2030 people to detect bowel cancer:
In this setting, with NPV = 99.5%, a negative test result may provide some reassurance that the subject is unlikely to have cancer. This high NPV value would be particularly notable if the cancer were relatively common. For example, if 5% of people in the population had bowel cancer, then a NPV of 99.5% would indicate that a person with a negative test result has much lower than the average population risk for bowel cancer. However if the prevalence of bowel cancer were 0.5%, a negative test result in this setting would be uninformative.

Relation to negative post-test probability

Although sometimes used synonymously, a negative predictive value generally refers to what is established by control groups, while a negative post-test probability

Pre- and post-test probability

Pre-test probability and post-test probability are the subjective probabilities of the presence of a condition before and after a diagnostic test, respectively...

 rather refers to a probability for an individual. Still, if the individual's pre-test probability of the target condition is the same as the prevalence in the control group used to establish the negative predictive value, then the two are numerically equal.

See also

• Positive predictive value
  Positive predictive value
  In statistics and diagnostic testing, the positive predictive value, or precision rate is the proportion of subjects with positive test results who are correctly diagnosed. It is a critical measure of the performance of a diagnostic method, as it reflects the probability that a positive test...
  
  
• Sensitivity and specificity
  Sensitivity and specificity
  Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as classification function. Sensitivity measures the proportion of actual positives which are correctly identified as such Sensitivity and specificity are statistical...
  
  
• Binary classification
  Binary classification
  Binary classification is the task of classifying the members of a given set of objects into two groups on the basis of whether they have some property or not. Some typical binary classification tasks are...
  
  

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