The positive and negative predictive values are the proportions of positive and negative
results in statistics and diagnostic tests that are true positive and true negative results.
The PPV and NPV describe the performance of a diagnostic test or other statistical measure.
A high result can be interpreted as indicating the accuracy of such a statistic.
The PPV and NPV is not intrinsic to the test—it depends also on the prevalence.
The PPV can be derived using Bayes' theorem.
Although sometimes used synonymously, a positive predictive value generally refers to what
is established by control groups, while a post-test probability 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 positive predictive value, the two are
numerically equal.
In information retrieval, the PPV statistic is often called the precision.
Definition Positive predictive value
The positive predictive value is defined as
where a "true positive" is the event that the test makes a positive prediction, and
the subject has a positive result under the gold standard, and a "false positive" is the
event that the test makes a positive prediction, and the subject has a negative result under
the gold standard.
The complement of the PPV is the false discovery rate:
Negative predictive value 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 complement of the NPV is the false omission rate:
Relationship Although sometimes used synonymously, a negative
predictive value generally refers to what is established by control groups, while a
negative post-test probability 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.
The following diagram illustrates how the positive predictive value, negative predictive
value, sensitivity, and specificity are related.
Note that the positive and negative predictive values can only be estimated using data from
a cross-sectional study or other population-based study in which valid prevalence estimates
may be obtained.
In contrast, the sensitivity and specificity can be estimated from case-control studies.
Worked example Suppose the fecal occult blood screen test
is used in 2030 people to look for bowel cancer: The small positive predictive value indicates
that many of the positive results from this testing procedure are false positives.
Thus it will be necessary to follow up any positive result with a more reliable test
to obtain a more accurate assessment as to whether cancer is present.
Nevertheless, such a test may be useful if it is inexpensive and convenient.
The strength of the FOB screen test is instead in its negative predictive value – which,
if negative for an individual, gives us a high confidence that its negative result is
true.
Problems with positive predictive value and negative predictive value
Other individual factors Note that the PPV is not intrinsic to the
test—it depends also on the prevalence.
Due to the large effect of prevalence upon predictive values, a standardized approach
has been proposed, where the PPV is normalized to a prevalence of 50%.
PPV is directly proportional to the prevalence of the disease or condition.
In the above example, if the group of people tested had included a higher proportion of
people with bowel cancer, then the PPV would probably come out higher and the NPV lower.
If everybody in the group had bowel cancer, the PPV would be 100% and the NPV 0%.
To overcome this problem, NPV and PPV should only be used if the ratio of the number of
patients in the disease group and the number of patients in the healthy control group used
to establish the NPV and PPV is equivalent to the prevalence of the diseases in the studied
population, or, in case two disease groups are compared, if the ratio of the number of
patients in disease group 1 and the number of patients in disease group 2 is equivalent
to the ratio of the prevalences of the two diseases studied.
Otherwise, positive and negative likelihood ratios are more accurate than NPV and PPV,
because likelihood ratios do not depend on prevalence.
When an individual being tested has a different pre-test probability of having a condition
than the control groups used to establish the PPV and NPV, the PPV and NPV are generally
distinguished from the positive and negative post-test probabilities, with the PPV and
NPV referring to the ones established by the control groups, and the post-test probabilities
referring to the ones for the tested individual.
Preferably, in such cases, a large group of equivalent individuals should be studied,
in order to establish separate positive and negative predictive values for use of the
test in such individuals.
Different target conditions PPV is used to indicate the probability that
in case of a positive test, that the patient really has the specified disease.
However there may be more than one cause for a disease and any single potential cause may
not always result in the overt disease seen in a patient.
There is potential to mixup related target conditions of PPV and NPV, such as interpreting
the PPV or NPV of a test as having a disease, when that PPV or NPV value actually refers
only to a predisposition of having that disease.
An example is the microbiological throat swab used in patients with a sore throat.
Usually publications stating PPV of a throat swab are reporting on the probability that
this bacteria is present in the throat, rather than that the patient is ill from the bacteria
found.
If presence of this bacteria always resulted in a sore throat, then the PPV would be very
useful.
However the bacteria may colonise individuals in a harmless way and never result in infection
or disease.
Sore throats occurring in these individuals is caused by other agents such as a virus.
In this situation the gold standard used in the evaluation study represents only the presence
of bacteria but not a causal bacterial sore throat illness.
It can be proven that this problem will affect positive predictive value far more than negative
predictive value.
To evaluate diagnostic tests where the gold standard looks only at potential causes of
disease, one may use an extension of the predictive value termed the Etiologic Predictive Value.
See also Binary classification
Sensitivity and specificity False discovery rate
Relevance Receiver-operator characteristic
Gain Diagnostic odds ratio
References and notes