13 Research methods, statistics, critical review and evidence-based practice13.5 Diagnostic studies
13.5.4 Prevalence and predictive values in diagnostic studies
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Written by Resident Doctor Committee · Published
Predictive values in the 2x2 table
Predictive values are read along rows defined by the test result. Sensitivity and specificity are read down columns defined by disease status.
The worked primary care sample of 200 has 36 true positives (TP), 32 false positives (FP), 4 false negatives (FN) and 128 true negatives (TN).
Its sensitivity is 90%, its specificity 80% and its prevalence (TP + FN) / 200 = 20%.
Positive predictive value
Positive predictive value (PPV) is the proportion of positive results that are true positives: PPV = TP / (TP + FP) = 36/68, about 52.9%.
PPV is the probability of disease given a positive result, whereas sensitivity is the probability of a positive result given disease.
PPV answers how likely a screen-positive person is to truly have the condition, and one tool in one sample can give widely different PPVs for different conditions.
When people act only on positive results, PPV shows the test's practical usefulness, because it depends only on the test-positive row.
The threshold with the highest PPV is the one at which a positive result most likely reflects true disease.
Negative predictive value
Negative predictive value (NPV) is true negatives divided by everyone who tests negative, not by everyone without the disorder: NPV = TN / (TN + FN) = 128/132, about 97.0%.
NPV is the probability that someone with a negative result is truly free of the condition, so here about 3% of negative screens are missed cases.
NPV is specific to each condition, so use the figure for the named disorder rather than a pooled figure for the tool.
Prevalence as pre-test probability
Pre-test probability equals the prevalence in the population the patient comes from, not the incidence, which counts new cases over time.
Sample prevalence estimates pre-test probability only if the sample represents the clinical population.
Accuracy figures from a selected clinical sample describe that sample and cannot give the prevalence in an unstudied population.
A case-control design fixes sample prevalence (100 cases and 100 controls give 50%), so its PPV and NPV are not clinical probabilities.
Why predictive values move with prevalence
Predictive values change with prevalence, while sensitivity, specificity and the likelihood ratios built from them do not. The table holds sensitivity at 90% and specificity at 80%.
Setting | Prevalence | True positives / all positives | PPV | NPV |
|---|---|---|---|---|
Community screening | 2% | 18/214 | 8.4% | 99.7% |
Primary care | 20% | 36/68 | 52.9% | 97.0% |
Psychiatric outpatients | 40% | 360/480 | 75.0% | 92.3% |
The positive likelihood ratio stays at 4.5 and the negative likelihood ratio at 0.125 in every setting.
PPV rises and NPV falls as prevalence rises, so the outpatient PPV of 75% cannot be applied to community screening.
A lower proportion of true positives in a lower-prevalence setting reflects the prevalence, not a worse test.
In practice, sensitivity and specificity can still shift with case mix, so use figures from a comparable population.
Choosing a screening tool
High sensitivity most justifies adopting a screening tool, because screening exists to avoid missing true cases.