Positive Predictive Value

The probability that an individual with a positive diagnostic test result truly has the condition being tested for.

Source: Altman & Bland 1994

Positive predictive value is the probability that a person who tests positive genuinely has the condition. It tells a patient with a positive result how seriously to take it, since a high value means a positive test very likely reflects real disease. This probability depends strongly on how common the disease is: when it is rare, even a good test throws up many false positives, so a positive result may still more often be wrong than right. The trustworthiness of a positive is what it conveys. Sackett and colleagues (1991) describe this measure.

Source: Sackett et al. 1991

Positive predictive value is calculated as the number of true positives divided by the total number with a positive result, that is true positives plus false positives. It therefore depends on the test's sensitivity and specificity and on the prevalence of the condition in the population tested. So positive predictive value is calculated from the proportion of positive results that are correct, combining the test's characteristics with the prevalence, meaning the same test yields different positive predictive values in populations with different prevalences, and this dependence on prevalence distinguishes it from sensitivity and specificity, which are properties of the test.

Source: Altman & Bland 1994

Prevalence strongly affects positive predictive value: when the condition is common, a positive result is more likely to be correct and the positive predictive value is high; when the condition is rare, even a good test produces many false positives relative to true positives, lowering the positive predictive value. So positive predictive value rises with prevalence and falls as prevalence declines, which means it must be interpreted in the context of the population tested, since a high positive predictive value in a high-prevalence setting does not carry over to a low-prevalence one, and this is why screening rare conditions yields many false positives.

Source: Altman & Bland 1994

Positive predictive value is the probability that a person with a positive result has the condition, while sensitivity is the probability that a person with the condition tests positive. Sensitivity is a property of the test, fixed across populations, whereas positive predictive value depends on prevalence and describes what a positive result means for a patient. So the two differ in direction and dependence: sensitivity conditions on disease status and is prevalence-independent, while positive predictive value conditions on the test result and varies with prevalence, making positive predictive value the more directly useful quantity for interpreting an individual patient's positive result.

Source: Altman & Bland 1994

Positive predictive value is useful because it directly answers the clinical question of how likely a patient with a positive result is to have the condition, which is what matters when acting on a positive test. It translates the test's performance into a probability relevant to the individual result. So positive predictive value is useful for interpreting a positive test in practice, guiding how confidently disease can be diagnosed and further action taken, though because it depends on prevalence it must be considered in the context of the specific population, which is why it is used alongside the prevalence-independent measures of sensitivity and specificity.

Source: Altman & Bland 1994