Positive and negative predictive values (PPV and NPV) are often used in statistical analysis in medical studies. However, some docs get confused as to what these values actually mean, how they differ from sensitivity and specifity, and how they are calculated.
The first key to understanding these values is to remember that predictive values are a function of prevalence. The second key is that positive and negative predictive values are probabilities that a positive test result is actually a true positive.
The most important value of the above four for clinical care is the positive predictive value of a test or observation. It is the percentage of positive findings that correctly identify the presence of a condition in a patient sample.
An example would be a group of men with high PSA values. The percentage or proportion of these men that were then found to have prostate cancer would be the positive predictive value of a high PSA value. It should be noted that the positive predictive value rises with a rising prevalance and falls with a decreasing prevalence.
The sensitivity and specificity of a patient sample must be known to calculate positive and negative predictive values.
The equations to be used are as follows:
Sensitivity = (true positive observations/total patients with the condition) x 100
Specificty = (true negative observations/total patients without the condition) x 100
Positive predictive value = true positive observations/total positive observations) x 100
Negative predictive value = true negative observations/total negative observations) x 100
So, to put it simply, sensitivity and specificity compare positive and negative tests against the entire population that does or does not have the disease and positive and negative predictive values extract a number compared against only a subset of the entire population – that is, the total positives or total negatives.
If you have a population of 300 patients and 100 of them have a disease and 200 do not. You use a screening test that detects 80 true positives and 20 false negatives out of the 100 patients that actually have the disease. You also detect 30 false positives and 170 true negatives out of the 200 patients that do not have the disease.
The sensitivity is 80% because you detected 80 out of 100 patients that actually have the disease. The sensitivity is 85% because you correctly detected 170 out of 200 patients that do not have the disease.
The positive predictive value is 80/110 which is the 80 true positives divided by the total number of positives (both true and false) which is 80 + 30. The negative predictive value is 170/190 which is the number of true positives divided by the total number of negatives (both positive and negative) which is 170 + 20.
Remember, observations in conditions with low prevalance have a lower positive predictor value even with a high sensitivity and specificity because the true positives value is in the numerator of the equation.