Diagnostic test performance

What it is

Everything here comes off one 2 by 2 table, so hold the table first. Disease present and test positive is a, the true positive. Disease absent and test positive is b, the false positive. Disease present and test negative is c, the false negative. Disease absent and test negative is d, the true negative. Sensitivity is the proportion of people with the disease who have a positive test result: sensitivity = a/(a+c), that is true positives over true positives plus false negatives. Specificity is the proportion of people without the disease who have a negative test result: specificity = d/(b+d), that is true negatives over true negatives plus false positives. The short rule written beside them: specificity rules in the disease, sensitivity rules out the disease. The two that clinicians use run the other way round. Positive predictive value is the proportion of people with a positive test who have the disease, PPV = a/(a+b), and it says how likely it is that the patient has the disease. Negative predictive value is the proportion of people with a negative test who do not have the disease, NPV = d/(c+d). Both depend on the accuracy (likelihood ratio) of the test and on the prevalence, the pre-test probability, of the disease; prevalence is the patients who have the disease over the whole population, and predictive values are affected by it. Where the cut off is set decides both numbers: raise it and specificity improves, lower it and sensitivity improves. An ideal marker would separate the healthy population from the disease population completely, with no false positive cases, which means 100 percent specificity, and no false negative results, which means 100 % sensitivity. In the real world there is always an overlap between the disease population and the healthy population, so markers are not 100 % sensitive and not 100% specific, and the only lever left is choosing the cut off. Screening men above the age of 40 for prostate cancer shows the trade. A low cut off of 4 picks up all disease patients, 100 % sensitivity, but specificity will be 60 %, and the other 40 % who have levels above 4 are false positive because they are healthy. Moving the cutoff to 10 gives a specificity almost 80 % and a sensitivity near 80 %, close enough to each other to be used in screening; the healthy people who overlap above that cutoff are false positives and may have prostatitis, while those below it are false negatives from sampling error, small tumor sample or early disease. A cutoff of 20 gives specificity 100 % with zero false positives, but sensitivity around 50 %, so about half the patients with tumour are missed and the test cannot be used as screening. Higher cutoffs of tumour markers give better specificity; lower cutoffs give better sensitivity.