A diagnostic accuracy study asks a simple question, how well does this test tell the sick from the healthy. The answer lives in a 2×2 table, and a handful of numbers read off it describe the test from every angle. The trap is that two of them, the predictive values, quietly change with the setting, so a test that looks excellent in one clinic can disappoint in another. Reporting the full set, with intervals, is what a careful reader and the STARD guideline expect.

1Start with the 2×2 table

Every diagnostic result is one of four things. A true positive, where the test is positive and the disease is present. A false positive, positive but healthy. A false negative, negative but diseased. A true negative, negative and healthy. Put the test on the rows and the true disease status on the columns, and every measure of accuracy is a ratio read off this one table.

The diagnostic 2×2 table Disease + Disease − Test + Test − True positive TP False positive FP False negative FN True negative TN Sensitivity reads down the Disease + column, specificity down the Disease − column.
Figure 1. The whole study in one table. Correct results sit on the green diagonal, errors on the red one. Every accuracy measure is a ratio of these four cells.

2Sensitivity and specificity belong to the test

Sensitivity is how many of the diseased the test catches, read down the disease-positive column. Specificity is how many of the healthy it clears, read down the disease-negative column. Both are properties of the test itself, and they do not change when you move it to a population where the disease is more or less common. That stability is why they are the headline numbers of a diagnostic study, and why they always belong with a confidence interval.

3Predictive values change with prevalence

The predictive values answer the question a patient actually asks, given my result do I have the disease. That depends on how common the disease is to begin with. Take a test with 95% sensitivity and 90% specificity.

  • In a clinic where one patient in three already has the disease, a positive result is right about eight times in ten.
  • In population screening where one in a hundred has it, the same positive result is a false alarm more often than not.

The test did not change, the prevalence did. This is why a predictive value borrowed from a study with a different case mix can badly mislead.

The same test, a different answer Positive predictive value Disease prevalence screening, ~9% clinic, ~80%
Figure 2. Positive predictive value for a fixed test with 95% sensitivity and 90% specificity. It is low when the disease is rare and high when it is common, which is why the same test can look weak in screening and strong in a clinic.

4Likelihood ratios apply to one patient

A likelihood ratio folds sensitivity and specificity into a single number you can apply to an individual. The positive likelihood ratio is how much more likely a positive result is in a diseased person than in a healthy one, and the negative likelihood ratio does the same for a negative result. They do not depend on prevalence, which makes them a clean way to describe how much a result should move your thinking.

Reading a likelihood ratio LR+ above 10, or LR− below 0.1 large shift LR+ 5 to 10, or LR− 0.1 to 0.2 moderate shift LR+ 2 to 5, or LR− 0.5 to 0.2 small shift Anywhere near 1 not useful
Figure 3. A rough guide to likelihood ratios. Values far from 1 change a diagnosis a lot, values near 1 barely move it. A positive ratio above 10 or a negative ratio below 0.1 is usually called strong evidence.

5Report intervals and follow STARD

A point estimate without a confidence interval hides how much of the result could be chance, and STARD, the reporting guideline for diagnostic accuracy studies, expects intervals throughout and a flow diagram of who was tested. A few errors come up again and again, and each is visible from the methods and results alone.

Five diagnostic reporting mistakes reviewers catch Reporting accuracy alone, which hides where the errors are No confidence intervals on sensitivity and specificity Predictive values from a case-control sample read as general No STARD flow diagram of who was tested and excluded Indeterminate results quietly dropped from the table
Figure 4. Every item here is visible from the paper alone, without the raw data. Each one is a common reason a diagnostic study is sent back, and all are easy to avoid.

6Calculate the numbers in seconds, free

You can get every measure from your own 2×2 table with our free diagnostic test calculator. Enter the four counts and it returns sensitivity, specificity, predictive values, likelihood ratios and accuracy, each with a 95% confidence interval, plus a prevalence field that re-expresses the predictive values for your setting and the matching R code. Everything runs in your browser. The harder work, ROC curves, comparing two tests and choosing a cut-off, is where a statistician earns their fee.