Evidence explained: How good is my test?

Case study

Suppose your next patient this afternoon is Mr A, a 75-year-old gentleman who wants to discuss his lower urinary tract symptoms. He had a prostate specific antigen (PSA) test done last month and, when he phoned up, was told by a receptionist that it was ‘normal’. He’s now wondering how sure he can be that he doesn’t have prostate cancer? How do you respond and why?

What Mr A is really asking about is the validity of the PSA test: How reliable is a negative PSA test at ruling out prostate cancer? To be able to answer him properly we need to understand:

How accurate the test is

What a positive/negative test means

These basic statistical properties of tests are the positive predictive value (PPV), negative predictive value (NPV), sensitivity and specificity. These are fundamental properties of all tests; understanding them helps us know which tests are best to use, and how to counsel patients both before and after them. They are also on the AKT curriculum (just in case you needed extra motivation …).

Diagnostic accuracy studies pit new tests against the current ‘gold standard’ test to see how well they perform. All participants get both a new test (we’ll call this this ‘index test’) and the existing gold standard test (we call this the ‘reference test’), and from the results you can work out the sensitivity, specificity, PPV and NPV of the new test. You will usually see this data from these studies presented in 2 × 2 tables (as in Table 1).

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Table 1.

How to construct a 2 × 2 ‘test table’.

Index test	Reference test
	Test positive	Test negative
Test positive	A = True positives	B = False positives
Test negative	C = False negatives	D = True negatives

Table 2 tells you what each property of a test addresses and how to calculate it. If you get a question on this in an exam, always construct a 2 × 2 table like the one above as a starting point. You can then just apply these formulae to it.

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Table 2.

Meanings and formulae.

	Question this addresses	Formula (from Table 1)
Sensitivity	How good is this test at picking up people who have the condition?	a/(a + c)
Specificity	How good is this test at correctly excluding people without the condition?	d/(b + d)
Positive predictive value	If a person tests positive, what is the probability that they have the condition?	a/(a + b)
Negative predictive value	If a person tests negative, what is the probability that they do not have the condition?	d/(c + d)

So you will see that sensitivity and specificity tell us about the test ‘in general’, whereas PPV and NPV are really helpful in telling you what a particular test result means for the patient in front of you (the NPV might be particularly helpful in your chat with Mr A in the example above). It is worth remembering that a sensitive test is good at ruling a condition out, and a specific test is good at ruling it in (some people find this easier to remember as ‘SPIN’ and ‘SNOUT’). So, for example a d-dimer test (something I am sure we have all been caught out by before) is very sensitive but not specific, so it’s great for ruling out but not for ruling in. If the test comes back negative then it is highly unlikely that you have a clot, but a raised d-dimer doesn’t necessarily mean you do have a clot (there are lots of other reasons for it being high).

All too often patients and doctors alike assume that a positive test means a 100% chance of having the disease, or that a negative test totally rules it out. This certainly is not the case; understanding PPV’s and NPVs tells you why.