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Let's take a look at some exanples...

Accuracy of Prostate Cancer Screening Tests

Two methods are commonly used to screen for prostate cancer: PSA (a blood test), and digital rectal exam (DRE). In this example, researchers used an abnormal PSA as an indicator for prostate cancer,  using a cut off of 4.0 micrograms per milliliter. The researchers found that this test had a sensitivity of 0.67 or 67%. In other words,two-thirds of all the cases who truly have prostate cancer were detected. One-third of the cases of prostate cancer go undiagnosed. On the other hand, when the PSA test indicated no disease, in almost all cases there was no disease. The specificity was 97%.

Test Characteristics of PSA and DRE
 
Sensitivity
Specificity
Positive Predictive Value
Abnormal PSA
(> 4.0 micrograms/milliliter)
0.67
0.97
0.43
Abnormal DRE
0.50
0.94
0.24

Adapted from: Kramer BS, Brown ML, Prorok PC, Potosky AL, Gohagan JK. Prostate cancer screening: what we know and what we need to know. Ann Int Med 1993;119:914-923

PSA then was  very good for giving a 'clear' prognosis, but was not a very good test for detecting disease (only 43% of the positive results actually had prostate cancer) For a positive result, the clinician will perform a follow-up procedure.

The other common test is the digital rectal exam (DRE). DRE has a low sensitivity of 50%, and the specificity is also lower than PSA.  Positive predictive value is even worse than PSA.

Accuracy of One or Two INDEPENDENTLY Administered Prostate Cancer Screening Tests

What if you used two tests?  Let's add these data to the table:

Test Characteristics of PSA and DRE
 
Sensitivity
Specificity
Positive Predictive Value
Abnormal PSA
(> 4.0 micrograms/milliliter)
0.67
0.97
0.43
Abnormal DRE
0.50
0.94
0.24
Abnormal DRE or Abnormal PSA
0.84
0.92
0.28
Abnormal DRE and Abnormal PSA
0.34
0.995
0.49

Adapted from: Kramer BS, Brown ML, Prorok PC, Potosky AL, Gohagan JK. Prostate cancer screening: what we know and what we need to know. Ann Int Med 1993;119:914-923

If either one or the other test is positive,  then  sensitivity is increased, but specificity reduced.

What if both tests are positive? Will using a higher standard for declaring disease result in lower sensitivity?  This is the case,  sensitivity goes down while the test becomes more specific. This approach does produce the highest positive predictive value.

If  the goal is to have the highest positive predictive value, the best choice is to require both tests to be abnormal. However, what is the consequence of  letting two-thirds of the prostate cancer cases go undiagnosed?   PSA is obtained from a simple blood draw. DRE is uncomfortable but temporary, so there is not much long-term consequence from either of the test procedures. Abnormal test results however, are often followed by biopsies which are costly, uncomfortable, and have significant co-morbidities associated with them. We don't want to put men through the follow-up unnecessarily. Prostate cancer is often slow growing and is not communicable. If the consequences of watchful waiting are not great, we may be willing to let a sizeable proportion of men who actually have prostate cancer go undiagnosised. The choice of tests and how to use them for screening purposes is heavily influenced by the consequences of making a wrong decision.

The PSA and DRE example used  two independent tests. What if a test is performed in a series?

Accuracy of Two Screening Tests Administered in Series

Consider a population in which there are 500 diabetic individuals among a total population of 10,000, i.e.  a 5% prevalence. Suppose you administer a non-fasting blood sugar test with a sensitivity of 350/500 (70%) and a specificity of 7600/9500 (80%).

table

 

Think About It!

Come up with an answer to this question and then click on the icon to the left to reveal the answer.

Using this one test administered to a population of 10,000 people, with prevalence of disease at 5%, how many people did you miss who had diabetes? How many false positives are there?


Think About It!

Come up with an answer to this question and then click on the icon to the left to reveal the answer.

What should we do about the 2250 persons for whom the test was positive? Should there be a second test?

 

We started with 10,000 people, 315 of these we have labeled as positive out of the total of 500 that have diabetes. Net sensitivity for the series is is 63%, 315 out of 500. Net specificity includes the 7600 persons correctly identified as negative with the first test plus the 1710 inidividuals who were ruled out  with the second test divided by the total of those without diabetes, 9500, for a net specificity of 98%.

The  net specificity is much higher by using the two tests in a series that by just using the first test in a population with a prevalence of 5%. A significant advantage is gained from performing the simple test up front, identifying individuals who are positive, and following up in this group with the more complex and costly test.