Home Screening Tests

Pre-Work: Home Screening Tests

Instructions: Read the article “Understanding Sensitivity and Specificity with the Right Side of the Brain” along with the scenario below and then answer the following questions.

Scenario: In Irvine, 11,477 people have G6PD deficiency out of a total population of 149,058. As a pharmacy owner in the city, two separate companies have approached you to purchase/place their screening test in your pharmacy. Tests A requires 35 µL of blood, results are available in 5 minutes using the device, and costs $40. Test B requires saliva from a mouth swab, the sample needs to be mailed back to the company for analysis (3 business days for results), and costs $15. The technical specifications of each test is listed below:

Test A can correctly identify 5000 of the 11,477 with G6PD deficiency, but also identifies 13,500 healthy people as having G6PD deficiency

Test B can correctly identify 9000 of the 11,477 with G6PD deficiency, but also identifies 27,000 healthy people as having G6PD deficiency

Questions:

1. For each test, calculate its sensitivity, specificity, PPV, and NPV

2. If a patient were to purchase this test, clearly and concisely describe in patient friendly language what sensitivity and specificity mean/measure

3. If a patient were to purchase this test, clearly and concisely describe in patient friendly language what positive and negative predictive value mean/measure

4. If the prevalence of G6PD deficiency were to increase, how would this affect the sensitivity/specificity of these tests?

5. If the prevalence of G6PD deficiency were to decrease, how would this affect the positive/negative predictive values of these tests?

Clinical review

Understanding sensitivity and specificity with the right
side of the brain
Tze-Wey Loong

Can you explain why a test with 95% sensitivity might identify only 1% of affected people in the
general population? The visual approach in this article should make the reason clearer

I first encountered sensitivity and specificity in medical
school. That is, I remember my eyes glazing over on
being told that “sensitivity = TP/TP+FN, where TP is
the number of true positives and FN is the number of
false negatives.” As a doctor I continued to encounter
sensitivity and specificity, and my bewilderment turned
to frustration—these seemed such basic concepts; why
were they so hard to grasp? Perhaps the left (logical)
side of my brain was not up to the task of
comprehending these ideas and needed some help
from the right (visual) side. What follows are diagrams
that were useful to me in attempting to better visualise
sensitivity, specificity, and their cousins positive predic-
tive value and negative predictive value.

Sensitivity and specificity
I will be using four symbols in these diagrams (fig 1).

Let us start by looking at a hypothetical population
(fig 2). The size of the population is 100 and the
number of people with the disease is 30. The
prevalence of the disease is therefore 30/100 = 30%.

Now let us imagine applying a diagnostic test for
the disease to this population and obtaining the results
shown in figure 3. The test has correctly identified
most, but not all of the people with the disease. It has
also correctly labelled as disease free most, but not all,
of the well people. Calculating sensitivity and
specificity will allow us to quantify these statements.

Sensitivity refers to how good a test is at correctly
identifying people who have the disease. When
calculating sensitivity we are therefore interested in
only this group of people (fig 4). The test has correctly
identified 24 out of the 30 people who have the

….is a well person

….is a person with a disease

….is a negative test result

….is a positive test result

and therefore….

….is a well person who tests negative (a true negative)

….is a person with a disease who tests positive (a true positive)

….is a well person who tests positive (a false positive)

….is a person with a disease who tests negative (a false negative)

Fig 1 Key to symbols

Fig 2 Hypothetical population

Fig 3 Results of diagnostic test on hypothetical population

Fig 4 Sensitivity of test

Department of
Community,
Occupational, and
Family Medicine,
National University
of Singapore,
Singapore
Tze-Wey Loong
clinical teacher
(part time)

Correspondence to:
T-W Loong, King
George’s Medical
Centre, Block 803
King George’s
Avenue, [01-144,
Singapore 200803,
Singapore
tzewey@
singnet.com.sg

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716 BMJ VOLUME 327 27 SEPTEMBER 2003 bmj.com

disease. Therefore the sensitivity of this test is
24/30 = 80%.

Specificity, on the other hand, is concerned with
how good the test is at correctly identifying people who
are well (fig 5). The test has correctly identified 56 out
of 70 well people. The specificity of this test is therefore
56/70 = 80%.

Having a high sensitivity is not necessarily a good
thing, as we can see from figure 6. This test has
achieved a sensitivity of 100% by using the simple
strategy of always producing a positive result. Its
specificity, however, clearly could not be worse, and the
test is useless. By contrast, Figure 7 shows the result a
perfect test would give us.

Predictive values
Now let us consider positive predictive value and nega-
tive predictive value. We will again use the population
introduced in figure 3. Positive predictive value refers
to the chance that a positive test result will be correct.
That is, it looks at all the positive test results. Figure 8
shows that 24 out of 38 positive test results are correct.
The positive predictive value of this test is therefore
24/38 = 63%.

On the other hand, negative predictive value is
concerned only with negative test results (fig 9). In our
example, 56 out of 62 negative test results are correct,
giving a negative predictive value of 56/62 = 90%.

The interesting thing about positive and negative
predictive values is that they change if the prevalence
of the disease changes. Let’s assume that the
prevalence of disease in our population has fallen to
10%. If we were to use the same test as before, we would
obtain the results in figure 10. The sensitivity and

Fig 5 Specificity of test

Fig 6 Test with 100% sensitivity

Fig 7 Perfect test

Fig 8

Positive predictive value

Fig 9

Negative predictive value

Positive predictive value
Negative predictive value

Fig 10 Results of testing population with disease prevalence of 10%

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specificity have not changed (sensitivity = 8/10 = 80%
and specificity = 72/90 = 80%), but the positive predic-
tive value is now 8/26 = 31% (compared with 63% pre-
viously) and the negative predictive value is
72/74 = 97% (compared with 90% previously).

In fact, for any diagnostic test, the positive
predictive value will fall as the prevalence of the disease
falls while the negative predictive value will rise. This is
not really so mystifying if we consider the prevalence to
be the probability that a person has the disease before
we do the test. A low prevalence simply means that the
person we are testing is unlikely to have the disease
and therefore, based on this fact alone, a negative test
result is likely to be correct. The following real example
should make this clearer.

A real example
So far we have been discussing hypothetical cases. Let us
now take a look at the use of the antinuclear antibody
test in the diagnosis of systemic lupus erythematosus. I
have massaged the numbers slightly to make them
easier to illustrate, but they are close to reported figures
in both the United Kingdom and Singapore.1 2 The
prevalence of systemic lupus erythematosus is 33 in
100 000, and the antinuclear antibody test has a sensi-
tivity of 94% and a specificity of 97%. To visualise this we
need to imagine 1000 of the 10 by 10 squares used in
the earlier figures (fig 11). Only one of these squares
contains some patients with the disease.

Figure 12 shows the result of applying the
antinuclear antibody test to this population. There are
many more true negative results than false negative
results and many more false positive than true positive
results. The test therefore has a superb negative predic-
tive value of 99.99% and a depressingly low positive
predictive value of about 1%. In practice, since most
diseases have a low prevalence, even when the tests we

use have apparently good sensitivity and specificity we
may end up with dismal positive predictive values.

Knowing that the positive predictive value of this
test is 1%, we may then ask: does a positive test result in
a female patient with arthritis, malar rash, and
proteinuria really mean that she has only a 1% chance
of actually having systemic lupus? The answer is no.

Only this square contains some
patients with systemic lupus
erythematosus (33 of them)

999 of squares consist
entirely of well individuals

Fig 11 Prevalence of systemic lupus erythematosus Fig 12 (top) Results of antibody nuclear test in systemic lupus
erythematosus; (bottom) negative and positive predictive values

No of true positives = 31

No of false positives = 3067

No of true negatives = 96 900

No of false negatives = 2

Negative predictive value = 96 900

96 900 + 2

= 99.99%

Positive predictive value = 31

31 + 3067

≅ 1%

Clinical review

718 BMJ VOLUME 327 27 SEPTEMBER 2003 bmj.com

Look at it this way—the patient is not a member of the
general population. She is from the population of
people with symptoms of systemic lupus erythemato-
sus, and in this population the prevalence is much
higher than 33 in 100 000. Hence the positive pre-
dictive value of the test in her case is going to be much
higher than 1%.

Using both sides of the brain
I hope that having worked through sensitivity and
specificity from scratch you will be wondering why it
initially seemed so confusing. It may be because of our
dependence on the left (linguistic) side of the brain.
When told that a test has a sensitivity of 94% and a
positive predictive value of 1%, our left brain has
difficulty grasping how a test can be 94% sensitive and
yet be correct only 1% of the time. It is partly misled by
the huge difference between prevalence, on the one
hand, and sensitivity and specificity on the other.
The prevalence of systemic lupus erythematosus is
0.033% while the sensitivity and specificity of the test
are about 95%; this difference is of several orders of
magnitude. If, for example, we developed a test with
sensitivity and specificity of 99.999% rather than 95%,
we would be able to boast of a positive predictive value
of 97%.

Competing interests: None declared.

1 Johnson AE, Gordon C, Palmer RG, Bacon PA. The prevalence and inci-
dence of SLE in Birmingham, England. Relationship to ethnicity and
country of birth. Arthritis Rheum 1995;38:551-8.

2 Boey ML. Systemic lupus erythematosus. Singapore Med J 1992;33:291-3.

Who invented that bleeping thing?

While preparing a talk on Thomas Fogarty, of balloon catheter
fame, I stumbled on information about a different gentleman
who was a joint winner with Fogarty of the much coveted
MIT-Lemelson prize. This person is someone who affects nearly
all doctors every day. Indeed, if he had not recently died, I am
sure many of us would love to get our hands on him. However, as
you read on and discover what a truly remarkable man he was,
you may see him and his invention in a different light.

Al Gross was born in 1918 in Toronto but grew up in
Cleveland, Ohio. He had a childhood interest in amateur radio
and went on to study for a diploma in electronics. He was a bright
student, and his area of interest lay in unexplored radio
frequencies above 100 MHz. He wanted to invent a small, mobile,
two way radio, and by1938, two years into his diploma, he had
invented the first handheld radios (“walkie-talkies”), which could
communicate for up to 30 miles. These caused quite a stir with
the military, who deemed their invention as “top secret.” They
quickly commandeered the idea and furthered its use to
introduce ground to air communication for fighter pilots and to
detonate bombs at a distance, such as for blowing up bridges.

After time, these long range radios were made public
knowledge, and, as a result, in 1946 citizen band (CB) radio was
invented, the familiar mode of communication of taxi drivers and
truckers.

A more sinister twist in Gross’s career occurred in 1949, when
he invented the telephone pager system. However, his first large
scale attempt to sell pagers to doctors did not meet with the
success he had anticipated. “In Philadelphia, there was a hospital
convention, and we set up the pager there. We demonstrated the
pager to all the hospital administrators, doctors, and nurses, and
they absolutely refused to go along with the idea,” said Gross.
“They claimed it would disturb the patient, the nurses wouldn’t
want to carry it, and the doctors would be disturbed in their game
of golf.”

Although the idea initially failed to catch on, New York’s Jewish
Hospital did install his paging system in 1950, and the Federal
Communications Commission officially approved it in 1958,
marking the era of mass production. The name “pager” is derived
from the Motorola Pageboy 1, one of the first commercially
available models.

As we are daily reminded, pagers are here to stay. Recent
estimates suggest that there are now over 60 million pagers in use
worldwide. All I can say in their defence is that, when you are out
on a Saturday night in the rain, and taxi control gets a cab to you
in five minutes using CB radio communication, perhaps you will
see your pager in a different light.

Fraser Smith research registrar, St James’s Hospital, Dublin, Republic
of Ireland

No of true positives

No of true negatives

No of well people

Specificity

Sensitivity

Divided by

No of people with the disease

Divided by

● For a given test, the lower the prevalence of the disease, the lower the positive predictive value
● Since most diseases have a low prevalence in the general population, even a test with an
apparently good sensitivity and specificity (>90%) may have a very low positive predictive value
● However, if this test is applied to a person with symptoms or signs of the disease, the positive
predictive value will be higher, as that person is from a population with a higher prevalence of
the disease

No of true negatives

No of negative results

NPV Divided by

No of people with the disease

PPV

No of true positives

Divided by

Summary points

Clinical review

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