statistical aspects of screening tests

8/12/2019 Statistical Aspects of Screening Tests

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Statistical aspects of screening tests,

including knowledge of and ability to

calculate, sensitivity, specificity, positive

and negative predictive values, and the useof ROC curvesDiagnosis and Screening: Statistical aspects of

screening tests, including knowledge of andability to calculate, sensitivity, specificity,

positive and negative predictive values; and theuse of ROC curves

The validity of a screening test

The measures of sensitivity and specificity describe how well the proposed

screening test performs against an agreed 'Gold Standard' test. In medicine,

a gold standard test or criterion standard test is adiagnostictest or

benchmark that is regarded as definitive. This can refer to diagnosing a

disease process, or the criteria by which scientific evidence is evaluated. The

actual gold standard test may be too unpleasant for the patient, too

impractical or too expensive to be used widely as a screening test.

Assessment of test performance is usually presented in a two by two table(3.2.1). The disease status (as assessed through the Gold Standard) is

conventionally put in the top row and the screening test result in the first

column.

Table 3.2.1

Disease status as determined by 'Gold Standard'

Disease No Disease

Test

positive

True positives

(a)

False positives

(b)

Total test positives

(a+b) Positive predictive

value

Test False negatives True negatives Total test negatives Negative predictive

value
http://en.wikipedia.org/wiki/Diagnostichttp://en.wikipedia.org/wiki/Diagnostichttp://en.wikipedia.org/wiki/Diagnostichttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Negative_predictive_valuehttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Positive_predictive_valuehttp://en.wikipedia.org/wiki/Diagnostic


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negative (c) (d) (c+d)

Total with disease(a+c)

Total without disease(b+d)

Total screened

(a+b+c+d)

Sensitivity

Specificity

True positives= number of individuals with disease and

apositive screening test (a)

False positives= number of individuals without disease but have

apositivescreening test (b)

False negatives= number of individuals with disease but have

a negativescreening test (c)

True negatives= number of individuals without disease and

a negativescreening test (d)

Sensitivity and specificity

Sensitivityis defined as the ability of the test to detect all those with

disease in the screened population. This is expressed as the proportion of

those with disease correctly identified by a positive screening test result

Sensitivity =

number of true positives

= a/ (a+c)

total with disease

Specificityis defined as the ability of the test to identify correctly those free

of disease in the screened population. This is expressed as the proportion of

those without disease correctly identified by a negative screening test result

Specificity =

number of true negatives

= d/ (b+d)

total without disease

Positive and negative predictive values
http://en.wikipedia.org/wiki/Specificity_(tests)http://en.wikipedia.org/wiki/Specificity_(tests)http://en.wikipedia.org/wiki/Specificity_(tests)


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The positive predictive value (PPV) describes the probability of having

the disease given a positive screening test result in the screened population.

This is expressed as the proportion of those with disease among all

screening test positives.

PPV =

number of true positives

= a / (a+b)

total test positives

The negative predictive value (NPV)describes the probability of not

having the disease given a negative screening test result in the screened

population. This is expressed as the proportion of those without disease

among all screening test negatives.

NPV =number of true negatives

= d / (c+d)

total test negatives

The effect of disease prevalence

Sensitivity and specificity are independent of prevalence of disease,

i.e. test specific (they describe how well the screening test performs against

the gold standard).

PPV and NPV however are disease prevalence dependant, i.e.

population specific. PPV and NPV give information on how well a test

screening test will perform in a given population with known prevalence.

Generally a higher prevalence will increase the PPV and decrease the NPV.

Knowledge of expected disease prevalence in the target population is

necessary when a screening activity is introduced to mitigate the potential

harms and costs (see ethical, economic, social, legal aspects).

Practical examples using sensitivity, specificity, Gold (reference)

Standard, positive predictive value, and negative predictive value

(amended fromhttp://www.musc.edu/dc/icrebm/sensitivity.html)

A new ELISA (antibody test) is developed to diagnose HIV infections. Serum

from 10,000 patients that were positive by Western Blot (the Gold Standard
http://www.musc.edu/dc/icrebm/sensitivity.htmlhttp://www.musc.edu/dc/icrebm/sensitivity.htmlhttp://www.musc.edu/dc/icrebm/sensitivity.html


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assay) was tested, and 9,990 were found to be positive by the new ELISA

screening test. The manufacturers then used the ELISA to test serum from

10,000 nuns who denied risk factors for HIV infection. 9,990 were negative

and the 10 positive results were negative by Western Blot.

Test performance assessment populations

HIV

Infected Not infected

ELISA test

+ 9,990 (a) 10 (b)

- 10 (c) 9,990 (d)

10,000 (a+c) 10,000 (b+d)

Sensitivity = a/(a+c)

= 9990/(9990+10)

= 99.9%

Specificity= b/(b+d)

= 9990/(9990+10)

= 99.9%

With a sensitivity of 99.9% and a specificity of 99.9%, the ELISA appears to

be an excellent test.

Application to population level

The test is applied to a million people where 1% are infected with

HIV(assuming the sensitivity and specificity remain the same) (Table 1).

Of the million people, 10,000 would be infected with HIV. Since the new

ELISA is 99.9% sensitive, the test will detect 9,990 (true positives - a)

people who are actually infected and miss 10 (false negative - c). Looking at

those numbers the test appears very good because it detected 9,990 out of

10,000 HIV infected people. But there is another side to the test. Of the 1

million people in this population, 990,000 are not infected. Looking at the

test results of the HIV negative population (the specificity of the assay is

99.9%), 989,010 are found to be not infected by the ELISA (true negatives -

d), but 990 individuals who are found to be positive by the ELISA (false

positives --b). If these test results were used without confirmatory tests (the

gold standard Western Blot), 990 people or approximately 0.1% of the


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population would have been told that they are HIV infected when in reality,

they are not.

Table 1

1% Prevalence

HIV

Infected Not infected

Test

+ 9990 (a) 990 (b)Test positives

a+b

Positive Predictive Val

= 9990/(9990+=91%

- 10 (c) 989,010 (d)

Test

negatives

c+d

Negative Predictive

d/(c+d) =989,010/(10

= 99.9%

HIV positive

10,000

HIV

negative999,000

Total screened=

a+b+c+d

Sensitivity =

99,9%

Specificity

= 99,9%

Sensitivity and specificity are not the only performance features because

they do not address the problems of the prevalence of disease in differentpopulations. For that, the understanding of the positive and negative

predictive value is crucial. The paragraphs below outline the effects of

prevalence on the predictive value of test results in two different

populations.

Population A

Blood donors have already been screened for HIV risk factors before they

are allowed to donate blood, so that the HIV sero-prevalence in this

population is closer to 0.1% instead of 1% (Table 2).For every 1,000,000

blood donors, 1,000 are HIV positive. With a sensitivity of 99.9%, the ELISA

would pick up 999 of those thousand, but would fail to pick up one HIV sero-

positive individual. Of the 999,000 uninfected individuals, the test would

label 998,001 individuals assero-negative (true negatives). The ELISA

would, however, falsely label 999 individuals as sero-positive (false-


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positives). Testing the blood donor pool results in as many false positive as

true positive results.

(Table 2)

,1% Prevalence

HIV

+ -

Test

+ 999 (a) 999 (b)Test positives

1,998

Positive Predictive Valu

a/(a+b)

=50%

- 1 (c) 998,001 (d) Test negatives998,002

Negative Predictive Valu

d/(c+d)=99.999%

HIV positive1000

HIV negative999,000

Totala+b+c+d

Sensitivity

99.9%

Specificity

99.9%

Population B

The second population consists of former IV drug users attending drug

rehabilitation units, with a prevalence of 10% (Table 3). For a million of

these individuals, 100,000 would be HIV-infected and 900,000 would be HIV

negative. The HIV ELISA would yield 99,900 true positives and 100 false

negatives. Of the 900,000 HIV negative individuals, the ELISA will find

899,100 to be negative but falsely label 900 as positive.

(Table 3)

0% Prevalence

HIV

+ -

Test + 99,900 900 Test positivesPositive Predictive Valu

a/(a+b)


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(a) (b) 100,800 =99%

-100

(c)

899,100

(d)

Test negatives

899,200

Negative Predictive Valu

d/(c+d)

=99.999%

HIV negative100,000

HIV negative900,000

Total screened=a+b+c+d

Sensitivity

99.9%

Specificity

99.9%

Summary of example

The sensitivity and specificity of the test has not changed. It is just that the

predictive value of the test has changed depending on the population being

tested.

The positive predictive value is how many of the test-positives truly have the

disease. In the first example with a 1% sero-positive rate, the ELISA has a

positive predictive value of 0.91 (91%). When looking at the blood donor

pool with a 0.1% sero-prevalence, the positive predictive value is only 0.5

(50%), whereas in the high- prevalence population of intravenous drug

users, the positive predictive value is 0.99 (99%).

Although the sensitivity of the ELISA does not change between populations,

the positive predictive value changes drastically from only half the people

that tested positive being truly positive in a low- incidence population to

99% of the people testing positive being truly positive in the high-

prevalence population. The negative predictive value of the ELISA also

changes depending on the prevalence of the disease.

False positive results produced by high sensitivity of the screening test can

easily be excluded by a confirmatory test with high specificity.

Information on the possibility of false positive results and subsequent action

should be provided to individuals prior to being screened (see informed

consent).

The use of receiver operating characteristic (ROC) curves


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The two most common uses of ROC curves in medicine are:

- to set a cut-off value for a test result (for continuous diagnostic variables)

- to compare the performance of different tests measuring the same

outcome (test validation)

In order to set the cut-off value for a continuous diagnostic variable (e.g.

blood lactate level as a marker for risk of death in A&E admissions) the

proportion of true-positives and false-positives are calculated for possible

values. These proportions are sensitivity and 1-specificity. The ROC curve is

a graphical display of the how the proportions of true positives and false

positives change for each of the possible pre-determined values.

The choice of a particular cut-off value for a test is essentially a decisioninformed by the attempt to maximize sensitivity and specificity. Generally,

there is a trade-off between sensitivity and specificity, and the decision must

be based on their relative importance. However, the decision to use a

diagnostic test depends not only on the ROC analysis but also on the

ultimate benefit to the patient. The prevalence of the outcome, which is the

pre-test probability, must also be known.

In situations where there are multiple laboratory tests for a particular

condition, the area under each respective ROC curve (AUROC) can be usedto compare the overall performance of those tests. The perfect test would

have an AUROC of 1, whereas a test with no diagnostic capability would

have an AUROC of 0.5. An AUROC of 0.5 indicates that a test based on that

variable would be equally likely to produce false positive or true positive

results. This equality is represented by a diagonal line from (0,0) to (1,1)

on the graph of the ROC curve. The AUROC is usually calculated with

statistical packages.

The figure below shows an example of ROC curves for both lactate and ureaas markers for risk of death. Eye-balling the figure suggests that urea is a

better diagnostic variable than lactate:


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Receiver operating characteristic (ROC) curves for lactate and urea.

Bewick et al. Critical Care 2004 8:508 doi:10.1186/cc3000

A ROC curve can demonstrate several things:

1.

It shows the trade-off between sensitivity and specificity (any increase in

sensitivity will be accompanied by a decrease in specificity and vice-versa)

2. The closer the curve follows the left-hand border and then the top border

of the ROC space, the more accurate the test.

3.

The closer the curve comes to the 45-degree diagonal of the ROC space,the less accurate the test.

4.

The area under the curve (AUROC) can be used to assess test accuracy,

and to compare the performance of different tests.

Summary

ROC analysis provides a useful mean to assess the diagnostic accuracy of a

test and to compare the performance of more than one test for the same

outcome. However, the usefulness of the test must be considered in the lightof the clinical circumstances.

Origin of ROC

'ROC analysis is part of a field called "Signal Detection Theory" developed

during World War II for the analysis of radar images. Radar operators had to


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decide whether a blip on the screen represented an enemy target, a friendly

ship, or just noise. Signal detection theory measures the ability of radar

receiver operators to make these important distinctions. Their ability to do

so was called the 'Receiver Operating Characteristics'.

Dr Murad Ruf and Dr Oliver Morgan 2008

statistical aspects of screening tests

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