1 Diagnostic tests Subodh S Gupta MGIMS, Sewagram.

1

Diagnostic tests

Subodh S Gupta

MGIMS, Sewagram

Standard 2 X 2 tableStandard 2 X 2 table(For Diagnostic Tests)

Disease StatusDisease Status

Present Present (D+)(D+)

Absent Absent (D-)(D-) TotalTotal

Diagnostic Diagnostic testtest

Positive Positive (T+)(T+) aa bb a+ba+b

Negative Negative (T-)(T-) cc dd c+dc+d

TotalTotal a+ca+c b+db+d NN

Gold Gold StandardStandard

Standard 2 X 2 tableStandard 2 X 2 table(For Diagnostic Tests)



Absent Absent (D-)(D-)

Diagnostic Diagnostic testtest

Positive Positive (T+)(T+) TPTP FPFP

Negative Negative (T-)(T-) FNFN TNTN

Gold Gold StandardStandard

Gold standard

In any study of diagnosis, the method being evaluated has to be compared to something

The best available test that is used as comparison is called the GOLD STANDARD

Need to remember that all gold standards are not always gold; New test may be better than the gold standard

Test parameters

Sensitivity = Pr(T+|D+) = a/(a+c)

--Sensitivity is PID (Positive In Disease)Specificity = Pr(T-|D-) = d/(b+d)

--Specificity is NIH (Negative In Health)




Diagnostic Diagnostic TestTest




Gold StandardGold Standard

Test parameters

False Positive Rate (FP rate) = Pr(T+|D-) = b/(b+d) False Negative Rate (FN rate) = Pr(T-|D+) = c/(a+c) Diagnostic Accuracy = (a+d)/n









Test parameters

Positive Predictive Value (PPV) = Pr(D+|T+) = a/(a+b)

Negative Predictive Value (NPV) = Pr(D-|T-) = d/(c+d)









Sensitivity = 90/(90+10), Specificity = 95/(95+5)

FP rate = 5/ (95+5); FN Rate = 10/ (90+10)

Diagnostic Accuracy = (90+95) / (90+10+5+95)

PPV = 90/(90+5); NPV = 95/(95+10)





Positive Positive (T+)(T+) 9090 55 9595

Negative Negative (T-)(T-) 1010 9595 105105

TotalTotal 100100 100100 200200

Test parameters: Example


Sensitivity 90%

Specificity 95%

False Negative Rate 10%

False Positive Rate 5%PPV 94.7%

NPV 90.5%

Diagnostic Accuracy 92.5%

PPV & NPV with Prevalence

Healthy population vs sick population

Healthy Sick

Predictive Values in hospital-based data

Predictive Values in population-based data

Prevalence = 50%PPV = 94.7%

NPV = 90.5%Diagnostic Accuracy = 92.5%







TotalTotal 100100 100100 200200

Test Parameters: Example


Prevalence = 5%PPV = 48.6%

NPV = 99.4%Diagnostic Accuracy = 94.8%







TotalTotal 100100 19001900 20002000



Prevalence = 0.5%PPV = 8.3%

NPV = 99.9%Diagnostic Accuracy = 95%







TotalTotal 100100 1990019900 2000020000



Prevalence = 0.05%PPV = 0.9%

NPV = 100%Diagnostic Accuracy = 95%







TotalTotal 100100 199900199900 200000200000



Prevalence 50% 5% 0.5% 0.05%

Sensitivity 90% 90% 90% 90%

Specificity 95% 95% 95% 95%

PPV 94.7% 48.6% 8.3% 0.9%

NPV 90.5% 99.4% 99.9% 100%

Diagnostic Accuracy

92.5% 94.8% 95% 95%

PPV & NPV with Prevalence

Trade-offs between Sensitivity and Specificity

BE-Workshop-DT-July2007 21

When we use Diagnostic test clinically, we do not know who actually has and does not have the target disorder, if we did, we would not need the Diagnostic Test.

Our Clinical Concern is not a vertical one of Sensitivity and Specificity, but a horizontal one of the meaning of Positive and Negative Test Results.

Sensitivity and Specificity solve the wrong problem!!!


When a clinician uses a test, which question is important ?

If I obtain a positive test result, what is the probability that this person actually has the disease?

If I obtain a negative test result, what is the probability that the person does not have the disease?

Test parameters

Sensitivity = Pr(T+|D+) = a/(a+c)Specificity = Pr(T-|D-) = d/(b+d)PPV = Pr(D+|T+) = a/(a+b)NPV = Pr(D-|T-) = d/(c+d)









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Likelihood Ratios

Likelihood Ratio is a ratio of two probabilities Likelihood ratios state how many time more

(or less) likely a particular test results are observed in patients with disease than in those without disease.

LR+ tells how much the odds of the disease increase when a test is positive.

LR- tells how much the odds of the disease decrease when a test is negative

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The likelihood ratio for a positive result (LR+)

tells how much the odds of the disease

increase when a test is positive.

The likelihood ratio for a negative result (LR-)

tells you how much the odds of the disease

decrease when a test is negative

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The LR for a positive test is defined as:

LR (+) = Prob (T+|D) / Prob(T+|ND)

LR (+) = [TP/(TP+FN)] [FP/(FP+TN)]

LR (+) = (Sensitivity) / (1-Specificity)

Likelihood Ratios

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The LR for a negative test is defined as:

LR (-) = Prob (T-|D) / Prob(T-|ND)

LR (-) = [FN/(TP+FN)] [TP/(FP+TN)]

LR (-) = (1-Sensitivity) / (Specificity)

Likelihood Ratios

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What is a good ‘Likelihood Ratios’?

A LR (+) more than 10 or a LR (-) less than

0.1 provides convincing diagnostic evidence.

A LR (+) more than 5 or a LR (-) less than

0.2 is considered to give strong diagnostic

evidence.

Likelihood Ratio for a positive test = (90/100) / (5/100)

= 90/ 5 = 18

Likelihood Ratio for a negative test = (10/100) / (95/100)

= 10/ 95 = 0.11







TotalTotal 100100 100100 200200

Likelihood Ratio: Example


Exercise

In a hypothetical example of a diagnostic test, serum levels of a biochemical marker of a particular disease were compared with the known diagnosis of the disease. 100 international units of the marker or greater was taken as an arbitrary positive test result:

Example

Disease Disease StatusStatus

PresePresent nt

AbsenAbsentt

TotalTotal

MarkerMarker

>=10>=1000431431 3030 461461

<100<100 2929 116116 145145

TotalTotal 460460 146146 606606

Exercise

Initial creatine phosphokinase (CK) levels were related to the subsequent diagnosis of acute myocardial infarction (MI) in a group of patients with suspected MI. Four ranges of CK result were chosen for the study:

Exercise


PresenPresent t

AbsentAbsent TotalTotal

CPKCPK>=280>=280 9797 11 9898

80-27980-279 118118 1515 133133

40-7940-79 1313 2626 3939

1-391-39 22 8888 100100

TotalTotal 230230 130130 360360

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Odds and Probability

Probability of Disease = (# with disease) /

(# with & # without disease) = a/ (a+b)

Odds of a disease = (# with disease) /

(# without disease) = a/ b

Probability = Odds/ (Odds+1);

Odds = Probability / (1-Probability)


PresentPresent Absent Absent TotalTotal

aa bb a+ba+b

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Use of Likelihood Ratio

Employment of following three step procedure:

1. Identify and convert the pre-test probability to pre-test odds.

2. Determine the post-test odds using the formula,

Post-test Odds = Pre-test Odds * Likelihood Ratio

3. Convert the post-test odds into post-test probability.

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Likelihood Ratio: Example

A 52 yr woman presents after detecting 1.5 cm

breast lump on self-exam. On clinical exam,

the lump is not freely movable. If the pre-test

probability is 20% and the LR for non-movable

breast lump is 4, calculate the probability that

this woman has breast cancer.

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Likelihood Ratio: Solution

First step

Pre-test probability = 0.2

Pre-test odds = Pre-test prob / (1-pre-test prob)

Pre-test odds = 0.2/(1-0.2) = 0.2/0.8 = 0.25

Second step

Post-test odds Pre-test odds * LR

Post-test odds = 0.25*4 = 1

Third step

Post-test probability = Post-test odds / (1 + Post-test odds)

Post-test probability = 1/(1+1) = ½ = 0.5

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Receiver Operating Characteristic (ROC)

Finding a best test

Finding a best cut-off

Finding a best combination

probably negative

Equivocal

Probably positive

Definitive positive

1 - specificity

a

b

d

c

1 - specificity

sen

sitiv

ity

a

b

d

c

ROC curve constructed from multiple test thresholds

Diseased

Notdiseased

Multiple thresholds evaluated in test

b c da

Receiver Operating Characteristic (ROC)

ROC Curve allows comparison of different tests for the same condition without (before) specifying a cut-off point.

The test with the largest AUC (Area under the curve) is the best.

Features of good diagnosis study

Comparative (compares new test against old test).

Should be a “gold standard”Should include both positive and

negative resultsUsually will involve “blinding” for both

patient, tester and investigator.


USERS GUIDES TO THE MEDICAL LITERATURE

How to use an Article about a Diagnostic Test?

Are the results of the study valid?

What are the results and will they help me in

caring for my patients?

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1. Was there an independent, ‘blind’ comparison with a ‘gold’ standard’ of diagnosis?

2. Was the setting for the study as well as the filter through which the study patients passed, adequately described?

3. Did the patient sample include an appropriate spectrum of disease?

4. Have they done analysis of the pertinent subgroups

5. Where the tactics for carrying out the test described in sufficient detail to permit their exact replication?

Methodological Questions for Appraising Journal Articles about Diagnostic Tests

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6. Was the reproducibility of the test result (precision) and its interpretation (observer variation) determined?

7. Was the term ‘ normal’ defined sensibly?

8. Was precision of the test statistics given?

9. Was the indeterminate test results presented?

10. If the test is advocated as a part of a cluster or sequence of tests, was its contribution to the overall validity of the cluster or sequence determined?

11. Was the ‘ utility’ of the test determined?

Thank you

1 Diagnostic tests Subodh S Gupta MGIMS, Sewagram.

Documents

d disease status present

negative slide

d totala

positive test result

negative test results

dn disease status present

specificity slide

gold new test