1 Epidemiological Measures I Screening for Disease.
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Transcript of 1 Epidemiological Measures I Screening for Disease.
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Epidemiological Measures I
Screening for Disease
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Terminology• ReliabilityReliability ≡ agreementagreement of
ratings/diagnoses, “reproducibility”– Inter-rater reliabilityInter-rater reliability ≡
agreement between two independent raters
– Intra-rater reliabilityIntra-rater reliability ≡ agreement of the same rater with him/herself
• ValidityValidity ≡ ability to discriminate without error
• AccuracyAccuracy ≡ a combination of reliability and validity
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Validity• Compare screening test results to a gold
standard (“definitive diagnosis”)• Each patient is classified as either true positive
(TP), true negative (TN), false positive (FP), or false negative (FN)
Test D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
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SensitivityTest D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
SEN ≡ proportion of cases that test positive or the proportion of those with the disease of interest
that our test is able to detect.
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Sensitivity
• Sensitivity = TP/TP+FN• Sensitivity =Test positive/Those with
disease
• SnOUT; A very sensitivity test is useful because it allows us to rule out diseases. If you test negative on a very sensitive test then you are probably disease free.
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Specificity
SPEC ≡ proportion of noncases that test negative
Test D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
FPTN
TN
disease w/out those
TNSPEC
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Specificity
• sPIN• ;a very specific test enables us to rule in
those with a disease. A positive outcome on a specific test is most likely indicative of disease.
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Attributes
• Both sensitivity and specificity are intrinsic attributes of a test.
• They do not change with the disease prevalence.
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PREDICTIVE VALUES
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Predictive Value PositiveTest D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
PVP ≡ proportion of positive tests that are true cases
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Predictive Value NegativeTest D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
PVN ≡ proportion of negative tests that are true non-cases
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Prevalence
• [True] prevalence = (TP + FN) / N
• Apparent prevalence = (TP + FP) / N
Test D+ D− Total
T+ TP FP TP+FP
T− FN TN FN+TN
Total TP+FN FP+TN N
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Predictive value attributes
• Both the positive and negative predictive values are affected by prevalence.
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Conditional Probability Notation
• Pr(A|B) ≡ “the probability of A given B”
• For example Pr(T+|D+) ≡ “probability test positive given disease positive” = SENsitivity
• SPEC ≡ Pr(T−|D−)
• PVP = Pr(D+|T+)
• PVN= Pr(D−|T−)
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ExampleLow Prevalence Population
D+ D− Total
T+
T−
Total 1000 1,000,000
Conditions: N = 1,000,000; Prevalence = .001
Prevalence = (those with disease) / N
Therefore:
(Those with disease) = Prevalence × N
= .001× 1,000,000 = 1000
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Example: Low Prevalence Population
D+ D− Total
T+
T−
Total 1000 999,000 1,000,000
Number of non-cases, i.e., TN + FP
1,000,000 – 1,000 = 999,000
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Example: Low Prevalence Population
D+ D− Total
T+ 990
T−
Total 1000
TP = SEN × (those with disease) = 0.99 × 1000 = 990
Assume test SENsitivity = 99% i.e., Test will pick up 99% of those with disease
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Example: Low Prevalence Population
D+ D− Total
T+ 990
T− 10Total 1000
FN = 1000 – 990 = 10
It follows that:
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Example: Low Prevalence Population
D+ D− Total
T+
T− 989,010Total 999,000
TN = SPEC × (those without disease) = 0.99 × 999,000 = 989,010
Suppose test SPECificity = .99i.e., it will correctly identify 99% of the noncases
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Example: Low Prevalence Population
D+ D− Total
T+ 9,990T− 989,010
Total 999,000
FPs = 999,000 – 989,010 = 9,900
It follows that:
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Example: Low Prevalence Population
D+ D− Total
T+ 990 9,990 10,980
T− 10 989,010 989,020
Total 1000 999,000 1,000,000
PVPT = TP / (TP + FP) = 990 / 10,980 = 0.090
Low PVP
It follows that the Predictive Value Positive is :
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Example: Low Prevalence Population
D+ D− Total
T+ 990 9,990 10,980
T− 10 989,010 989,020
Total 1000 999,000 1,000,000
PVNT= TN / (all those who test negative) = 989010 / 989020 = .9999
It follows that the Predictive Value Negative is:
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Example: High prevalence population
D+ D− Total
T+ 99,000 9,000 108,000
T− 1,000 891,000 892,000
Total 100,000 900,000 1,000,000
SEN = 99000 / 100,000 = 0.99
SPEC = 891,000 / 900,000 = 0.99
Prev = 100000 / 1,000,000 = 0.10
Same test parameters but used in population with true prevalence of .10
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Example: High prevalence population
D+ D− Total
T+ 99,000 9,000 108,000
T− 1,000 891,000 892,000
Total 100,000 900,000 1,000,000
PVP = 99,000 / 108,000 = 0.92
PVN = 891,000 / 892,000 = 0.9989
Prevalence = 100000 / 1,000,000 = 0.10
An HIV screening test is used in one million people. Prevalence in population is now 10%. SEN and SPEC are again 99%.
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PVPT and Prevalence• As PREValence
increases PVPT also increases
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Screening Strategy• First stage
high SENS (don’t want to miss cases)
• Second stage high SPEC (sort out false positives from true positives)
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Selecting a Cutoff Point• There is often an overlap in test results
for diseased and non-diseased population
• Sensitivity and specificity are influenced by the chosen cutoff point used to determine positive results
• Example: Immunofluorescence test for HIV based on optical density ratio (next slide)
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Low Cutoff High sensitivity and low specificity
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High Cutoff Low sensitivity and high specificity
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Intermediate Cutoff moderate sensitivity & moderate specificity
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Again ,Snout and Spin• Best strategy is to start with a very
sensitive screening test.
• A negative test on a sensitive test rules out the disease
• You then proceed to rule in or confirm the disease by doing a test with high specificity.
• A positive test on a specific test rules in or confirms the diagnosis.