Chapter 10 Screening for Disease - Kids in Prison Program · Chapter 10 Screening for Disease. 2...
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1 Chapter 10 Screening for Disease
Transcript of Chapter 10 Screening for Disease - Kids in Prison Program · Chapter 10 Screening for Disease. 2...
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Chapter 10
Screening for Disease
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Terminology• Reliability ≡ agreement of
ratings/diagnoses, “reproducibility”
– Inter-rater reliability ≡agreement between two independent raters
– Intra-rater reliability ≡agreement of the same rater with him/herself
• Validity ≡ ability to discriminate without error
• Accuracy ≡ a combination of reliability and validity
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Inter-Rater Reliability• Two independent
raters
• Cross-tabulate
• Observed proportion in agreement NOTadequate because a certain amount of agreement is due to chance
Rater B
Rater A + − Total
+ a b g1
− c d g2
Total f1 f2 N
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Kappa (κ)
1 1 2 2e 2= [Expected agreement due to chance]
f g f gp
N
Rater B
Rater A + − Total
+ a b g1
− c d g2
Total f1 f2 N
o = [Observed agreement; chance corrected]a d
p notN
o e
e
1
p p
p
[Agreement corrected for chance]
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κ Benchmarks
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Example 1: Flip two coins
o e
e
.5 .5 0.0 [no extra agreement above chance]
1 1 .5
p p
p
Toss B
Toss A Heads Tails Total
Heads 25 25 50
Tails 25 25 50
Total 50 50 100
To what extent are results reproducible?
1 1 2 2e 2 2
50 50 50 50.5
100
f g f gp
N
25 25= = .5 [Overall agreement is 50%]
100o
a dp
N
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Example 2
obs exp
exp
.91 .6276 .758
1 1 .6276
p p
p
Rater B
Rater A + − Total
+ 20 4 24
− 5 71 76
Total 25 75 100
To what extent are these diagnoses reproducible?
“substantial” agreement
1 1 2 2exp 2 2
25 24 75 76.6276
100
f g f gp
N
20 71= = .9100
100obs
a dp
N
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§10.3 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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Sensitivity
Test 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
FNTP
TP
w/diseasethose
TPSEN
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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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Predictive Value Positive
Test 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
FPTP
TP
positive test whothose
TPPVP
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Predictive Value Negative
Test 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
FNTN
TN
negative test whothose
TNPVN
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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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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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Example
Low 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− 10
Total 1000
FN = 1000 – 990 = 10
It follows that:
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Example: Low Prevalence Population
D+ D− Total
T+
T− 989,010
Total 999,000
TN = SPEC × (those without disease)
= 0.99 × 999,000
= 989,010
Suppose test SPECificity = .99
i.e., it will correctly identify 99% of the noncases
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Example: Low Prevalence Population
D+ D− Total
T+ 9,990
T− 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
Strikingly 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
goes down, PVPT
is affected
• Figure shows
relation between
PVP, PREV, &
SPEC (test SEN =
constant .99)
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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
