Transcript TESTING A TEST

TESTING A TEST
Ian McDowell
Department of Epidemiology &
Community Medicine
January 2008
The Challenge of Clinical
Measurement
• Diagnoses are based on information, from formal
measurements and/or from your clinical judgment
• This information is seldom perfectly accurate:
– Random errors can occur (machine not working?)
– Biases in judgment or measurement can occur (“this kid
doesn’t look sick”)
– Due to biological variability, this patient may not fit the
general rule
– Diagnosis (e.g., hypertension) involves a categorical
judgment; this often requires dividing a continuous score
(blood pressure) into categories. Choosing the cutting-point
is challenging
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Therefore…
• You need to be aware …
– That we express these complexities in terms of
probabilities
– That using a quantitative approach is better than just
guessing!
– That you will gradually become familiar with the
typical accuracy of measurements in your chosen
clinical field
– That the principles apply to both diagnostic and
screening tests
– Of some of the ways to describe the accuracy of a
measurement
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Attributes of Tests or Measures
• Safety, Acceptability, Cost, etc.
• Reliability: consistency or reproducibility;
this considers chance or random errors (which
sometimes increase, sometimes decrease, scores)
• Validity: “Is it measuring what it is supposed to
measure?” By extension, “what diagnostic
conclusion can I draw from a particular score on this
test?”
Validity may be affected by bias, which refers to
systematic errors (these fall in a certain direction)
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Reliability and Validity
Reliability
Low
Validity
Low
High
••
••••
•
• •
Biased
result!
• •
•
•
High •
•
Average of these
inaccurate results is not bad.
This is probably how
screening questionnaires (e.g.,
for depression) work
•
•
••
••
••
☺
•
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Ways of Assessing Validity
• Content or “Face” validity: does it make
clinical or biological sense? Does it include
the relevant symptoms?
• Criterion: comparison to a “gold standard”
definitive measure (e.g., biopsy, autopsy)
– Expressed as sensitivity and specificity
• Construct validity (this is used with
abstract themes, such as “quality of life” for
which there is no definitive standard)
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Criterion, or “Gold Standard”
The clinical observation or simple test is judged
against
• More definitive (but expensive or invasive) tests,
such as a complete work-up,
Or against
• Eventual outcome (for screening tests, when
workup of well patients is unethical)
Sensitivity and specificity are calculated
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2 x 2 Table for Testing a Test
Test score:
Test positive
Test negative
Validity:
Gold standard
Disease Disease
Present Absent
a (TP)
b (FP)
c (FN)
d (TN)
Sensitivity Specificity
= a/(a+c) = d/(b+d)
TP = true positive; FP = false positive…
Golden Rule: always calculate based on the gold standard
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A Bit More on Sensitivity
= Test’s ability to detect disease when it is
present
a/(a+c) = TP/(TP+FN)
Mnemonics:
- a sensitive person is one who is aware of
your feelings
- (1 – seNsitivity) = false Negative rate
= how many cases are missed by the
screening test?
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…and More on Specificity
Ability to detect absence of disease when it is
truly absent (can it detect non-disease?)
d/(b+d) = TN/(FP+TN)
• Mnemonics:
– a specific test would identify only that type of
disease. “Nothing else looks like this”
– (1- sPecificity) = false Positive rate (How many
are falsely classified as having the disease?)
• The FP idea will arise again, so keep it in
mind!
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Most Tests Provide a Continuous Score.
Selecting a Cutting Point
Test scores for a
healthy population
Sick population
Healthy
scores
Pathological
Possible cut-point
scores
Move this way to
Move this way to
increase sensitivity
increase specificity
(include more of
(exclude healthy people)
sick group)
Crucial issue: changing cut-point can improve 11
sensitivity or specificity, but never both
Clinical applications
• A specific test can be useful to
rule in a disease. Why?
D+ DT+ a b
T- c d
– Very specific tests give few false positives.
So, if the result is positive, you can be sure the
patient has the condition (‘nothing else would
give this result’): “SpPin”
• A sensitive test can be useful for ruling
a disease out:
–A negative result on a very sensitive test
(which detects all true cases) reassures you that
the patient does not have the disease: “SnNout”
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Problems with Wrong Results
• False Positives can arise due to other factors (such
as taking other medications, diet, etc.) They entail
cost and danger of investigations, labeling, worry
– This is similar to Type I or alpha error in a test of
statistical significance: the possibility of falsely
concluding that there is an effect of an intervention.
• False Negatives imply missed cases, so potentially
bad outcomes if untreated
– cf Type II or beta error: the chance of missing a true
difference
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Practical Question:
“Doctor, how likely am I to have this disease?”
= Predictive Values
• Sensitivity & specificity don’t tell you this,
because they work from the gold standard.
• Now you need to work from the test result,
but you won’t know whether this person is a
true positive or a false positive (or a true or
false negative). Hmmm…
How accurately will a positive (or negative)
result predicts disease (or health)?
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Positive and Negative Predictive Values
• Based on rows, not columns
• Positive Predictive Value (PPV) = a/(a+b)
= Probability that a positive score is a true positive
• NPV = d/(c+d); same for a negative test result
D+ Db
T+ a
d
T- c
• BUT… there’s a big catch:
• We are now working across the columns, so PPV & NPV
depend critically on how many cases of disease there are
(prevalence).
• As prevalence goes down, PPV goes down (it’s harder to
find the smaller number of cases) and NPV rises.
• So, PPV and NPV must be determined for each clinical
setting,
• But this is then immediately useful to clinician: reflects
this population, so tell us about this patient
Prevalence and Predictive Values
B. Primary care
A. Specialist referral hospital
D+
D-
T+
50
10
T-
5
100
D+
D-
T+
50
100
T-
5
1000
Sensitivity = 50/55 = 91%
Specificity = 100/110 = 91%
Sensitivity = 50/55 = 91%
Specificity = 1000/1100 = 91%
Prevalence = 55/165 = 33%
Prevalence = 55/1155 = 3%
PPV = 50/60 = 83%
NPV = 100/105 = 95%
PPV = 50/150 = 33%
NPV = 1000/1005 = 99.5%
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Imagine you know Sensitivity & Specificity.
To work out PPV and NPV you need to guess
prevalence, then work backwards:
Fill cells in following order:
“Truth”
Disease
Disease
Present
Absent
Test Pos
4th
7th
5th
6th
Test Neg
Total
2nd
3rd
(from estimated prevalence)
(from sensitivity) (from specificity)
Total
8th
9th
1st
PV
10th
11th
Gasp…!
Isn’t there an easier way to do all this…?
Yes (good!)
But first, you need a couple more concepts (less good…)
• Before you apply a diagnostic test, prevalence gives
your best guess about the chances that this patient
has the disease.
• This is known as “Pretest Probability of Disease”:
(a+c) / N in the 2 x 2 table:
a
b
• It can also be expressed as odds of
c
d
disease: (a+c) / (b+d), as long as
N
the disease is rare
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Test scores are continuous scales.
You can use this to combine sensitivity and specificity:
Meet Receiver Operating Characteristic Curves
Work out Sen and Spec for every possible cut-point, then plot these.
Area under the curve indicates the information provided by the test
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Sensitivity
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1-Specificity ( = false positives)
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Note:
the theme of
sensitivity &
(1-specificity)
will appear
again!
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This Leads to … Likelihood Ratios
• Defined as the odds that a given level of a
diagnostic test result would be expected in a patient
with the disease, as opposed to a patient without:
true positives / false positives. [TP / FP]
• Advantages:
– Combines sensitivity and specificity into one number
– Can be calculated for many levels of the test
– Can be turned into predictive values
• LR for positive test = Sensitivity / (1-Specificity)
• LR for negative test = (1-Sensitivity) / Specificity
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Practical application: a Nomogram
1) You need the LR for this test
2) Plot the likelihood ratio on
center axis (e.g., LR+ = 20)
▪
▪
3) Select pretest probability
(prevalence) on left axis
(e.g. Prevalence = 30%)
4) Draw line through these
points to right axis to indicate
post-test probability of
disease
Example:
Post-test probability = 91% 21
Chaining LRs Together (1)
• Example: 45 year-old woman presents with
“chest pain”
– Based on her age, pretest probability that a
vague chest pain indicates CAD is about 1%
• Take a fuller history. She reports a 1-month
history of intermittent chest pain, suggesting
angina (substernal pain; radiating down arm;
induced by effort; relieved by rest…)
– LR of this history for angina is about 100
The previous example:
1. From the
History:
She’s young;
pretest
probability
about 1%
LR 100
Pretest probability
rises to 50%
based on history
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Chaining LRs Together (2)
45 year-old woman with 1-month history of
intermittent chest pain…
After the history, post test probability is now about
50%. What will you do?
Something more precise (but also more costly):
• Record an ECG
– Results = 2.2 mm ST-segment depression.
LR for ECG 2.2 mm result = 10.
– Overall post test probability is now >90% for
coronary artery disease (see next slide)
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The previous example: ECG Results
Post-test
probability
now rises
to 90%
Now start pretest
probability
(i.e. 50%, prior to
ECG, based on
history)
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