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Statistics
• Objectives:
1. Try to differentiate between the P value and alpha
value
2. When to perform a test
3. Limitations of different tests and how to over come
them
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Statistics
• Why should I care about the statistics?
I can prove anything by statistics except the truth (George
Canning)
• What are statistics?
Statistics are used much like a drunk uses a lamppost: for
support, not illumination (Vin Scully)
• What is a theory?
A supposition or a system of ideas intended to explain
something, especially one based on general principles
independent of the thing to be explained
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• How to prove a theory
1. Null Hypothesis ( H0 )
2. Alternate Hypothesis
• Calculate statistics like mean, median, standard
deviation, normal distribution curve, standard
normal distribution curve, Z value etc
• Next step, checking whether our results are random
by chance vs real
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• Traditional Method: Define critical values and see whether we reached them or not
• P value method:
1.
What is P value?
p-value is the probability of obtaining a test statistics at least as extreme as the
one that was actually observed, assuming that the null hypothesis is true
2.
What is α value (type 1 error)
Level of significance 0.01%, 0.005%, 0.1%
What is the relation between P value and α value
If P value < α value then the null hypothesis is rejected
If P value > α value, we fail to reject null hypothesis.
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Diagnosis
• We make the diagnosis based on the either pattern reorganization
or probability.
• Pattern reorganization could be considered as a pre-test
probability
• When do we need to perform a test?
1.
When we are in doubt?
2.
When our lawyers are asking?
3.
Do we need a test during low probability scenarios?
4.
Do we need a test when we are certain about the diagnosis?
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• Always think pretest probability
• Lets assume, zero is normal and 100 is the diagnosis.
• Disease is a spectrum
0%
100%
Low probability
Test threshold
High probability
Treatment threshold
We shouldn’t perform any diagnostic test at ends
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Critical appraisal tests
• Specificity: It’s the ability of the test to correctly
identify those patients without the disease.
Specificity=true negatives/(true negative + false
positives)
• Sensitivity: It’s the ability of the test to correctly
identify those patients with the disease.
Sensitivity= true positives/(true positive + false
negative)
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• Positive Predictive Value
How likely is it that this patient has the disease given
that the test result is positive?
PV+= true positive/(true positive + false positive)
• Negative Predictive Value
How likely is it that this patient has the disease that
the test result is negative?
PV-= true negatives/(true negatives +false negatives)
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Why are we having ,four tests instead of
two?
• This is our favorite 2x2 table lets see whether it is
going to give us an answer.
Have
disease
Doesn’t
have disease
Positive test
TP
FP
Positive
predictive
value
Negative test
FN
TN
Negative
Predictive
value
Sensitivity
Specificity
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Have disease
Doesn’t have
disease
Positive Test
20
5
80
Negative Test
5
20
80
25
25
50 patients total
Sensitivity: 80
Specificity:80
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Have disease
Doesn’t have
disease
Positive test
Negative test
8
16
33.3
2
24
92
10
40
Sensitivity 80
50
Specificity 80
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Have disease
Doesn’t have
disease
Test positive
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4
85
Test negative
6
16
72
30
Sensitivity 80
20
Specificity 80
50 patients
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Examples in an article
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• Pre-test probability
• Post-test Probability
• Likelihood Ratio (LR):
How likely the test result found is to be found in
diseased when compared with non disease
Probability of an individual with a condition having positive
result
Probability of an individual without condition having a positive
result
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Rule in infection: High LR+
Rule out infection: High LRPost test odds: Pre-test odds x LR
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D dimers and PE
• A 56 year old male with a history of stage 3
colorectal cancer s/p colectomy nearly 3 weeks back
presented to emergency department for having
chest pain, and trouble breathing. Since surgery he
started noticing bilateral lower extremity swelling.
PE significant for the bilateral edema, vitals are
significant for the HR of 115/mt, RR 19/mt, and 02
sats of 92%.
• D dimers by quantitative ELISA are 150 ng/ml (black
in color/negative).
• Next Step: Do you want to get a CTA or not
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• A 56 year old male who was discharged from the
hospital nearly 4 days back for the hip fracture s/p
repair presented to ED for having right sided chest
pain. His vitals are afebrile, HR 120/mt, RR 20/mt,
02 sats of 96%. PE exam is negative for any edema. D
dimers were ordered, and the box is black in color.
• Next Step: CTA or not
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• A 56 year old male without any PMH presented to
the ED for having right sided chest pain. His vitals
are afebrile, HR 120/mt, RR 20/mt, 02 sats of 96%.
PE exam is negative for any edema. D dimers were
ordered, and the box is black in color.
• Next Step?
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• Quantitative rapid ELISA post test probability if the
test (d-dimers) is negative
Low pretest probability- 0.5 to 2%
Moderate High pretest probability- 5 to 6%
High pretest probability- 19 to 28%
• Negative predictive value (NPV) of 94.2% (ranges
from 91%-100% depending on study)
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• Sensitivity: 95%
• Specificity: 40-68% in patients without PE. It falls more if
we add CRF
• Now we know the answers for the three questions.
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1.
How to incorporate discussions about statistics during
rounding
2.
How will we educate our learners to evaluate pre-test
probability before ordering a test
3.
How will we make our learners to exercise clinical
scenarios of both positive and negative results before
ordering the test instead of after getting the result
4.
How will we educate them about advancing further in
diagnostic algorithm
5.
Do we really need to bother about all these numbers
and statistics ?
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