8 - bmi 201 presentation 8 scotch
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BMI presentationTRANSCRIPT
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Decision Analysis
Matthew Scotch, PhD, MPH
BMI 201
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Diagnostic Problem
• Patient presents with symptoms and is suspected of having a disease.
• Physician orders a diagnostic test to assist in making a diagnosis.
• Test result is either positive (indicating disease) or negative (indicating no disease).
• In truth, the patient either has the disease or does not have the disease.
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2 X 2 tables• To characterize (and/or evaluate) a
diagnostic (or screening) test, we use a 2 X 2 table
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Definitions
• True Positive (TP): Diseased person correctly receives a positive test result.
• False Positive (FP): Non-diseased person incorrectly receives a positive test result.
• True Negative (TN): Non-diseased person correctly receives a negative test result.
• False Negative (FN): Diseased person incorrectly receives a negative test result.
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2 x 2 Table
TRUTH
Disease
TRUTH
No Disease Total
Test
PositiveTrue
Positive
False
PositiveTest
NegativeFalse
Negative
True
Negative
Total Grand Total
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2 x 2 TableTest for Hyperparathyroidism
TRUTH
Disease
TRUTH
No Disease Total
Test
Positive90 5 95
Test
Negative10 895 905
Total 100 900 1000
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Definitions
• Sensitivity: Proportion of those with true disease who test positive.
• Specificity: Proportion of those who truly do not have disease who test negative.
NOTE: Sensitivity and specificity are also often expressed as a percentage and not a proportion; proportion is preferred; to convert a percentage to a proportion, divide by 100
82% = 0.82
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• Positive Predictive Value (PPV) Probability that disease exists given that the test is
positivePPV = P (D+ | T+)
• Negative Predictive Value (NPV)Probability that disease does not exist given that the test is negative
NPV = P (D- | T-)• Prevalence Rate of true disease in the group being tested Prevalence = P (disease+)
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Calculating Sensitivity and Specificity
TRUTH
Disease No Disease
Total
Test Result
Positive a b a + b
Negative c d c + d
Total a + c b + d a+b+c+d
a / (a + c)
sensitivity
d / (b +d)
specificity
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Calculating Sensitivity and Specificity
• Sens = TP/TP + FN• Spec = TN/TN+FP
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Test for Hyperparathyroidism
TRUTH
Hyperpara-thyroidism
TRUTH
No Hyperpara-thyroidism
Total
Test
Positive90 5 95
Test
Negative10 895 905
Total 100 900 1000
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ExampleHyperparathyroidism
TRUTH
Disease No Disease Total
Test Result
Pos 90 5 a + b
Neg 10 895 c + d
Total 100 900 a+b+c+d
a / (a + c)90/100 = .90
Sensitivity
d / (b +d)895/900 = .994
Specificity
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Predictive Values
• Predictive values help in deciding whether to believe the results for an individual patient
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Predictive Values
• Positive Predictive Value (PPV): Likelihood that the patient has the disease if the test is positive
• PPV = TP/TP+FP
• Negative Predictive Value (NPV): Likelihood that the patient does not have the disease if the test is negative
• NPV = TN/TN+FN
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2 x 2 TableSensitivity and Specificity
TRUTH
Disease
TRUTH
No Disease Total
Test
PositiveTrue
Positive
False
PositiveTest
NegativeFalse
Negative
True
Negative
Total Grand Total
Sensitivity Specificity
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2 x 2 TablePositive and Negative Predictive Values
TRUTH
Disease
TRUTH
No Disease Total
Test
PositiveTrue
Positive
False
PositiveTest
NegativeFalse
Negative
True
Negative
Total Grand Total
PPV
NPV
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ExampleHyperparathyroidism
TRUTH
Hyperpara-thyroidism
No Hyperpara-thyroidism
Total
Test Result
Positive 90 5 95
Negative 10 895 905
Total 100 900 1000
90 / 95 = .957
PPV
895 / 905 = .989
NPV
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Using Predictive Values• Critical to the interpretation of test results
• Sensitivity and specificity are inherent characteristics of the test and are constant
• Positive and Negative Predictive Values are affected by the context and the characteristics of the person being tested– (More on this point later in this lecture)
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PPV and Prevalence
• The lower the prevalence, the lower the PPV and the higher the NPV
• Low Prevalence = Higher FP
• Screening for a rare disease:– Most will be classified as FPs (b) or TN (d)
• What is impact on high FPR?– To individual?– To healthcare system?
Content from Dubrow, R. CDE 508A: Principles of Epidemiology I. Yale University. 2007
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NPV and Prevalence
• The higher the prevalence, the higher the PPV and the lower the NPV– Higher FNs– People remain undetected and can spread
disease
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Bayes’ Theorem
• Quantitative method for calculating post-test probability using:– Pretest probability– Sensitivity of test– Specificity of test
• Derived from definition of conditional probability and from properties of probability
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Bayes’ Theorem
• Conditional probability is the probability that event A will occur given event B occurs
• Generally, we want probability disease is present (event A) given a positive test (event B)
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Bayes’ Theorem Notation
• TPR = Sensitivity = TP/(TP+FN)• FNR = 1-Sensitivity = 1-(TP/(TP+FN))• TNR = Specificity = TN/(TN+FP)• FPR = 1-Specificty = 1- (TN/(TN+FP))
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Bayes’ Theorem
• We can reformulate this in terms of a positive test (PPV)
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Bayes’ Theorem• We can reformulate this in terms of a negative
test (NPV)
• Or, NPV = [(1-Prev)(Spec)]/[(1-Prev)Spec + Prev(1-Sens)]
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Application of Bayes’ Theorem
• Pre-test probability of heart disease = 0.95• TPR = 0.65• FPR = 0.20• Substitute Bayes’ Theorem for a Positive Test
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Application of Bayes’ Theorem
ASSUMPTIONS5% of women aged 40 with a palpable breast mass cancer have breast cancer (prevalence)99% of women with breast cancer and a palpable mass have positive mammography exam (sensitivity is 0.99)9.6% of women without breast cancer get positive tests (specificity is 0.904; false positive rate is 0.096)
EVIDENCEA woman in this age group with a palpable breast mass has a positive mammography test
PROBLEMWhat’s the probability that she has breast cancer?
Source: Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2 nd Edition. Springer-Verlag. 2001
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Example
• For the patient 40 with a palpable mass– p(B|A) is test’s sensitivity: 0.99– p(B|A’) is test’s false positive rate: 0.096– p(A) is prevalence of disease: 0.05
– Probability of breast cancer given a positive screening test estimated based on Bayes’ theorem in a 40 year women with a palpable breast mass
(0.99)(0.05) / [(0.99)(0.05) + (0.096)(0.95)] = 0.35
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References
• Petitti, D. BMI 502: Foundations of Biomedical Informatics Methods I. Arizona State University. 2012.
• Shortliffe EH, Perreault LE. Medical Informatics: Computer Applications in Health Care and Biomedicine. 2nd Edition. Springer-Verlag. 2001
• Dubrow, R. CDE 508A: Principles of Epidemiology I. Yale University. 2007.