Sensitivity

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Sensitivity Specificity

• Categorical Data Analysis (CHL5210)
• Tutorial Presentation
• Andy (Ai) Ni
• Oct 9, 2007

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Sensitivity Specificity

• Measure how good a test is at detecting binary
  features of interest (disease/no
  disease)

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Sensitivity Specificity

• There are 100 people with 30 having disease A
• A test designed to identify who has the disease
  and who does not
• We want to evaluate how good the test is

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Sensitivity Specificity
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Sensitivity Specificity
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Sensitivity Specificity

• Sensitivity P (test disease)
• Specificity P (test- disease-)

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Sensitivity Specificity

• Usually the true disease status is determined
  by some gold standard method
• For a specific test, sensitivity increases as
  specificity decreases and vice versa

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Sensitivity Specificity

• Is a test perfect if it has high sensitivity AND
  high specificity?
• Suppose there are 1 million people with 0.1
  infected with HIV
• A test can identify HIV infected people with
  99.9 sensitivity and 99.9 specificity

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Sensitivity Specificity
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Sensitivity Specificity
0.1 Prevalence
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Sensitivity Specificity

• Positive Predictive Value (PPV)
• P (disease test)
• Negative Predictive Value (NPV)
• P (disease- test-)
• Prevalence P (disease)

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Sensitivity Specificity

• The lower the prevalence, the lower the PPV, and
  the higher the NPV
• The higher the prevalence, the higher the PPV,
  and the lower the NPV

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Sensitivity Specificity

• Type I error a P (reject Ho Ho)

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Sensitivity Specificity

• Type I error a P (reject Ho Ho)
• 1 P (accept Ho
  Ho)

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Sensitivity Specificity

• Type I error a P (reject Ho Ho)
• 1 P (accept Ho
  Ho)

Disease -
test -
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Sensitivity Specificity

• Type I error a P (reject Ho Ho)
• 1 P (accept Ho
  Ho)
• So type I error is in fact (1 specificity)

Disease -
test -
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Sensitivity Specificity

• Power 1 Type II error b

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Sensitivity Specificity

• Power 1 Type II error b
• 1 P (accept Ho Ho-)

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Sensitivity Specificity

• Power 1 Type II error b
• 1 P (accept Ho Ho-)
• P (reject Ho Ho-)

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Sensitivity Specificity

• Power 1 Type II error b
• 1 P (accept Ho Ho-)
• P (reject Ho Ho-)

Disease
Test
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Sensitivity Specificity

• Power 1 Type II error b
• 1 P (accept Ho Ho-)
• P (reject Ho Ho-)
• So power is in fact sensitivity

Disease
Test
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Sensitivity Specificity

• SAS code
• There is no direct procedure for sensitivity and
  specificity
• Use proc freq to do the job

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Sensitivity Specificity

• To get the 2X2 table
• data sample
• input Test Disease Count
• datalines
• 0 0 6 0 1 2 1 0 4 1 1 11
• run
• proc freq datasample
• weight Count
• tables TestDisease
• run

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Sensitivity Specificity

• To get the CI and test
• title sensitivity
• proc freq datasample
• where Disease1
• weight Count
• tables Test
• exact binomial
• run