# Stats for diagnostic tests

```					Statistics for diagnostic
tests
Dr Rahul Joshi
November 2005
Definitions (1)
 Sensitivity:
Proportion of people with the target
disorder who have a positive test

 Specificity:
Proportion of people without the target
disorder who have a negative test
SnNout
   SnNout: When a test (or sign or
symptom) has a high Sensitivity, a
Negative result rules out the diagnosis

   Eg. The sensitivity of a history of ankle
swelling for diagnosing ascites is 93%;
therefore if a person does not have a
history of ankle swelling it is highly
unlikely that the person has ascites
SpPin
   When a test (or sign or symptom) has a
high Specificity, a Positive result rules in
the diagnosis

   Eg. The specificity of a fluid thrill for
diagnosing ascites is 92%; therefore if a
person does have a fluid thrill, it rules in
the diagnosis of ascites

   Eg. Yes to >3 CAGE questions has a high
specificity for alcohol dependency
Definitions (2)
  Positive predictive value:
Proportion of people with a positive test who have the target
disorder

  Negative predictive value:
Proportion of people with a negative test who do not have the
target disorder

  Likelihood ratio:
The likelihood that a given test result would be expected in a
patient with the target disorder compared with the likelihood
that that same result would be expected in a patient without
the target disorder
Definitions (3)
 Pre-test odds:
The odds that the patient has the target disorder
before the test is carried out

 Post-test odds:
The odds that the patient has the target disorder
after the test is carried out

 Post-test probability:
The proportion of patients with that particular test
result who have the target disorder
Return of the 2x2 table!
Disease   Disease   TOTALS
present   absent
Test       a         b         a+b
positive
Test        c        d         c+d
negative
TOTALS      a+c       b+d      a+b+c+d
Formulae (1)
   Sensitivity =           a / (a+c)
   Specificity =           d / (b+d)
   LR+ =                   sens / (1-spec)
   LR- =                   (1-sens) / spec
   PPV =                   a / (a+b)
   NPV =                   d / (c+d)
(LR+ = Likelihood ratio for a positive (+) result)
(PPV = Positive Predictive Value, NPV = Neg predictive value)
Formulae (2)
 Prevalence = (a+c) / (a+b+c+d)
 Pre-test odds = prev / (1-prev)

 Post-test odds = pre-test odds x LR

 Post-test probability =

Post-test odds / Post-test odds + 1
Serum ferritin for diagnosing iron-
deficiency anaemia (I.D.A)

I.D.A     I.D.A
present   absent
Ferritin
positive
731       270
(<65
mmol/l)
Ferritin
negative      78       1500
(>65)

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