Lesson #10

Screening Tests

D D’

+

-

TP

FN

FP

TN

Sensitivity = Se = P( + | D )TP

= TP + FN

Specificity = Sp = P( - | D’ )TN

= TN + FP

Ca no Ca

+

-

95

5

20

180

100 200

Se95

= 100

Sp

= .95

180=

200= .90

Ca no Ca

+

-

95

5

200

1800

100 2000

Se95

= 100

Sp

= .95

1800=

2000= .90

Positive Predictive Value (PPV)

PPV = P( D | + )

Not the same as Se!

The simplest form of Bayes’ Theorem is:

P(A) P(B | A)P(A | B) =

P(A) P(B | A) + P(A' ) P(B | A' )

P(D) P( | D)=

P(D) P( | D) + P(D' ) P( | D' )+

+ +

PPV = P(D | +)

P( ) P(B | )P( | B) =

P( ) P(B | ) + P( ) PA A

AA (B |A A' ' )A

P( ) P( | )=

P( ) P( | ) + P( )D D

D D P( | )D' D'+

+ +

PPV = P(D | +)

P( ) P( | )P( | ) =

P( ) P( | ) + A A

AA A A'P( ) P

BB

B B( | ' )A

P( ) P( | )=

P( ) P( | ) + P( )D D

D D P( | )D' D'+

+ +

PPV = P(D | +)

p

1-p

Se1-Sp

p(Se)=

p(Se) + (1 - p)(1 - Sp)

Se = .95 Sp = .90 p = .02

p(Se)=

p(Se) + (1 - p)(1 - Sp)PPV

(.02)(.95)=

(.02)(.95) + (.98)(.10)

= .162.019

= .019 + .098

.019=

.117

Ca no Ca

+

-

95

5

200

1800

100 2000

Ca no Ca

+

-

95

5

20

180

100 200

95"PPV" = = .862

115

95"PPV" = = .322

295

Ca

No Ca

P(Ca and +) = P(TP)= (.02)(.95) = .019

+.10

Sp = .90

-

.02

.98

+Se = .95

.05

-

P(No Ca and +) = P(FP)= (.98)(.10) = .098

P(+) = .117