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Overview :
If some performance measures for a test are known but others
are not, it is often possible to calculate the missing values from those that
are known.
Key for equations
• SE = sensitivity
• SP = specificity
• PPV = positive predictive value
• NPV = negative predictive value
• ACC = accuracy
(1)
sensitivity =
= (( 1 + (((NPV^(-1)) - 1) * (((SP^(-1)) - 1)^(-1)) *
((PPV^(-1)) - 1)))^(-1))
(2)
specificity =
= (( 1 + (((PPV^(-1)) - 1) * (((SE^(-1)) - 1)^(-1)) * ((NPV^(-1))
- 1)))^(-1))
(3)
positive predictive value =
= (( 1 + (((SP^(-1)) - 1) * (((NPV^(-1)) - 1)^(-1)) *
((SE^(-1)) - 1)))^(-1))
(4)
negative predictive value =
= (( 1 + (((SE^(-1)) - 1) * (((PPV^(-1)) - 1)^(-1)) *
((SP^(-1)) - 1)))^(-1))
(5)
accuracy =
= ((1 + (((((PPV ^ (-1)) - 1) ^ (-1) ) + (((SP ^ (-1)) - 1)
^ (-1)))^(-1)) + (((((SE ^ (-1)) - 1) ^ (-1) ) + (((NPV ^ (-1) ) - 1) ^ (-1)))^(-1))) ^ (-1))
(6)
positive predictive value =
= ((1 + (((SE ^ (-1)) - (ACC ^ (-1))) * (((((ACC ^ (-1)) -
1) * (((SP ^ (-1)) - 1) ^ (-1))) - 1) ^(-1)))) ^ (-1))
where:
• The equation does not apply if SE = SP = ACC
(7)
sensitivity =
= ((1 + (((PPV ^ (-1)) - (ACC ^ (-1))) * (((((ACC ^ (-1)) -
1) * (((NPV ^ (-1)) - 1) ^ (-1))) - 1) ^(-1)))) ^ (-1))
where:
• The equation does not apply if PPV = NPV = ACC
(8)
specificity =
= (( 1 + ((((SE ^ (-1)) + (PPV ^ (-1)) - (ACC ^ (-1)) - 1) ^
(-1)) * ((ACC ^ (-1)) - 1) * ((PPV ^
(-1)) -1))) ^ (-1))
(9)
positive predictive value =
= (( 1 + ((((SP ^ (-1)) + (NPV ^ (-1)) - (ACC ^ (-1)) - 1) ^
(-1)) * ((ACC ^ (-1)) - 1) * ((SP ^
(-1)) -1))) ^ (-1))
(10)
specificity =
= ((((((ACC ^ (-1)) - 1) * (((SE ^ (-1)) - 1) ^ (-1)) *
((NPV ^ (-1)) - 1)) + (ACC ^ (-1)) - (NPV ^ (-1)) + 1)) ^ (-1))
(11)
sensitivity =
= ((((((ACC ^ (-1)) - 1) * (((SP ^ (-1)) - 1) ^ (-1)) *
((PPV ^ (-1)) - 1)) + (ACC ^ (-1)) - (PPV ^ (-1)) + 1)) ^ (-1))
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Parameter Known?
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Equations to
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SE
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SP
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PPV
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NPV
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ACC
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Apply
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Y
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Y
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Y
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N
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N
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4 (NPV)
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5 (ACC)
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Y
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Y
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N
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Y
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N
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3 (PPV)
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5 (ACC)
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Y
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Y
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N
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N
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Y
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6 (PPV)
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4 (NPV)
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Y
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N
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Y
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Y
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N
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2 (SP)
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5 (ACC)
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Y
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N
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Y
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N
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Y
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8 (SP)
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4 (NPV)
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Y
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N
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N
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Y
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Y
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10 (SP)
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3 (PPV)
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N
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Y
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Y
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Y
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N
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1 (SE)
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5 (ACC)
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N
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Y
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Y
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N
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Y
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11 (SE)
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4 (NPV)
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N
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Y
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N
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Y
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Y
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9 (PPV)
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1 (SE)
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N
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N
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Y
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Y
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Y
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7 (SE)
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2 (SP)
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Implementation Notes:
• Some of the
equation numbers differ from that in Einstein et al (1997). Equations with
similar structure are grouped together
• Substituting
variables for some of the more complex structures makes implementing the
equations somewhat easier.
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