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))
|
Parameter Known? |
Equations to |
||||||||
|
SE |
SP |
PPV |
NPV |
ACC |
Apply |
||||
|
Y |
Y |
Y |
N |
N |
4 (NPV) |
5 (ACC) |
|||
|
Y |
Y |
N |
Y |
N |
3 (PPV) |
5 (ACC) |
|||
|
Y |
Y |
N |
N |
Y |
6 (PPV) |
4 (NPV) |
|||
|
Y |
N |
Y |
Y |
N |
2 (SP) |
5 (ACC) |
|||
|
Y |
N |
Y |
N |
Y |
8 (SP) |
4 (NPV) |
|||
|
Y |
N |
N |
Y |
Y |
10 (SP) |
3 (PPV) |
|||
|
N |
Y |
Y |
Y |
N |
1 (SE) |
5 (ACC) |
|||
|
N |
Y |
Y |
N |
Y |
11 (SE) |
4 (NPV) |
|||
|
N |
Y |
N |
Y |
Y |
9 (PPV) |
1 (SE) |
|||
|
N |
N |
Y |
Y |
Y |
7 (SE) |
2 (SP) |
|||
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.
