Obtaining cell values when prevalence, sensitivity and specificity are known

Let us represent the 25% prevalence using a 2*2 table. Assuming that we are dealing with a total of 100 individuals, 25 of them will be disease +ve, while the remaining 75 will be disease –ve. Since the Total Disease +ve is the sum of cells ‘a’ and ‘c’, we enter 25 instead of (a+c). Similarly, we substitute (b+d) with the value 75 (the total number of disease –ve people):

The ICMR advisory states that the sensitivity of the test ranges from 50.6% to 84%. Sensitivity is given by the formula:

For ease of calculation, we will take the lower value of sensitivity as 50% (instead of 50.6%). This means that

Solving, we obtain the value of cell ‘a’ as:

a= 25*(50/100) = 25*0.5 = 12.5

As cell ‘a’= 12.5, cell ‘c’= (25-12.5) = 12.5

Similarly, the specificity of the test ranges from 99.3% to 100%. Specificity is given by the formula:

For ease of calculation, we will take the lower value of specificity as 99% (instead of 99.3%). This means that

Solving, we obtain the value of cell ‘d’ as:

d= 75*(99/100) = 75*0.99 = 74.25

Since cell ‘d’ = 74.25, cell ‘b’ = (75-74.25) = 0.75

Substituting, we obtain a 2*2 contingency table as under:

From the above calculations, it is apparent that the cell value of cells ‘a’ and ‘c’ are dependent on test sensitivity; cell values of cells ‘b’ and ‘d’ are dependent on test specificity. Therefore, when test sensitivity is high, cell ‘a’ will contain a large proportion of disease +ve persons (a+c). In turn, this will reduce the proportion of persons in cell ‘c’ (False –ve). Similarly, when test specificity is high, cell ‘d’ will contain a large proportion of disease –ve persons (b+d). This will decrease the proportion of persons in cell ‘b’ (False +ve).

In a nutshell,

• high test sensitivity= high True positives (cell ‘a’) and low False negatives (cell ‘c’)
• high test specificity= high True negatives (cell ‘d’) and low False positives (cell ‘b’)
• low test sensitivity= low True positives (cell ‘a’) and high False negatives (cell ‘c’)
• low test specificity= low True negatives (cell ‘d’) and high False positives (cell ‘b’)

With all cell values now obtained, we can calculate both Positive Predictive Value (PPV) and Negative Predictive Value (NPV).