Question

In a screening program of 10,000 people, the disease prevalence was 1%.

The sensitivity was 90.0% and the specificity was 99.0%.

Complete the table with all values:

	Disease		Total
	yes	no
Screen yes
Screen no
Total			10000

Show your work and calculate as a percent to one decimal place. In other words: x/y = z.n %

Positive predictive value is: __/__ = __ . _ %

Negative predictive value is: __/__ = __ . _ %

Answer 1

Formula for Positive predicitve value (PPV) = (sensitivity x prevalence
(sensitivity x prevalence) + (1-specificity)* (1-prevalence )

By replacing the values, for eg; sensitivity as 0.90 etc., we would get the value of PPV to be
0.4761 or 47.61%

Similarly,

Negative predicitve value (NPV) = (specificity x ( 1 - prevalence )   
(1 - sensitivity) x prevalence + (specificity) * (1-prevalence )

By replacing the values, for eg; specificity as 0.99 etc., we would get the value of NPV to be
0.9989 or 99.89%

Now, we would need to complete the table. The known values also include the total number of screened people, which is 10,000 Nos.

From the remaining calculations as mentioned below,

True Positive Cases = (total number of screened people) * (prevelance)*(sensitivity)
= 10,000*0.01*0.90

90 Nos.

False negative = (total number of screened people) * (prevelance)*(1-sensitivity )

10 Nos.

False positive = (total number of screened people) * (1- prevelance)*(1-specificity)

= 99 Nos.

True negative = (total number of screened people) * (1- prevelance)*(specificity)

= 9801 Nos.

Screen yes Disease yes

Screen no Disease no

90	99
10	9801

Total = 90=10+99+9801 = 10,000 Nos.