Some characteristics of tests are impacted by the prevalence of disease in the population being studied. In particular, predictive values and diagnostic accuracy are impacted by the prevalence of disease. So, for this example, the prevalence is 50/150 = 33.3%. To see what happens when the prevalence is increased or decreased, 80% and 5% were chosen.

Positive Predictive Value with 80% prevalence:
The numerator is (prevalence)(sensitivity) = (0.80)(0.90) = 0.72
The denominator is [(prevalence)(sensitivity) + (1-prevalence)(1-specificity)] = [(0.80)(0.90) + (0.20)(1-0.95)] = [(0.72)+(0.01)] = 0.73

So, the positive predictive value is 0.72/0.73 = 0.986 = 98.6%

Positive Predictive Value with 5% prevalence:
The numerator is (prevalence)(sensitivity) = (0.05)(0.90) = 0.045
The denominator is [(prevalence)(sensitivity) + (1-prevalence)(1-specificity)] = [(0.05)(0.90) + (0.95)(0.05)] = [(0.045)+(0.0475)] = 0.0925

So, the positive predictive value is 0.045/0.0925 = 0.1375 = 13.8%

Negative Predictive Value with 80% prevalence:
The numerator is (1-prevalence)(specificity) = (1-0.80)(0.95) = (0.20)(0.95) = 0.19
The denominator is [(1-prevalence)(specificity) + (prevalence)(1-sensitivity)] = [(0.20)(0.95)+(0.80)(0.10)] = [0.19+0.08] = 0.27

So, the negative predictive value is 0.19/0.27 = 0.704 = 70.4%

Negative Predictive Value with 5% prevalence:
The numerator is (1-prevalence)(specificity) = (1-0.05)(0.95) = (0.95)(0.95) = 0.9025
The denominator is [(1-prevalence)(specificity) + (prevalence)(1-sensitivity)] = [(0.95)(0.95)+(0.05)(1-0.90)] = [0.9025+0.005] = 0.9075

So, the negative predictive value is 0.9025/0.9075 = 0.994 = 99.4%

Some characteristics of tests are impacted by the prevalence of disease in the population being studied. In particular, predictive values and diagnostic accuracy are impacted by the prevalence of disease. So, for this example, the prevalence is 50/150 = 33.3%. To see what happens when the prevalence is increased or decreased, 80% and 5% were chosen.

Positive Predictive Value with 80% prevalence:

The numerator is (prevalence)(sensitivity) = (0.80)(0.90) = 0.72

The denominator is [(prevalence)(sensitivity) + (1-prevalence)(1-specificity)] = [(0.80)(0.90) + (0.20)(1-0.95)] = [(0.72)+(0.01)] = 0.73

So, the positive predictive value is 0.72/0.73 = 0.986 = 98.6%

Positive Predictive Value with 5% prevalence:

The numerator is (prevalence)(sensitivity) = (0.05)(0.90) = 0.045

The denominator is [(prevalence)(sensitivity) + (1-prevalence)(1-specificity)] = [(0.05)(0.90) + (0.95)(0.05)] = [(0.045)+(0.0475)] = 0.0925

So, the positive predictive value is 0.045/0.0925 = 0.1375 = 13.8%

Negative Predictive Value with 80% prevalence:

The numerator is (1-prevalence)(specificity) = (1-0.80)(0.95) = (0.20)(0.95) = 0.19

The denominator is [(1-prevalence)(specificity) + (prevalence)(1-sensitivity)] = [(0.20)(0.95)+(0.80)(0.10)] = [0.19+0.08] = 0.27

So, the negative predictive value is 0.19/0.27 = 0.704 = 70.4%

Negative Predictive Value with 5% prevalence:

The numerator is (1-prevalence)(specificity) = (1-0.05)(0.95) = (0.95)(0.95) = 0.9025

The denominator is [(1-prevalence)(specificity) + (prevalence)(1-sensitivity)] = [(0.95)(0.95)+(0.05)(1-0.90)] = [0.9025+0.005] = 0.9075

So, the negative predictive value is 0.9025/0.9075 = 0.994 = 99.4%