Question

3. A particular diagnostic test for disease X has a sensitivity of 90% and a specificity of 90%. What is the negative predictive value of the test?

Answer 1

I had to check on this one. It is not possible to get from sensitivity/specificity to PPV/NPV without an estimate of the population prevalence of the disease.

It has apparently been suggested that the PPV/NPV values be normalized assuming a 50% prevalence rate. I don't know whether 50% is an acceptable estimate of prevalence for your class. Once you have the prevalence, you should build a table like the one from Wikipedia: http://en.wikipedia.org/wiki/Sensitivity_and_specificity

Populate each box with a % as follows:
The first box is Positive for Condition and for Disease.
Since the test has a sensitivity of 90% and 50% of the population is assumed to have the disease:
\[\frac{ TruePositive }{ AllTests }=\frac{ TruePositive }{ AllPositive }*\frac{ AllPositive }{ AllTests }\]
\[\frac{ TruePositive }{ AllTests }=Sensitivity*Prevalence(50pct)\]

The formula above will work with other values for prevalence. The rest of the algebra is pretty straightforward.