Sensitivity and Specificity
To understand these two terms, we have to look at a 2 X 2 Table.
This is truly the easiest way. Along the top of the table, we
will look at the test result, knowing that every test can have
a positive or a negative value (and of course some have indeterminate
values, but we will not include this). Along the left side of
the table, we will have a population that either does or does
not have the disease in question.
| 2 X 2 Table |
Result of Test |
| Positive |
Negative |
| Population, positive is with disease and negative
is without |
Positive |
a |
b |
| Negative |
c |
d |
The sensitivity is the probability of the test being positive
when someone has the disease (a) when compared to the whole population
who has the disease. Because some of the tests are false negatives
(a person who is positive for the disease but tests as negative),
the whole population who has the disease is a + b. Thus, the sensitivity
is a/a+b. The sensitivity is better the less false negatives we
have.
The specificity is the probability of the test being negative
when someone does not have the disease (d) when compared to the
whole population who does not have the disease. Because some of
the test are false positives (a person who does not have the disease
but tests as positive), the whole population who does not have
the disease is c+d. Thus, the specificity is d/c+d. The specificity
is better with the fewer false positives that we have.
The Positive Predictive Value (PPV) is another probability. In
this case, we want to know the probability of the test being positive
when someone has the disease (a), compared to all the positive
test results (a + c). This truly gives you the probability of
a positive test result if you have the disease, and is thus a/a+c.
In this case, the fewer false positives the better.
The Negative Predictive Value (NPV) is the probability of the
test being negative in someone who does not have the disease (d)
when compared to all those who have a negative test result (b
+ d). This gives you the probability of a negative test result
if you do not have the disease and is thus d/b+d. In this case,
the fewer false negatives the better.
