The paper introduces a new index, \( J \), for evaluating the performance of diagnostic tests. This index aims to provide an objective measure of how well a test can distinguish between diseased and healthy individuals. The formula for the index is:
\[ J = \frac{a d - b c}{(a + b)(c + d)} \]
where:
- \( a \) is the number of correctly diagnosed diseased individuals,
- \( b \) is the number of false negatives (diseased individuals misdiagnosed as healthy),
- \( c \) is the number of correctly diagnosed healthy individuals,
- \( d \) is the number of false positives (healthy individuals misdiagnosed as diseased).
Key features of the index include:
1. The range of values is from 0 to 1, with 0 indicating no discriminatory power and 1 indicating perfect discrimination.
2. The index is zero if the test reports the same proportion of positive results for both diseased and control groups.
3. The index is 1 only when there are no false positives or false negatives.
4. The index is independent of the relative sizes of the control and diseased groups.
5. The index is independent of the absolute sizes of the control and diseased groups.
The paper also discusses the standard error of the index, which is crucial for assessing the reliability of the index values. For small sample sizes, special statistical procedures are needed to compare two diagnostic tests effectively. The index can be used to compare the performance of different diagnostic tests, with the difference between their indexes evaluated using the \( t \)-test.The paper introduces a new index, \( J \), for evaluating the performance of diagnostic tests. This index aims to provide an objective measure of how well a test can distinguish between diseased and healthy individuals. The formula for the index is:
\[ J = \frac{a d - b c}{(a + b)(c + d)} \]
where:
- \( a \) is the number of correctly diagnosed diseased individuals,
- \( b \) is the number of false negatives (diseased individuals misdiagnosed as healthy),
- \( c \) is the number of correctly diagnosed healthy individuals,
- \( d \) is the number of false positives (healthy individuals misdiagnosed as diseased).
Key features of the index include:
1. The range of values is from 0 to 1, with 0 indicating no discriminatory power and 1 indicating perfect discrimination.
2. The index is zero if the test reports the same proportion of positive results for both diseased and control groups.
3. The index is 1 only when there are no false positives or false negatives.
4. The index is independent of the relative sizes of the control and diseased groups.
5. The index is independent of the absolute sizes of the control and diseased groups.
The paper also discusses the standard error of the index, which is crucial for assessing the reliability of the index values. For small sample sizes, special statistical procedures are needed to compare two diagnostic tests effectively. The index can be used to compare the performance of different diagnostic tests, with the difference between their indexes evaluated using the \( t \)-test.