Two independent diagnostic tests
Both need to be positive for a positive diagnosis
Either one or both tests need to be negative for a negative diagnosis. Can the following equations be used ?
Combined sensitivity for A and B =Sensitivity of A x Sensitivity of B
Combined specificity for A and B =Specificity of A + Specificity of B - (Specificity of A x Specificity of B)
I can plot Receiver Operator Characteristic curves for each test-would be interested in statistic packages that can combine two tests as well
The two tests may be quite different, but I would be surprised if they could be considered stochastically independent since they are both taken on the same subject. Normally when we talk about stochastic independence it is in cases where the observed subjects are different. I think the lack of stochastic independence prevents using any simple formulas to come up with the joint sensitivity/specificity.
Dear Indra,
If you want to use several independent variables (as in your case these are the results of several diagnostic tests) which are continuous and one dependent categorical variable (final diagnosis with categories either "positive" or "negative") conventional univariate methods such as ROC analysis are inappropriate. You must use multivariate methods, e.g., discriminant analysis, artificial neural networks, support vector machines, etc., and a confusion table (also called "confusion matrix", "classification table", "cross-tabulation", "crosstab", or "contingency table" with percentages), which allows you to calculate overall sensitivity and specificity. An example of 2 x 2 classification table (and additional calculations for sensitivity and specificity) is here: http://work.thaslwanter.at/Stats/html/_images/Sensitivity_Specificity_Example.png. You can use binomial logistic regression which gives probabilities for each final diagnosis as well.
IMPORTANT: some classification methods, e.g., discriminant analysis, are based on strict assumptions. You have to check if these assumptions are met before using a method for classification. Otherwise the method is inappropriate.
If both of your independent variables are categorical, i.e., result is either "positive" or "negative" but not numerical expression (for instance 5.5 mmol/l or 25Hz), then you can manually calculate test outcomes, which are required for the classification table.
Most of the methods (including crosstab with percentages) mentioned in my reply can be found in statistical packages such as SPSS.
- Badges
- Science topic
- Similar topics
- Medicine
- Physiology
- Biosignals
- Biomedical Signal Processing
- Statistical Analysis