Comparing Non-normal groups to a control group

[#1]

Hi all,

We are comparing three different assays (A, B, C) to see how well they detect a disease condition. We have four groups where 1 = disease and 2, 3, and 4 = different benign conditions.

The question is two-fold

1. What test would you use within an assay to see if they can detect a difference to the control (= disease) group
1. Data is non normal distributed
2. Data contains 0 making transformation difficult, because log transformation won’t work
2. What metric or number can we use to determine which assay performed best?

Thank you in advance

[#2]

You might want to use logistic regression, where the disease class is Y and Assay is X. I am going to leave the labels 1-4 as they are, but I am going to tell JMP that the order is 2, 3, 4, and 1, because it assumes that the last level (1 now) is the target class (disease). Here is what it looks like when you regress Y versus X separately:

The ROC Curve is a diagnostic tool to assess discrimination (sensitivity versus 1-specificity) that might help you. It might also be helpful to use all three assays simultaneously as predictors to see if one is better. Here is nominal logistic regression that way:

So it appears that Assay C does better than the other two assays. Now what is the best model? Is the relationship linear? Here is the fit and test of the cubic model:

It seems that a linear predictor is sufficient.

What do the other classes (2-4) represent? Are there really 3 normal classes and 1 abnormal class? Also, is this study exploratory or confirmatory?

I attached your JMP data table after I saved scripts to repeat the analysis that I show here