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For two groups (patient and control, 20-30 participants in each group) I have data on 3 biomarkers. The variables are continuos and not normally distributed. I want to see in what biomarker the difference is the most and the least pronounced.

I am fairly new in statistics and can not find the right test to run.

Thankful for your suggestions!

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  • $\begingroup$ Addition: What I have tried so far is to run a Mann-Whitney test to see if there actually is a difference between the groups. However, I fail to find a test to quantify the difference in each variable, to be able to compare and see what variable shows the biggest difference. $\endgroup$
    – Med stud Karl
    Commented Sep 30, 2021 at 9:20

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There are many topics that are appropriate for getting "spot help" on this forum as you see when you look at today's questions. This is not actually one of them. Your research involves many, many statistical issues requiring a great deal of study for success to be around the corner. Or partner with a biostatistician quickly. Also be prepared to find that the sample size is too small to allow even an experienced biostatistician to do very much. The adequacy of the sample size depends on the signal:noise ratio in the response variable.

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  • $\begingroup$ Thank you for taking your time to answer my question! This is acutally a exercise-example given to me. I see that there are many issues to overcome. But for me, as a novice in this learning opportunity, is there some test that could be done to asses what biomarker differs the most between the groups? Like I mentioned above, I have tried the Mann-Whitney, which I understand tests the null hypothesis, and from that I have interpreted that there is only significant change in one of the biomarkers between the groups. $\endgroup$
    – Med stud Karl
    Commented Sep 30, 2021 at 12:01
  • $\begingroup$ I don't think it's possible to make progress on this problem without understanding statistical models, but if the response variable is binary (meaning that your sample size is far, far too small), you can compute 3 concordance probabilities (c-index; area under the ROC curve) and confidence intervals for them. These are [0,1] translations of the Wilcoxon statistic and measure pure discrimination ability. $\endgroup$
    – Frank Harrell
    Commented Sep 30, 2021 at 12:04
  • $\begingroup$ I do not understand how the response variable (in this case a continuous biomarker) can be binary? And what do you mean when saying "meaning that your sample size is far, far too small"? I am sensing I do not have a solid enough statistical background for this. Thank you again. $\endgroup$
    – Med stud Karl
    Commented Sep 30, 2021 at 12:21
  • $\begingroup$ Yes work with a biostatistician. But most biostatisticians would not know the Peter O'Brien trick in this case. Predict the probability of being in the second group as a function of 3 predictors (the 3 biomarkers). Then do a global test of no association with at least 3 degrees of freedom. This tests whether there is a signal from any of the 3 markers in predicting group membership. $\endgroup$
    – Frank Harrell
    Commented Sep 30, 2021 at 15:25
  • $\begingroup$ If you don't find evidence that at least one of the markers is associated with group (using this chunk test), then stop. If you do, then you can use the partial tests from the regression model (binary logistic model) to see which biomarkers adds predictive information to the other two. $\endgroup$
    – Frank Harrell
    Commented Sep 30, 2021 at 15:26

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