Fit Model Ordinal Logistic Y = data ranks for complex non-normally distributed data

Question

I need a sanity check on an analysis method I derived based on a couple of posts on this forum and on the answers to a previous question.

Namely, I need to determine the effects of Treatment and Biomarker levels on a clinical measure that is not normally distributed and cannot be transformed into a normally distributed response variable. Since JMP 11.1 does not provide non-parametric multi-variable models, I used a work-around: I derived the ranks of the clinical measures and used those ranks (Ordinal distribution) as the response variable in an ordinal logistic model with Treatment and Biomarker levels as Effect variables.

Am I violating key assumptions of the Logistic model by using my work-around approach?

If I do, what would be an acceptable alternative (note: binning the response variable in 2 – 4 bins is not desirable)?

Thank you

Mark_Bailey · Answer

A couple more thoughts:

* The Distribution platforms shows that you have a response that is not normally distributed, without a doubt! But that is not the assumption of regression. The assumption is about the distribution of the errors. Standard least squares regression assumes that the errors are normally distributed, binary logistic regression assumes that the errors are binomially distributed, Poisson log-linear regression assumes that the errors are Poisson distributed, and so on.* The correct model for the errors is often related to the physical process by which responses are generated.
* Your Residual by Predicted Plot in the second journal suggests that the normal distribution is not good for the errors, but this pattern suggests to me that there is something unusual about your clinical measure.

* Did you try adding higher-order transforms of the Biomarker A1 to the linear predictor? Try adding the square and cubic terms to the Effects list in the Fit Model dialog and see what happens to the regression. (I don't think that this alone will help with the non-normal errors).
* What is the clinical measure such that it limits at 0 and at 1, and all the data piles up near one of these two boundaries?* Since it is limited to [0,1], like probability, you might try applying the logit transform to the measure. Select Clinical Measure in the Y list in the Fit Model dialog, then click the red triangle next to Transform and select Logit.

sornasst · Answer

Hi Mark,

Thank you for your valuable input. Find attached 2 JMP Journal files:

* Distribution report for the Clinical Response Variable I described earlier
* Fit Model > Standard Least Square report for the analysis as you suggested

Best regards,

Thierry

Clinical_Measure_Distribution.jrn

Least_Square_Report.jrn

Mark_Bailey · Answer

A couple of things to think about:

* You always give up information (and estimation efficiency) when you convert continuous measurement data into categorical data. What does the regression look like when you use the clinical measure directly as the response?
* The distribution assumption is about the errors, not the response. How did you determine that the normal distribution is not an appropriate model for the errors?
* How did you determine that a transformation was not possible/helpful?
* Using the ranks will likely lead to too many categorical levels. That outcome is OK (actually desirable) when you perform a non-parametric test, but it will adversely affect your regression because you will many, many rare outcomes (biased estimates, separation problem).
* You have two choices for the logits used in multinomial logistic regression: ordinal (cumulative logits) and nominal (generalized logits). The association of these logits (ordinal and nominal) is somewhat historic. You should think about model flexibility (common parameters or unique parameters) for each logit.

I will post more if I think of something else.