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I have a biomarker ratio (amyloid 42/40) and I am having issues modelling it. This is the proportion of a biomarker to another biomarker and it is important in diagnosing dementia. I am using as both an exposure and an outcome but obviously, this distribution of the variable is more problematic when I am looking at the variable as an outcome. I would appreciate any suggestions as to what modelling approaches you have used with such data. These are the residual plots for a Gamma log link model.

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    $\begingroup$ Please edit the question to provide more information about your data and what questions you are trying to answer. Explain the original data that went into constructing this ratio; it's often better to work with the original data than to convert to a ratio for analysis. Regardless, the distribution of values doesn't matter much at all for a predictor variable, and a skewed distribution of an outcome variable isn't a problem provided that there is corresponding skew in predictors. The more information you can provide in the question, the more likely you are to get a helpful answer. $\endgroup$ Commented Dec 13, 2024 at 19:54
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    $\begingroup$ What problems are you concerned about? $\endgroup$ Commented Dec 14, 2024 at 1:38
  • $\begingroup$ Non-normality, outliers, if the models I am using are best for the data. $\endgroup$ Commented Dec 15, 2024 at 18:08

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The proportional odds model is a great option for modeling an ordinal or continuous outcome that may be non-normally distributed, skewed, or contain outliers.

Tons of great resources on the PO model here: https://www.fharrell.com/post/rpo/

The Wilcoxon test is great for comparing such an outcome between 2 groups, and the PO model can be thought of as an extension of the Wilcoxon test that allows you to adjust for covariates.

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