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I'm analysing some data for a study that has a normal (cognition) outcome, but the predictor of interest (biomarker) is heavily skewed at the top end. The vast majority of the data is pooled around very low numbers.

Log transformations probably wouldn't normalise the data and as I understand they make interpretation quite difficult, so that's not something I want to look at really.

My Question is - does anyone have any advice on model structure given this? Should the non-normal covariate be broken down into quartiles, as is common in the lit? Or would a traditional linear regression produce reasonable estimates? Or perhaps something like a generalized estimating equation would be more appropriate?

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    $\begingroup$ P.S. I understand there is no assumption of normality for independent variables in linear regression! But I also know that they don't give you very good estimates. I'm really just interested in what people think is the most instructive way to model this $\endgroup$ – Lach Apr 6 at 2:08
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For any regression model, the first and foremost question should be what kind of relationship are you modeling, and only after settling on that there's any point in discussing the sampling distributions associated with that relationship. In your case, a linear relationship is unlikely: would you really expect that a person with 10x higher concentration of the marker you are measuring should have multiple times higher cognition on your scale?

Log (base 10) transforming turns that 10x increase in concentration to an additive factor (of +1). A linear relationship between such a transformed variable and a typical psychometric scale is much more likely, and not too difficult to interpret. (Of course, this entirely depends on your variables, and these suggestions are just rules of thumb.)

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