To make your units comparable, you need to convert all the measurements to the same unit. Since you have three different units—pg/mL, ng/L, and u/mL—you can standardize them to one common unit.

You already know there's a 1-to-1 correspondence between these units, meaning 1 pg/mL is equivalent to 1 ng/L.

Here’s what you can do:

For Ab40, Ab42, and their ratio: These are already in pg/mL, which equals ng/L.

For p-tau217 (u/mL): Convert u/mL to ng/L.

i.e Concentration in ng/L=Concentration in u/mL×10^6

For p-tau181 (ng/L): This is already in ng/L.

After converting all biomarkers to the same unit (ng/L), you can proceed with your logistic regression analysis, ensuring that all predictor variables are in consistent units.

Hope this helps!

Purvi Patel , thank you so much, this is helpful indeed.

I'd think that standardizing units might not necessarily be mandatory for logistic regression. Would you say this is not true?

As of now, I've log transformed a lot of my data because it was highly skewed. But I've actually kept the original units (with the exception of the AB42/40 ratio where I made sure AB40 and 42 were measured in the same units).

In logistic regression, you don't always have to standardize the units of your predictor variables, but it can be helpful. Standardizing makes it easier to understand the coefficients because all the predictors are on the same scale. It also helps the model's calculations work better by avoiding problems caused by predictors having very different ranges. This keeps the algorithm running smoothly and finding the best model fit.

Log-transforming your data is a common and effective approach to address skewness, particularly in cases where the data spans several orders of magnitude. This transformation helps in stabilizing variance and making the distribution more normal-like, which is advantageous for many statistical analyses, including logistic regression. Overall, your approach to log-transforming skewed data and maintaining original units (where necessary) seems sound.

Thank you very much again!

Since the model then had very poor fit, I did start questioning whether the transformations I applied were sufficient. However, standardizing the data (raw, not log-transformed) did not seem to improve things a lot, so it must be that my predictors simply do not 'predict' my outcome very well.