# Validity of comparing specific predictors from two non-nested models

I’m working with a dataset comprising various physiological measurements (as well as some relevant demographic variables) of the femur in 289 participants. Multiple variables are indices for which I have both CT- and MRI- obtained measurements. I would like to compare the CT and MRI versions of one specific index (two variables, same index) with respect to how strongly they are associated with a specific disease/condition (coded 0, 1). My approach to this included running two separate multiple logistic regression models, adjusted using the same set of covariates, and comparing the odds ratios for the CT vs. MRI version of the index, in addition to comparing overall model fit (using AIC estimates).

My question – Is this a valid approach to answering my question? If not, why, and what is a more reasonable alternative?

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Would you be using exactly the same observations for both models, and is it the case that there are no missing data?

Exactly, same observations, no missing data.

Consider using the “adequacy index” I describe in my book Regression Modeling Strategies. Compute 3 likelihood ratio \chi^2 statistics: for the full model with both predictors (and adjustment variables) and for models leaving one predictor out each time. Compute the proportion of \chi^2 explained by each predictor after accounting for all other variables. “Adequacy” comes from the ratio of the \chi^2 without one of the variables to the whole model, i.e., the extent to which a model without the variable is adequate in explaining variation in outcome. This uses the gold standard log-likelihood. Also see methods in http://fharrell.com/postt/addvalue.

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Awesome, thank you so much! As the [mostly] lone analyst in my dept with graduate statistical training, but not quite a statistician (although I’m working toward becoming one), I really appreciate the feedback and this forum. I’ll be sure to read through the ML section in your book.

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