Replacing binary logistic regression with multinomial logistic regression? I am reviewing a study. It's authors wanted to investigate which of the care settings were more often used by women and which by men. Adjusting was done for age, comorbidity status. There were a total of 10 care settings. Thus, they did the following:
Binary logistic regression
sex ~ care_settings + covariates for adjusting

But IMHO they should have been used multiple logistic regression
care_settings ~ sex + covariates for adjusting

Could you have a comment on that. Is their approach correct?

The key question is what to predict / or what is the dependent variable.
If the study is about investigating the "correlation" between gender and care setting, or how to use care setting to predict gender, then the original formulation can be used.
If we want to use gender and other variable to "predict" care setting, then your formulation can be used.
In real world, to do a 10 class classification requires much more data than binary classification, I think this is another reason why the authors choose their formulation.
