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Suppose I want to investigate the impact of some binary independent variables (let’s say: sex and height [tall/short]) on my binary response (alcohol consumption for instance). The distribution of my variables is as following (number of observations - 419):

Dependent variable:
#   FALSE      TRUE 
#0.8400955% 0.1599045% 

Some independent variables:
    FALSE      TRUE 
0.97374702% 0.02625298% 
    FALSE      TRUE 
0.9451074%  0.0548926% 
    FALSE      TRUE 
0.96420048% 0.03579952%

I found some questions on stackexchange: 1, 2, and also some papers:

Logistic Regression in Rare Events Data
Predictive Performance of Logistic Regression for Imbalanced Data with Categorical Covariate

However, they both regard to dependent variable, while I have unbalanced the independent ones. I know, that my model will have low predictive power because of such unbalance, since it may not capture the characteristics of population (I mean that the distribution in population may differ).

But I am not sure whether I may use my independent variables to make any statistical inferences about the impact of independent variables on my dependent one? I am looking for a rule regarding the distribution/size of binary independent variables (e.g. 97% of FALSE and 3% of TRUE cases).

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    $\begingroup$ If you're interested in inference, then your primary concern should be power. An imbalance in regressors isn't a big deal so long as you have enough observations to give you your desired level of power. 1 tall person in 10 observations is a bad thing. 100 tall people in 1000 observations is better. $\endgroup$
    – Demetri Pananos
    Commented Nov 24, 2021 at 19:48
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    $\begingroup$ Without having looked at (for) those papers, be aware that most such papers deal with imbalance in the dependent variable. (Which IMO is no problem.) @DemetriPananos: do you want to post your comment(s) as an answer? Better to have a short answer than no answer at all. Anyone who has a better answer can post it. $\endgroup$
    – Stephan Kolassa
    Commented Nov 24, 2021 at 20:09

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