I detected a set of patients that have a high response to a drug. Each patient has 40 different reads ( 20 nominal and 20 continuous) resemble certain genetic and expression variations.
How should I fit a model to detect the variant(s) that is most related to response?
You can use multiple regression and see which variable has the highest standardized coefficient or the highest semipartial correlation. But if there is multicollinearity among you predictors (which is likely when you have so many) then the estimates for each individual predictor will not be very accurate. So you need to first check for multicollinearity and then reduce it to an acceptable level.
There are several ways to check (including the condition number [kappa] and variance inflation factors). There also are several ways to address multicollinearity and find it. If you do some searching on Google you will find many resources discussing this. I even provided a link for another question about this just yesterday.
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