Generalized linear model for cost data in spss

Hi guys, I urgently need your help on this: I want to apply a generalized linear model (GLM) to compare adjusted costs between 2 or more groups of patients, let’s say the name of this group variable is “cohort” (please check the photo). What is a correct way to do this in SPSS?
Is it correct to enter the total costs as the dependent variable (for all records in the database, independent of cohort assignment) and enter all independent variables (age, gender, premedication…) into the model, as we want to adjust the total cost for variability coming from these independent variables, as they are different between cohorts and have impact on the total cost. And then, after getting the predictive model values of total cost just simply compare them between the cohorts. Pay attention, this variable “cohort” was not included in the model!
Is this correct way of adjusting total cost for all independent variables different between cohorts, where we want to exclude or at least reduce their impact on total cost? Furthermore, after getting the adjusted costs for all the records in the database, is it correct to compare them between the cohorts, even though this variable was not included in the regression model?
Or I am making bias this way?
Could you please help me to deal with this in a right way? Thanks.