I am analyzing exam data collected from participants who applied to an academic program. The data was collected from 2014-2018, and applicants only took the exam once when applying to the program (after being rejected, they could not reapply). The exam's questions were changed in 2018, so the participants who applied to the program during 2014-2017 took a different exam than those who applied in 2018. Both exams were validated and measure the same construct.
To examine whether race, gender, family income, and parents' marital status were predictors of passing the exam (outcome is binary pass/fail), I ran a logistic regression model on the data collected from 2014-2017 separately from the 2018 data to account for the change in the exam. However, the 2018 data has low statistical power due to a small sample size, so my model has poor fit when running it exclusively with the 2018 data. Would it be methodologically sound for me to run the model on on all of the exam data (2014-2018) controlling for the exam change in the model (0 = original exam, 1 = updated exam), or should I use an alternative method?