Using negative binomial regression for non integer/rate data

First of all, thank you for viewing my thread and helping me.

I'm trying to run a negative binomial regression model for my retrospective research project. It involves looking at the relationship between patient variables such as surgery/non-surgery, transplant/non-transplant, type of ECMO treatment (a specialised bypass machine that helps replace the lungs and/or heart) with the number of blood product transfusions that the patient received during the course of ECMO treatment.

The number of blood products transfused = #PRBC, #platelets, #FFP and # of cryoprecipitate are all count data (number of bags of blood etc). But I know that the number of products correlates with the duration of ECMO treatment (the longer the treatment, the more products are required). So instead of modelling those factors with the total count, I want to model it with transfusion rate (for example #PRBC/day). Unfortunately the rate is no longer and integer and therefore NBR doesn't work.

Would anyone know how to solve this? I heard there's a way to 'log transform' the data, but I'm not sure how to proceed.

Thanks in advance!!!! Much appreciated