Testing a drug's effect on survival across multiple distinct studies
I have survival and other data for between ~1000 patients from different studies with indications varying from organ transplantation to cancer. Patients within this cohort will have been drawn from many different studies in which the objective - long-term graft survival, overall survival rate, metatstasis free survival, organ acute rejection rate, graft loss, etc. - was different. I want to essentially control for all the variables of disease (cancer, organ disease and severity), sex, age, etc. to find out the effect of one explanatory variable - use of drug X as opposed to drugs Y, Z, etc. - on survival/time to death of patients. In the case of organ transplantation, drug X is used as an immunosuppressant: it's primary objective is not to treat disease as such. In the case of the cancer studies however, drug X has a curative objective.
How can I test drug X's effect on only survival within this cohort?