Deciding kidney-offer admissibility dependent on patients’ lifetime failure rate

•We provide a flexible model for the kidney allocation problem.•The optimal policy changes dramatically between patients.•The model can serves both patient and the decision maker.•An easy software tool is available. We use developments in full-information optimal stopping to decide kidney-offer admissibility depending on the patient’s age in treatment, on his/her estimated lifetime probabilistic profile and his/her prospects on the waiting list. We allow for a broad family of lifetime distributions – the Gamma – thus enabling flexible modeling of patients survival under dialysis. We fully automate an appropriate recursive solution in a spreadsheet application. It yields the optimal critical times for acceptance of offers of different qualities, and the ensuing expected value-to-go as a function of time. The model may serve both the organizer of a donation program for planning purposes, and the particular surgeon in making the critical decision at the proper time. It may further serve the potential individual recipient, practicing present-day patient-choice. Numerical results and their discussion are included.