A risk-adjusted CUSUM in continuous time based on the Cox model

In clinical practice, it is often important to monitor the outcomes associated with participating facilities. In organ transplantation, for example, it is important to monitor and assess the outcomes of the transplants performed at the participating centers and send a signal if a significant upward trend in the failure rates is detected. In manufacturing and process control contexts, the cumulative summation (CUSUM) technique has been used as a sequential monitoring scheme for some time. More recently, the CUSUM has also been suggested for use in medical contexts. In this article, we outline a risk-adjusted CUSUM procedure based on the Cox model for a failure time outcome. Theoretical approximations to the average run length are obtained for this new proposal and for some discrete time procedures suggested in the literature. The proposed scheme and approximations are evaluated in simulations and illustrated on transplant facility data from the Scientific Registry of Transplant Recipients.