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Stat Med. 2014 Aug 15;33(18):3114-29. doi: 10.1002/sim.6139. Epub 2014 Mar 13.

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring.

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Department of Biostatistics, University of Michigan, 1415 Washington Heights, Ann Arbor, MI, U.S.A.


We develop a weighted cumulative sum (WCUSUM) to evaluate and monitor pre-transplant waitlist mortality of facilities in the context where transplantation is considered to be dependent censoring. Waitlist patients are evaluated multiple times in order to update their current medical condition as reflected in a time-dependent variable called the Model for End-Stage Liver Disease (MELD) score. Higher MELD scores are indicative of higher pre-transplant death risk. Moreover, under the current liver allocation system, patients with higher MELD scores receive higher priority for liver transplantation. To evaluate the waitlist mortality of transplant centers, it is important to take this dependent censoring into consideration. We assume a 'standard' transplant practice through a transplant model and utilize inverse probability censoring weights to construct a WCUSUM. We evaluate the properties of a weighted zero-mean process as the basis of the proposed WCUSUM. We then discuss a resampling technique to obtain control limits. The proposed WCUSUM is illustrated through the analysis of national transplant registry data.


control limits; cumulative sum (CUSUM); dependent censoring; failure time data; inverse probability weights; quality control; quality improvement; resampling; risk adjustment

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