Cumulative Sum Schemes for Surgical Performance Monitoring

Summary The standard cumulative sum (CUSUM), risk-adjusted CUSUM and Shiryayev–Roberts schemes for monitoring surgical performance are compared. We find that both CUSUM schemes are comparable in run length performance except when there is a high heterogeneity of surgical risks, in which case the risk-adjusted CUSUM scheme is more sensitive in detecting a shift in surgical performance. The Shiryayev–Roberts scheme is found to be less sensitive compared with the CUSUM schemes in detecting a deterioration in surgical performance. Using the Markov chain method, the exact average run length of a standard CUSUM scheme can be computed whereas the average run length of a risk-adjusted CUSUM scheme is approximated. For a risk-adjusted CUSUM scheme, the accuracy of the average run length depends on the fineness of the discretization of CUSUM values, which relies on the chart limit, shift to be detected optimally and in-control surgical risk distribution. A sensitivity analysis shows that the risk-adjusted CUSUM and Shiryayev–Roberts schemes still perform moderately well in detecting a deterioration and an improvement in surgical performances respectively even though there is a misspecification of the in-control surgical risk distribution. In general, the run length performance of the Shiryayev–Roberts scheme is comparatively less sensitive to a misspecification of the in-control surgical risk distribution.