To monitor a health event in patients with a specific risk of developing the event, a risk-adjusted cumulative sum chart is needed. The risk-adjusted cumulative sum chart proposed in the literature has some limitations. Setting appropriate control limits is not straightforward, there is no simple formula for constructing them, and they remain sensitive to changes in the underlying risk distribution and the baseline incidence rate. To overcome these limits, we propose a new risk-adjusted Bernoulli cumulative sum chart as a simple and efficient solution. Analyses of simulated and real data sets illustrate the performance and usefulness of the proposed procedure.
WoodallWH. Use of control charts in health-care and public-health surveillance (with Discussion). J Qual Technol2006; 38: 89–104.
3.
LucasJM. Counted data CUSUM’s. Technometrics1985; 27: 129–144.
4.
RossiGLampugnaniLMarchiM. An approximate cusum procedure for surveillance of health events. Stat Med1999; 18: 2111–2122.
5.
RogersonPAYamadaI. Approaches to syndromic surveillance when data consist of small regional counts. Morb Mortal Wkly Rep2004; 53: 79–85.
6.
HöhleMPaulM. Count data regression chart for the monitoring of surveillance time series. Comput Stat Data Anal2008; 52: 4357–4368.
7.
ReynoldsMRStoumbosZG. A CUSUM chart for monitoring a proportion when inspecting continuously. J Qual Technol1999; 31: 87–108.
8.
SteinerSHCookRJFarewellVTet al.Monitoring surgical performance using risk-adjusted cumulative sum charts. Biostatistics2000; 1: 441–452.
9.
ParsonnetVDeanDBernsteinAD. A method of uniform stratification of risk for evaluating the results of surgery in acquired adult heart disease. Circulation1989; 79: 12–13.
10.
ForbesTLSteinerSHLawlorDKet al.Risk-adjusted analysis of outcomes following elective open abdominal aortic aneurysm repair. Ann Vasc Surg2005; 19: 142–148.
11.
HarrisJRForbesTLSteinerSHet al.Risk-adjusted analysis of early mortality after ruptured abdominal aortic aneurysm repair. J Vasc Surg2005; 42: 387–391.
12.
AxelrodaDAGuidingerbMKMetzgercRAet al.Transplant center quality assessment using a continuously updatable, risk-adjusted technique (CUSUM). Am J Transpl2006; 6: 313–323.
13.
NovickRJFoxSAStittLWet al.Direct comparison of risk-adjusted and non–risk-adjusted CUSUM analyses of coronary artery bypass surgery outcomes. J Thorac Cardiovasc Surg2006; 132: 386–391.
14.
SibandaTSibandaN. The CUSUM chart method as a tool for continuous monitoring of clinical outcomes using routinely collected data. BMC Med Res Methodol2007; 7: 46–46.
15.
SpiegelhalterDJGriggOAKinsmanRet al.Sequential probability ratio tests (SPRTs) for monitoring risk-adjusted outcomes. Int J Qual Health Care2003; 15: 1–7.
16.
ChenTTChungKPHuFCet al.The use of statistical process control (risk-adjusted CUSUM, risk-adjusted RSPRT and CRAM with prediction limits) for monitoring the outcomes of out-of-hospital cardiac arrest patients rescued by the EMS system. J Eval Clin Pract2011; 17: 71–77.
17.
LokeCKGanFF. Joint monitoring scheme for clinical failures and predisposed risks. Qual Technol Quant Manag2012; 9: 3–21.
18.
JonesMASteinerSH. Assessing the effect of estimation error on risk-adjusted CUSUM chart performance. Int J Qual Health Care2012; 24: 176–181.
19.
BrookDEvansDA. An approach to the probability distribution of cusum run length. Biometrika1972; 59: 539–548.
20.
SiegmundD. Corrected diffusion approximations in certain random walk problems. Adv Appl Prob1979; 11: 701–719.
21.
SiegmundD. Sequential analysis, New York: Springer-Verlag, 1985.
