Monitoring paired binary surgical outcomes using cumulative sum charts

Correlated binary data are encountered in many areas of medical research, system reliability and quality control. For monitoring failures rates in such situations, simultaneous bivariate cumulative sum (CUSUM) charts with the addition of secondary control limits are proposed. Using an approach based on a Markov chain model, the run length properties of such a monitoring scheme can be determined for sudden, or gradual, changes in the failure rates. The proposed control charts are easy to implement, and are shown to be very effective at detecting small changes in the rate of undesirable outcomes, especially when the changes are gradual. This procedure is illustrated using bivariate outcome data arising from a series of paediatric surgeries. The methodology is sufficiently general that it may be adapted for multivariate normal, binomial or Poisson responses.