Monitoring binary outcomes using risk-adjusted charts: a comparative study

Monitoring binary outcomes when evaluating health care performance has recently become common. Classical statistical methodologies such as cumulative sum (CUSUM) charts have been refined and used for this purpose. For instance, the risk-adjusted CUSUM chart (RA-CUSUM) for monitoring binary outcomes was proposed for monitoring 30-day mortality following cardiac surgery. The RA-CUSUM inherits optimality properties of the original CUSUM charts in the sense of signaling early when there is change. However, although the RA-CUSUM is a powerful monitoring tool, it will always eventually signal a change with probability 1 even when there is no real change. In other words, the probability of a type I error for the RA-CUSUM is 1. It also turns out that, because of the skewed distribution of the run lengths of the RA-CUSUM, the median is often well below the mean, and as a consequence more than half of all its false alarms occur before the designed average run length. In addition, when the change to be detected occurs at a later time in the series of observations being monitored, the rate of false alarms increases, and the RA-CUSUM may not be appropriate. Therefore, if the price of false alarms is high, it is preferable to use methods that control the rate of false alarms. In this paper, we propose alternative sequential curtailed and risk-adjusted charts that control the type I error rate in the context of monitoring 30-day mortality following cardiac surgery. We explore the merits of each of these methodologies in terms of average run lengths as well as in terms of type I error probabilities, and we compare them to the RA-CUSUM chart. We illustrate the methodologies by using data on monitoring performance of seven surgeons from a medical center.