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

Abstract

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.

Flexible risk‐adjusted surveillance procedures for autocorrelated binary series

“…In our current simulation study we included RACUSUM to show what would happen if users chose that method instead of our tests. Note that the dependence structure is not accommodated in RACUSUM or in Gombay, Hussein, & Steiner (), so this is a new feature of this study. Furthermore, Kulldorff et al () demonstrated that the performance of the CUSUM test is very sensitive to the choice of the alternative parameter value.…”

“…We therefore set a horizon (a maximal sample n ) by which, if has not been rejected, the surveillance procedure will be re‐started. This makes our surveillance procedure a truncated one, thus providing better control over the probability of false alarms as in Gombay, Hussein, & Steiner (). The choice of n is beyond the scope of the current study, but it is related to the same choice in group sequential tests where it has been extensively studied.…”

“…Currently, the most popular monitoring statistics are based on Page's CUSUM strategy, where independence of observations is assumed and specification of the alternative parameter value under the alternative is required in the likelihood ratio statistic. Gombay, Hussein, & Steiner () compared the performance of the efficient‐score‐based procedure to the RACUSUM‐based surveillance in case of independent observations via Monte Carlo simulations. In our current simulation study we included RACUSUM to show what would happen if users chose that method instead of our tests.…”

“…Statistical methods for the surveillance of health care outcomes have recently gained momentum. In particular, risk‐adjusted cumulative sum (RACUSUM) charts have been developed for the surveillance of binary outcomes such as the 30‐day mortality rates of patients undergoing heart surgery (see, for instance, Steiner et al, ; Frisen, ; Grigg & Farewell, ; Grigg & Spiegelhalter, ; Gombay, Hussein, & Steiner, ).…”

Dynamic probability control limits for risk-adjusted Bernoulli CUSUM charts

“…We note that the approach of Gombay et al . is different from ours in the sense that they control the overall probability of a false alarm for a specified number of patients. We instead assume an ongoing monitoring scenario.…”