A simple signaling rule for variable life-adjusted display derived from an equivalent risk-adjusted CUSUM chart

The variable life-adjusted display (VLAD) is the first risk-adjusted graphical procedure proposed in the literature for monitoring the performance of a surgeon. It displays the cumulative sum of expected minus observed deaths. It has since become highly popular because the statistic plotted is easy to understand. But it is also easy to misinterpret a surgeon's performance by utilizing the VLAD, potentially leading to grave consequences. The problem of misinterpretation is essentially caused by the variance of the VLAD's statistic that increases with sample size. In order for the VLAD to be truly useful, a simple signaling rule is desperately needed. Various forms of signaling rules have been developed, but they are usually quite complicated. Without signaling rules, making inferences using the VLAD alone is difficult if not misleading. In this paper, we establish an equivalence between a VLAD with V-mask and a risk-adjusted cumulative sum (RA-CUSUM) chart based on the difference between the estimated probability of death and surgical outcome. Average run length analysis based on simulation shows that this particular RA-CUSUM chart has similar performance as compared to the established RA-CUSUM chart based on the log-likelihood ratio statistic obtained by testing the odds ratio of death. We provide a simple design procedure for determining the V-mask parameters based on a resampling approach. Resampling from a real data set ensures that these parameters can be estimated appropriately. Finally, we illustrate the monitoring of a real surgeon's performance using VLAD with V-mask.