RESEARCH ARTICLE
A simple signaling rule for variable life‐adjusted display
derived from an equivalent risk‐adjusted CUSUM chart
Philipp Wittenberg
1
| Fah Fatt Gan
2
| Sven Knoth
1
1
Department of Mathematics and
Statistics, Helmut Schmidt University,
Hamburg, Germany
2
Department of Statistics and Applied
Probability, National University of
Singapore, Singapore
Correspondence
Philipp Wittenberg, Department of
Mathematics and Statistics, Helmut
Schmidt University, Hamburg, Germany.
Email: pwitten@hsu‐hh.de
Funding information
Academic Research Fund Tier 1, Grant/
Award Number: R-155-000-159-112;
Ministry of Education, Singapore
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 statis-
tic 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 signal-
ing rules, making inferences using the VLAD alone is difficult if not mislead-
ing. 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 out-
come. Average run length analysis based on simulation shows that this partic-
ular 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.
KEYWORDS
control limits, health care, Parsonnet score, statistical process monitoring, V‐mask
1 | INTRODUCTION
Since its introduction by Lovegrove et al
1
and Poloniecki et al,
2
the variable life‐adjusted display (VLAD) has established
itself as a useful and highly popular charting procedure with “simple” interpretation for monitoring surgical perfor-
mance. It has been widely applied in various fields, for examples, cardiac surgery,
1-13
acute myocardial infarction,
14,15
trauma care,
16-18
intensive care unit,
19,20
surgical site infections,
21-23
esophagogastric surgery,
24,25
health care quality,
26,27
ileal pouch‐anal anastomosis,
28
lung cancer surgery,
29
liver, kidney, heart, and lung transplantation,
30-34
burns service,
35
mortality trends of neonatal deaths in low‐resource settings
36
, and hip fractures patients.
37
Received: 9 June 2017 Revised: 10 November 2017 Accepted: 25 January 2018
DOI: 10.1002/sim.7647
Statistics in Medicine. 2018;37:2455–2473. Copyright © 2018 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/sim 2455
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