QUT ePrints

Stability of Approximations of Average Run Length of Risk-Adjusted CUSUM Schemes Using the Markov Approach: Comparing Two Methods of Calculating Transition Probabilities

Webster, Ronald A. & Pettitt, Anthony N. (2007) Stability of Approximations of Average Run Length of Risk-Adjusted CUSUM Schemes Using the Markov Approach: Comparing Two Methods of Calculating Transition Probabilities. Communications in Statistics - Simulation and Computation, 36(3), pp. 471-482.

View at publisher

Abstract

Risk-adjusted CUSUM schemes are designed to monitor the number of adverse outcomes following a medical procedure. An approximation of the average run length (ARL), which is the usual performance measure for a risk-adjusted CUSUM, may be found using its Markov property. We compare two methods of computing transition probability matrices where the risk model classifies patient populations into discrete, finite levels of risk. For the first method, a process of scaling and rounding off concentrates probability in the center of the Markov states, which are non overlapping sub-intervals of the CUSUM decision interval, and, for the second, a smoothing process spreads probability uniformly across the Markov states. Examples of risk-adjusted CUSUM schemes are used to show, if rounding is used to calculate transition probabilities, the values of ARLs estimated using the Markov property vary erratically as the number of Markov states vary and, on occasion, fail to converge for mesh sizes up to 3,000. On the other hand, if smoothing is used, the approximate ARL values remain stable as the number of Markov states vary. The smoothing technique gave good estimates of the ARL where there were less than 1,000 Markov states.

Impact and interest:

3 citations in Scopus
Search Google Scholar™
3 citations in Web of Science®

Citation countsare sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

342 since deposited on 07 Oct 2008
92 in the past twelve months

Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 15045
Item Type: Journal Article
Keywords: Adverse outcomes, ARL, Markov property, Medical monitoring, Risk, adjusted CUSUM
DOI: 10.1080/03610910701208361
ISSN: 1532-4141
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400) > Applied Statistics (010401)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Taylor & Francis
Copyright Statement: This is an electronic version of an article published in [Communications in Statistics - Simulation and Computation 36(3):471-482]. [Communications in Statistics - Simulation and Computation] is available online at informaworldTM with http://dx.doi.org/10.1080/03610910701208361
Deposited On: 07 Oct 2008
Last Modified: 29 Feb 2012 23:37

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page