Stability of Approximations of Average Run Length of RiskAdjusted 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 RiskAdjusted CUSUM Schemes Using the Markov Approach: Comparing Two Methods of Calculating Transition Probabilities. Communications in Statistics  Simulation and Computation, 36(3), pp. 471482.

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Abstract
Riskadjusted 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 riskadjusted 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 subintervals of the CUSUM decision interval, and, for the second, a smoothing process spreads probability uniformly across the Markov states. Examples of riskadjusted 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.
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ID Code:  15045 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  Adverse outcomes, ARL, Markov property, Medical monitoring, Risk, adjusted CUSUM 
DOI:  10.1080/03610910701208361 
ISSN:  15324141 
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):471482]. [Communications in Statistics  Simulation and Computation] is available online at informaworldTM with http://dx.doi.org/10.1080/03610910701208361 
Deposited On:  07 Oct 2008 00:00 
Last Modified:  29 Feb 2012 13:37 
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