Premium
Risk‐adjusted CUSUM charts under model error
Author(s) -
Knoth Sven,
Wittenberg Philipp,
Gan Fah Fatt
Publication year - 2019
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.8104
Subject(s) - cusum , computer science , logistic regression , statistics , markov chain , robustness (evolution) , alarm , control chart , constant false alarm rate , false alarm , econometrics , mathematics , algorithm , biochemistry , chemistry , materials science , process (computing) , composite material , gene , operating system
In recent years, quality control charts have been increasingly applied in the healthcare environment, for example, to monitor surgical performance. Risk‐adjusted cumulative (CUSUM) charts that utilize risk scores like the Parsonnet score to estimate the probability of death of a patient from an operation turn out to be susceptible to misfitted risk models causing deterioration of the charts' properties, in particular, the false alarm behavior. Our approach considers the application of power transformations in the logistic regression model to improve the fit to the binary outcome data. We propose two different approaches of estimating the power exponent δ . The average run length (ARL) to false alarm is calculated with the popular Markov chain approximation in a more efficient way by utilizing the Toeplitz structure of the transition matrix. A sensitivity analysis of the in‐control ARL against the true value δ shows potential effects of incorrect choice of δ . Depending on the underlying patient mix, the results vary from robustness to severe impact (doubling of false alarm rate).