title: Computing exact bundle compliance control charts via probability generating functions.
abstract: Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.
authors.affiliation: Level 3 Communications, Broomfield, CO, USA.
authors.forename: Binchao
authors.initials: B
authors.lastname: Chen
authors.affiliation: Department of Industrial Engineering, Texas Tech University, Lubbock, TX, USA. timothy.matis@ttu.edu.
authors.forename: Timothy
authors.initials: T
authors.lastname: Matis
authors.affiliation: Healthcare Systems Engineering Institute, Northeastern University, Boston, MA, USA.
authors.forename: James
authors.initials: J
authors.lastname: Benneyan
mesh_terms: D000465:Algorithms; D055317:Evidence-Based Practice; D019983:Guideline Adherence; D006801:Humans; D015233:Models, Statistical; D011336:Probability; D011787:Quality of Health Care
keywords: Control charts; Convolutions; Health care; Probability generating function