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Type: Thesis
Title: Statistical Challenges in the Modelling and Analysis of Critical Care Mortality Data
Author: Bailey, Richard Leigh
Issue Date: 2020
School/Discipline: School of Mathematical Sciences
Abstract: Monitoring the performance of healthcare providers assists with maximising patient safety, maintaining quality control, and managing financial resources. However, such monitoring also attracts controversy, particularly when jurisdictions publish performance rankings, due to the effect on providers' reputations, referrals, and reimbursements for treatment. Thus, accurate and fair performance assessment is vital. The focus of this thesis is the performance of critical care providers in hospital intensive care units (ICUs). Patient mortality in hospital is the outcome that is monitored, and the standardised mortality ratio (SMR) is the performance indicator. Four inter-related methods of calculating SMRs are considered using a general multilevel model that contains patient- and provider-level attributes. Two options for the numerator of the SMR are either the observed mortalities or a smoothed version of the observed mortalities that allows for sampling variation. There are also two options for the denominator of the SMR, which represents the expected mortalities. The denominator adjusts for the patient casemix and either the actual or average provider attributes. This thesis presents the first known implementation of SMRs where the numerator is the smoothed observed mortalities, and both the numerator and denominator are based on a model containing (patient- and) provider-level attributes. The advantages and disadvantages of the four methods are discussed. The smoothed observed mortalities and the expected mortalities are defined in terms of intractable integrals. These integrals are evaluated numerically, often by adaptive quadrature. A much quicker but less accurate alternative is the Laplace approximation, and extending this technique may lead to a better compromise between speed and accuracy. In this thesis, the Laplace approximation is extended beyond that covered in the literature, and details are provided on how the integrals are expressible as series of any order. Comparisons against published results demonstrate that the newly developed extensions are much faster and almost as accurate as adaptive quadrature. The challenge of estimating SMR uncertainty is addressed by bootstrapping, and a non-parametric procedure is described for this purpose. Bootstrap procedures tend to be computationally intensive, which highlights a significant advantage of using extended versions of the Laplace approximation. The four variations of SMRs are calculated for a subset of the Australian and New Zealand Intensive Care Society (ANZICS) Adult Patient Database (APD). Deidentified patient records are voluntarily and retrospectively submitted to the APD by the majority of Australian and New Zealand adult ICUs. This thesis examines the in-hospital mortality data of 370,554 patient admissions to 170 ICUs between 2011 and 2015 inclusive. Risk-adjusted mortality generally decreased over time. Furthermore, risk-adjusted mortality was significantly higher for the ICUs of tertiary hospitals. This was re ected in the estimated SMRs when the expected mortalities were based on average ICU attributes. In this application, the smoothing of observed mortalities is recommended for the process of identifying unusually performing ICUs. There was also substantial variability in the estimated SMRs by each method. This was predominantly due to the variability within hospital types, and was largest for the ICUs of private hospitals.
Advisor: Metcalfe, Andrew
Solomon, Patricia
Moran, John
Dissertation Note: Thesis (Ph.D.) -- University of Adelaide, School of Mathematical Sciences, 2020
Keywords: bootstrap
critical care
intensive care unit
Laplace approximation
logistic regression
mortality data
multilevel model
standardised mortility ratio
Provenance: This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exceptions. If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at:
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