- Title
- Bayesian interval estimation and performance measurement
- Creator
- Lin, Yi-Fan
- Relation
- University of Newcastle Research Higher Degree Thesis
- Resource Type
- thesis
- Date
- 2019
- Description
- Research Doctorate - Doctor of Philosophy (PhD)
- Description
- Background: Quality measurement and reporting systems are used in healthcare internationally. Clinical indicators are increasingly being used to assess, compare and improve the quality of care provided by health care systems. In Australia, the Australian Council on Healthcare Standards records and reports hundreds of clinical indicators nationally across the healthcare system. These indicators are measures of performance in the clinical setting, and are used as a screening tool to help assess whether a standard of care is being met. Existing analysis and reporting of these indicators incorporate Bayesian methods to address sampling variation; however, such assessments are retrospective in nature, reporting upon the previous six or twelve months of data. The use of Bayesian methods within statistical process control for monitoring systems is an important pursuit to support more timely decision-making. Objectives: This thesis aimed to develop and assess a new graphical monitoring tool, similar to a control chart, utilising the benefits of Bayesian hierarchical models, and potentially improving the monitoring of the health care system. Methods: Simulations were developed based upon a factorial design parameter space to compare the traditional Bernoulli CUSUM (BC) chart with three charts utilising the Bayesian paradigm. The first two charts are based on the beta-binomial posterior predictive (BBPP) distribution with each of the more traditional “central” and “highest posterior density” (HPD) interval approaches to define the limits, named BBPPCI and BBPPHPD charts, respectively. The third chart was a Bayesian CUSUM, based on the beta-binomial posterior (BBP) distribution with the traditional Bernoulli CUSUM (BC) chart procedure, named the BBPBC chart. These charts were compared via heat maps, regression models and tree-based models to identify parameter spaces where the new charts were superior to the traditional BC chart, based on in-control and out-of-control average run lengths, assuming that the parameter representing the underlying clinical indicator rate (proportion of cases with an event of interest) required estimation. Results: The in-control ARLs for all charts were very high, exceeding traditional Shewhart charts. The newly developed BBPP chart with HPD interval estimation was found to have the best performance based on the out-of-control ARL (ARLout) for the case of when the underlying parameter changes immediately. The BBPPHPD chart had, on average, a smaller ARLout than the BC chart in 75% of the simulations conducted. Conclusions: Bayesian hierarchical models and the newly developed control charts utilising these models have been shown to offer value to the health care system. These new charts offer improved abilities to detect changes in the system, and can do so in a more timely manner than retrospective system reports. It is recommended that these charts continue to be explored and assessed for a broader parameter space and utilising traditional run rules. A final chapter in the thesis explored a Bayesian approach to a problem surrounding interval estimation that was recently addressed by frequentist methods. The article in question was the result of a practical application requiring inference for the weighted sum of two binomial proportions, which is related to the more common problem of inference for the difference between two proportions. Bayesian credible intervals were derived which perform better than the frequentist-based confidence intervals that were developed for the application, not only in terms of frequentist coverage, but especially in terms of intervals for extreme data outcomes.
- Subject
- average run length (ARL); run length (RL); Bernoulli CUSUM (BC) chart; beta binomial posterior predictive (BBPP) distribution; clinical indicator (CI); highest posterior density (HPD) interval; creduble interval (CrI); profile likelihood (PL)
- Identifier
- http://hdl.handle.net/1959.13/1407919
- Identifier
- uon:35793
- Rights
- Copyright 2019 Yi-Fan Lin
- Language
- eng
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| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | ATTACHMENT01 | Thesis | 88 MB | Adobe Acrobat PDF | View Details Download | ||
| View Details Download | ATTACHMENT02 | Abstract | 942 KB | Adobe Acrobat PDF | View Details Download |