Leiden University Student Repository

Kok, C. (4372)

How statistics can save lives: A mathematical comparison and improvement of statistical control charts in medical contexts

Master thesis | Mathematics (MSc)

Statistical process control is a widely used method of quality control, where control charts are used to monitor and measure variations in a process. In medical contexts, the most frequently used chart is the cumulative sum (CUSUM) chart, which is a chart based on the likelihood-ratio test. To use this chart in healthcare, it is important to adjust the chart to a patients individual risk to get a more accurate representation of the process that is monitored. To implement such CUSUM control charts it is necessary to specify the value of the parameter of interest that corresponds to the process being out of control. As this value often is arbitrary and difficult to determine when there is no prior knowledge, it is desirable to search for control charts that do not have this requirement and are based on statistical tests for composite hypotheses. The main purpose of this thesis is to find a suitable alternative for the riskadjusted CUSUM to use in healthcare. Various extensions of the...Show moreStatistical process control is a widely used method of quality control, where control charts are used to monitor and measure variations in a process. In medical contexts, the most frequently used chart is the cumulative sum (CUSUM) chart, which is a chart based on the likelihood-ratio test. To use this chart in healthcare, it is important to adjust the chart to a patients individual risk to get a more accurate representation of the process that is monitored. To implement such CUSUM control charts it is necessary to specify the value of the parameter of interest that corresponds to the process being out of control. As this value often is arbitrary and difficult to determine when there is no prior knowledge, it is desirable to search for control charts that do not have this requirement and are based on statistical tests for composite hypotheses. The main purpose of this thesis is to find a suitable alternative for the riskadjusted CUSUM to use in healthcare. Various extensions of the standard CUSUM are investigated, and a new risk-adjusted chart based on the generalized likelihood ratio test is introduced, where the process that is considered is assumed to be a medical process in discrete time, with binary outcomes. By investigating existing theory it turns out that the CUSUM and the standard generalized likelihood ratio (GLR) chart satisfy asymptotical optimality properties, where the biggest difference is that the optimality of the CUSUM chart depends on the value of the parameter in the alternative hypothesis, whereas the optimality of the GLR depends on the true value of the parameter in the process. There is mathematical justification for giving the CUSUM a head start to detect out of control situations quicker, and extensions for the GLR are also investigated. Using the theoretical knowledge, a risk-adjusted version of the GLR is introduced. The parameter in this test cannot be determined exactly, but should be approximated. Through many simulations, results for multiple charts are obtained. The CUSUM outperforms the GLR when the value in the alternative hypothesis is near the true value of the parameter of interest, but the GLR is a good competitor when there is no prior knowledge. The head start feature of the CUSUM is shown to be a really useful feature when there is some prior knowledge of the process. The main recommendations for using control charts in healthcare are that the CUSUM is a very clear chart to use, but the overall performance of the GLR is similar of even better. When a process is considered to be out of control, there are various ways to reset the chart and there is no general best choice in this matter. Further research is recommended, especially towards the risk-adjusted version of the GLR.Show less

Author

Kok, C.

Faculty

Faculty of Science

Supervisors

Pas, S.L. van der
Putter, H.

ECTS Credits

40

Language

en