Temporal control chart methods for homogeneous and inhomogeneous poisson processes
Student thesis: Doctoral Thesis
Related Research Unit(s)
Public health and health care surveillance has attracted considerable attention due to the severe impact of infectious diseases. Fast detection of increases in the incident rate of an adverse event is always desirable. Motivated by successful applications in industry quality control, the technique of control chart has been introduced to the domain of health care surveillance from traditional statistical process control (SPC). A common assumption in SPC is a stationary baseline process for an in-control state and a sustained step shift for an out-of-control state. However, this assumption does not hold in health care surveillance. In this thesis, we investigate the issues of inhomogeneous population size and linear drifts in health care surveillance. The cumulative sum (CUSUM) chart is one of the well known techniques for monitoring the Poisson process, and various CUSUM procedures have been developed to monitor rate changes of health events when population size changes over time. Average run length (ARL), which is commonly used in quality control, may not be appropriate in some situations when comparing control chart performance in health surveillance applications. This thesis provides a thorough statistical comparison of CUSUM-type procedures in the health care context based on different evaluation metrics. We show that different measures may favor different surveillance methods depending on the corresponding design criteria. We thus recommend a probabilistic measure as the criterion for the design and evaluation of CUSUM control charts in health care surveillance. The CUSUM method is typically designed for a pre-speciﬁed target shift size, which provides good detection ability when the true shift is close to the pre-speciﬁed value. However, its performance can be worse if the true shift is far from the target. In practice, the true shift size is an unknown factor rather than a known quantity, which lowers down the advantage of the CUSUM technique. The weighted CUSUM (WCUSUM) method and the adaptive CUSUM (ACUSUM) method are effective alternatives to account for the unknown shift issue. This dissertation presents a thorough comparison on the detection ability of several CUSUM-type methods, including CUSUM, WCUSUM, and ACUSUM, for monitoring the Poisson process mean subject to increasing population sizes. The results show that the ACUSUM method generally performs better than the traditional CUSUM and WCUSUM methods for a wide range of shift sizes, especially when the shift size is small. A real example of male thyroid cancer in New Mexico is provided to illustrate the difference between the investigated methods. Most of the studies focus on the case with step shifts in Poisson means. Relatively little attention has been paid to the case with linear drifts in Poisson means. We extend the window-limited generalized likelihood ratio (WGLR) test from the monitoring of normal means to Poisson processes, with a focus on linear drifts. The comparison results with the adaptive cumulative sum (CUSUM) charts and the weighted CUSUM (WCUSUM) charts show that the WGLR chart generally provides better detection performance than the other alternative methods in both the zero-state and steady-state cases. Finally, we investigate the performance of the exponentially weighted moving average (EWMA) chart for monitoring the Poisson process subject to linear drifts. We extend the Markov chain model from monitoring the Poisson process under step shift to the Poisson process with a linear drift to analyze the performance of the EWMA chart. The results show that the proposed method is capable of providing accurate average run length approximates compared with Monte Carlo simulations. Optimal design tables and sensitivity analysis are presented to facilitate the use of EWMA chart in practice.
- Public health surveillance, Charts, diagrams, etc, Poisson processes, Quality control, Statistical methods