Distribution-free control charts for mixed-type data based on rank of interpoint distances

Multivariate control charts have found wide application in healthcare, yet they primarily cater to continuous or categorical variables. However, the emergence of mixed-type data has sparked interest in adapting traditional control charts to handle such complexity. Unfortunately, existing methods often struggle to effectively manage this complexity, particularly in scenarios with limited historical in-control data. In response, this article introduces three distribution-free control charts specifically designed for monitoring mixed-type processes. The proposed approach revolves around computing distances between observations and a specified point, thereby reducing the data to a single dimension. Subsequently, the ranks of these one-dimensional distances are leveraged to develop monitoring statistics. Furthermore, to facilitate dimensionality reduction, a novel distance measure tailored for mixed-type data is introduced. Extensive validation of our proposed method is conducted through comprehensive simulation experiments. Moreover, we demonstrate the practical applicability of the proposed method using an example related to heart disease.

A monitoring framework for health care processes using Generalized Additive Models and Auto-Encoders

In recent years, there has been a considerable focus on developing effective methods for monitoring health care processes. Utilizing Statistical Process Monitoring (SPM) approaches, particularly risk-adjusted control charts, has emerged as a highly promising approach for achieving robust frameworks for this aim. Considering risk-adjusted control charts, longitudinal health care process data is typically monitored by establishing a regression relationship between various risk factors (explanatory variables) and patient outcomes (response variables). While the majority of prior research has primarily employed logistic models in risk-adjusted control charts, there are more intricate health care processes that necessitate the incorporation of both parametric and nonparametric risk factors. In such scenarios, the Generalized Additive Model (GAM) proves to be a suitable choice, albeit it often introduces higher computational complexity and associated challenges. Surprisingly, there are limited instances where researchers have proposed advancements in this direction. The primary objective of this paper is to introduce an SPM framework for monitoring health care processes using a GAM over time, coupled with a novel risk-adjusted control chart driven by machine learning techniques. This control chart is implemented on a data set encompassing two stroke types: ischemic and hemorrhagic. The key focus of this study is to monitor the stability of the relationship between stroke types and predefined explanatory variables over time within this data set. Extensive simulation results, based on real data from patients with acute stroke, demonstrate the remarkable flexibility of the proposed method in terms of its detection capabilities compared to conventional approaches.

Modeling the patient mix for risk-adjusted CUmulative SUM charts

The improvement of surgical quality and the corresponding early detection of its changes is of increasing importance. To this end, sequential monitoring procedures such as the risk-adjusted CUmulative SUM chart are frequently applied. The patient risk score population (patient mix), which considers the patients’ perioperative risk, is a core component for this type of quality control chart. Consequently, it is important to be able to adapt different shapes of patient mixes and determine their impact on the monitoring scheme. This article proposes a framework for modeling the patient mix by a discrete beta-binomial and a continuous beta distribution for risk-adjusted CUSUM charts. Since the model-based approach is not limited by data availability, any patient mix can be analyzed. We examine the effects on the control chart’s false alarm behavior for more than 100,000 different scenarios for a cardiac surgery data set. Our study finds a negative relationship between the average risk score and the number of false alarms. The results indicate that a changing patient mix has a considerable impact and, in some cases, almost doubles the number of expected false alarms.

Monitoring of high-yield and periodical processes in health care

Statistical control charts have found valuable applications in health care, having been largely adopted from operations research in manufacturing. However, the most common types are not best-suited to monitor high-yield processes (outcomes comprising true/false fractions, 'near-zero') and periodical processes (characterized by sequences of single populations of finite sizes), but rather to monitor variable vital signs levels and, to a lesser degree, service performance indicators. We discuss control charts that are most suitable for fraction non-conforming measurements. We focus particularly on high-yield and periodical processes, i.e. range in which out-of-control conditions are expected and should be identified. For these conditions, we discuss control charts based on the family of hypergeometric distributions, explaining and comparing their application to more traditional alternatives with two health care case studies. We demonstrate that hypergeometric-type control charts provide higher sensitivity in timely identification of changing rare event fractions and are well-suited for monitoring of periodical processes, while remaining more resistant to false alarms, versus their alternatives.

Statistical process monitoring to improve quality assurance of inpatient care

Background

Statistical Process Monitoring (SPM) is not typically used in traditional quality assurance of inpatient care. While SPM allows a rapid detection of performance deficits, SPM results strongly depend on characteristics of the evaluated process. When using SPM to monitor inpatient care, in particular the hospital risk profile, hospital volume and properties of each monitored performance indicator (e.g. baseline failure probability) influence the results and must be taken into account to ensure a fair process evaluation. Here we study the use of CUSUM charts constructed for a predefined false alarm probability within a single process, i.e. a given hospital and performance indicator. We furthermore assess different monitoring schemes based on the resulting CUSUM chart and their dependence on the process characteristics.

Methods

We conduct simulation studies in order to investigate alarm characteristics of the Bernoulli log-likelihood CUSUM chart for crude and risk-adjusted performance indicators, and illustrate CUSUM charts on performance data from the external quality assurance of hospitals in Bavaria, Germany.

Results

Simulating CUSUM control limits for a false alarm probability allows to control the number of false alarms across different conditions and monitoring schemes. We gained better understanding of the effect of different factors on the alarm rates of CUSUM charts. We propose using simulations to assess the performance of implemented CUSUM charts.

Conclusions

The presented results and example demonstrate the application of CUSUM charts for fair performance evaluation of inpatient care. We propose the simulation of CUSUM control limits while taking into account hospital and process characteristics.