Monitoring multistage healthcare processes using state space models and a machine learning based framework.

Monitoring healthcare processes, such as surgical outcomes, with a keen focus on detecting changes and unnatural conditions at an early stage is crucial for healthcare professionals and administrators. In line with this goal, control charts, which are the most popular tool in the field of Statistical Process Monitoring, are widely employed to monitor therapeutic processes. Healthcare processes are often characterized by a multistage structure in which several components, states or stages form the final products or outcomes. In such complex scenarios, Multistage Process Monitoring (MPM) techniques become invaluable for monitoring distinct states of the process over time. However, the healthcare sector has seen limited studies employing MPM. This study aims to fill this gap by developing an MPM control chart tailored for healthcare data to promote early detection, confirmation, and patient safety. As it is important to detect unnatural conditions in healthcare processes at an early stage, the statistical control charts are combined with machine learning techniques (i.e., we deal with Intelligent Control Charting, ICC) to enhance detection ability. Through Monte Carlo simulations, our method demonstrates better performance compared to its statistical counterparts. To underline the practical application of the proposed ICC framework, real data from a two-stage thyroid cancer surgery is utilized. This real-world case serves as a compelling illustration of the effectiveness of the developed MPM control chart in a healthcare setting.

Monitoring epidemic processes under political measures.

Statistical modeling of epidemiological curves to capture the course of epidemic processes and to implement a signaling system for detecting significant changes in the process is a challenging task, especially when the process is affected by political measures. As previous monitoring approaches are subject to various problems, we develop a practical and flexible tool that is well suited for monitoring epidemic processes under political measures. This tool enables monitoring across different epochs using a single statistical model that constantly adapts to the underlying process, and therefore allows both retrospective and on-line monitoring of epidemic processes. It is able to detect essential shifts and to identify anomaly conditions in the epidemic process, and it provides decision-makers a reliable method for rapidly learning from trends in the epidemiological curves. Moreover, it is a tool to evaluate the effectivity of political measures and to detect the transition from pandemic to endemic. This research is based on a comprehensive COVID-19 study on infection rates under political measures in line with the reporting of the Robert Koch Institute covering the entire period of the pandemic in Germany.

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.

Efficient algorithms for calculating the probability distribution of the sum of hypergeometric-distributed random variables.

In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions. While convoluting random variables following a binomial, geometric or Poisson distribution is a straightforward procedure, convoluting hypergeometric-distributed random variables is not. The problem is that there is no closed form solution for the probability mass function (p.m.f.) and cumulative distribution function (c.d.f.) of the sum of i.i.d. hypergeometric random variables. To overcome this problem, we propose an approximation for the distribution of the sum of i.i.d. hypergeometric random variables. In addition, we compare this approximation with two classical numerical methods, i.e., convolution and the recursive algorithm by De Pril, by means of an application in Statistical Process Monitoring (SPM). We provide MATLAB codes to implement these three methods for computing the probability distribution of the sum of i.i.d. hypergeometric random variables in an efficient way. The obtained results show that the proposed approximation has remarkable properties and may be helpful in all fields, where the problem of convoluting hypergeometric-distributed random variables occurs. Therefore, the approximation considered in this paper is well suited to make a change over established practices.•This article presents theoretical bases of three methods for determining the probability distribution of the sum of i.i.d. hypergeometric random variables: (1) direct convolution, (2) recursive algorithm by De Pril, (3) approximation.•We provide associated MATLAB codes (including context-specific customizations) for direct implementation of these methods and discuss technical aspects and essential details of the tweaks we have made.•A representative application example in SPM shows that the proposed approximation is considerably simpler in application than both other methods and it ensures a remarkable high accuracy of the results while reducing computational time considerably.

Generalized two-tailed hypothesis testing for quantiles applied to the psychosocial status during the COVID-19 pandemic.

Nonparametric tests do not rely on data belonging to any particular parametric family of probability distributions, which makes them preferable in case of doubt about the underlying population. Although the two-tailed sign test is likely the most common nonparametric test for location problems, practitioners face serious drawbacks, such as its lack of statistical power and its inapplicability when information regarding data and hypotheses is uncertain or imprecise. In this paper, we generalize the two-tailed sign test by embedding fuzzy hypotheses caused by uncertainty/imprecision regarding linguistic statements on fractions of underlying quantiles. By achieving this objective, (1) crucial limitations of the common two-tailed sign test are mitigated/overcome, (2) various further strengths are incorporated into the sign test (e.g., meeting the trade-off between point- and interval-valued hypotheses, facilitated formulation of fuzzy hypotheses, standardization of membership functions), and (3) shortcomings that often come along with fuzzy hypothesis testing are avoided (e.g., higher complexity, fuzzy test decision, possibilistic interpretation of test results). In addition, we conduct a comprehensive case study using a real data set on the psychosocial status during the COVID-19 pandemic. The results of the case study clearly indicate that the generalized two-tailed sign test is preferable to the two-tailed sign test with point- or interval-valued hypotheses.

Nonparametric fuzzy hypothesis testing for quantiles applied to clinical characteristics of COVID-19.

The sign test is one of the most popular nonparametric tests for location problems and allows testing for any quantile of a population. However, the common sign test has serious drawbacks such as loss of information by considering solely signs of observations but not their magnitudes, various problems related to handling of ties in the data, and the lack of embedding uncertainty regarding the fraction of underlying quantile. To address these issues, we present an extended sign test based on fuzzy categories and fuzzy formulated hypotheses that improves the generality, versatility, and practicability of the common sign test. This generalized test procedure is neat in theory and practice and avoids disadvantages that are often associated with fuzzy tests (e.g., a considerably higher complexity of the underlying model, a fuzzy test decision, and a possibilistic instead of a probabilistic interpretation of test results). In addition, we perform a comprehensive case study on COVID-19 in HIV-infected individuals with a focus on human body temperature and related measurement problems. The results of the study clearly indicate that fuzzy categories and fuzzy hypotheses improve the performance of the sign test.

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.