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Improved Statistical Monitoring Procedures for Attributes with Applications in Public Health Surveillance

Final Report Summary - SMPHS (Improved Statistical Monitoring Procedures for Attributes with Applications in Public Health Surveillance)

The statistical monitoring of health-related data over time is a scientific area closely related to the domain of statistical process control (SPC); the primary tool of SPC is the control chart. In case of public-health surveillance, the data are often discrete (count data), assuming to follow a specific, discrete, probability distribution. Usually, in these kinds of data an excessive number of zeros exists, while extra variation (i.e. overdispersion) is also present. Consequently, the application of the standard attributes control charts is not valid. Moreover, the distribution of the data cannot be well approximated by the Normal distribution. Thus, new improved schemes are needed in order to monitor effectively health-related processes, without leading to incorrect assessments. Motivated by these facts, the general objective of the two-year SMPHS project was (i) to develop improved statistical monitoring techniques that can be effectively used in the detection of changes in health-related and biological processes and (ii) to assess the effect of several violations of the main assumptions on the performance of the proposed schemes, providing effective solutions as well.

The SMPHS project started September 1st 2013 and for the next 24 months, focused on the study of improved control charts, i.e. the principal statistical tool of process monitoring. The development of each control chart requires specific assumptions, mainly for the process that it is monitored. Therefore, apart from proposing new improved techniques, the performance of the existing and the proposed ones, was examined under various non-standard situations, where the usual assumptions have been violated. New parametric distributional models were also considered, in order to capture the non-typical behavior of various real processes.

During the 1st year of the project (period 01/09/2013 - 31/08/2014), the research focused mainly on the development of new cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts; these charts had to be suitable for monitoring processes that demonstrate e.g. extra variation in the data or an excessive number of zero values. The research resulted in two new schemes, one of each type. Their performance can be exactly evaluated, all of its design parameters are integer-valued (or, at least, they can be transformed to integers) and no further approximations are necessary. Apart from the two new control charts, the performance of Shewhart-type control charts for zero-inflated processes (i.e. processes with an excessive number of zero values) was investigated, when their parameters are unknown and have to be estimated.
During the 2nd year of the project (period 01/09/2014 - 31/08/2015), the research focused mainly on studying the performance of control charts with memory (e.g. CUSUM and EWMA type) under various several non-standard situations. More specifically, it was assumed that the process under monitoring is appropriately described by (i) a general inflated Poisson distribution or (ii) by an integer-valued time series model. For the case (i), a new discrete probability model was defined, which also generalizes the usual zero-inflated Poisson distribution. Apart from serving as a possible baseline model of the process, its theoretical properties were further investigated. Two CUSUM-type charts were developed for monitoring processes of that type as well as simpler control schemes. Also, for the case (ii), four different integer-valued time-series models were considered, two with an infinite range of values and two with a finite range. Both models demonstrate overdispersion and there is serial correlation between the successive values. These characteristics are frequently met in practical applications. The performance of CUSUM-type charts was investigated for each of these models and proper adjustments in the values of the design parameters of these schemes were provided, in order to apply them in practice. 3 practical applications, based on real data, of the proposed CUSUM schemes were also offered.

Below, the findings and the main results of the SMPHS project are provided:
• Five new CUSUM control charts have been developed, which can be used for monitoring non-typical count data that arise from
o (i) a zero-inflated process,
o (ii) a general inflated process,
o (iii) a process with correlated counts from an infinite range and
o (iv) a process with correlated counts from a finite range.
• A new EWMA-type chart has been proposed, which can be used for monitoring any type of count data, (i)-(iv) included.
• The performance of control charts for zero-inflated process with estimated parameters has been studied, by using the distribution of the moment estimator. The exact distribution of this estimators was also derived.
• Finally, a new class of general inflated discrete probability distributions was defined, offering a broad class of probability model that can describe various types of count data. Simple control charting techniques were also provided.
In terms of published results, there are:
➢ Three scientific papers which have already been accepted,
➢ two other papers which are under revision (one of them is under minor revision) and
➢ three more papers which have been submitted for publication.
All papers have been submitted to or accepted by international peer-reviewed journals.
✓ Also, programming codes in Scilab (http://www.scicoslab.org/) and R (www.r-project.org) that accompany the theoretical findings of the research, have been developed and they are freely available through the official site of the project (http://www.univ-nantes.fr/07092425/0/fiche___pagelibre/) as well as from personal web-page of the fellow (https://sites.google.com/site/arakitz/rcodes).
These codes can be directly used from the practitioners, for designing the new schemes according to their needs and evaluating their performance. Furthermore, they can be used for reproducing all the numerical results that appear in the scientific papers.

It is expected that the new control schemes and techniques, offer modern solutions to real problems, by taking into account the violations of the usual assumptions, under which most of the control schemes that are available in the literature, have been developed so far. So, they promote the research in the area of statistical process monitoring, while they also offer solution to real problems. The programming codes have been developed as open-source softwares, so they are available without limitations to anyone interested in using these models. Reproducibility of the results is also available. Finally, in an era where data and information are collected at every moment and several characteristics are monitored for preventing unpleasant situations or for understanding the continuous changes in our world, these simple but efficient techniques, can be used as a part of an integrated monitoring system that would detect accurately, quickly and efficiently undesirable and uncommon situations.

GENERAL INFORMATION

Person in charge of scientific aspects:
Prof. Philippe Castagliola
E-mail: philippe.castagliola@univ-nantes.fr

Researcher:
Dr. Athanasios Rakitzis
E-mail: athanasios.rakitzis@univ-nantes.fr

Laboratory involved : IRCCyN, (Institut de Recherche en Communications et Cybernétique de Nantes) is a Joint Research Unit of CNRS (Centre National de la Recherche Scientifique), UMR CNRS 6597. Research at IRCCyN not only aims at producing new knowledge, but is also deeply technologically empowered in the sense that it focuses on the development of tools and methods in order to bring solutions to concrete problems raised by economical and social partners. Due in part to the collaboration with companies, members of IRCCyN also contribute to patents deposits, and to Start-up or Spin-of creations.

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under REA grant agreement n° 328037. The content of this webpage reflects only the author's views. The European Union is not liable for any use that may be made of the information contained therein.