A control chart based on Pearson residuals for a negative binomial regression: application to infant mortality data
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 7 October 2021
Issue publication date: 1 November 2022
Abstract
Purpose
The study aims to design a control chart based on an exponentially weighted moving average (EWMA) chart of Pearson's residuals of a model of negative binomial regression in order to detect possible anomalies in mortality data.
Design/methodology/approach
In order to evaluate the performance of the proposed chart, the authors have considered official historical records of death of children of Ecuador. A negative binomial regression model was fitted to the data, and a chart of the Pearson residuals was designed. The parameters of the chart were obtained by simulation, as well as the performances of the charts related to changes in the mean of death.
Findings
When the chart was plotted, outliers were detected in the deaths of children in the years 1990–1995, 2001–2006, 2013–2015, which could show that there are underreporting or an excessive growth in mortality. In the analysis of performances, the value of λ = 0.05 presented the fastest detection of changes in the mean death.
Originality/value
The proposed charts present better performances in relation to EWMA charts for deviance residuals, with a remarkable advantage of the Pearson residuals, which are much easier to interpret and calculate. Finally, the authors would like to point out that although this paper only applies control charts to Ecuadorian infant mortality, the methodology can be used to calculate mortality in any geographical area or to detect outbreaks of infectious diseases.
Keywords
Acknowledgements
Declarations of interest: none
Citation
García-Bustos, S., Cárdenas-Escobar, N., Debón, A. and Pincay, C. (2022), "A control chart based on Pearson residuals for a negative binomial regression: application to infant mortality data", International Journal of Quality & Reliability Management, Vol. 39 No. 10, pp. 2378-2399. https://doi.org/10.1108/IJQRM-03-2021-0062
Publisher
:Emerald Publishing Limited
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