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Introducing activation functions into segmented regression model to address lag effects of interventions
The interrupted time series (ITS) design is widely used to examine the effects of large-scale public health interventions and has the highest level of evidence validity. However, there is a notable gap regarding methods that account for lag effects of interventions. To address this, we introduced ac...
Autores principales: | , , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
BioMed Central
2023
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10668529/ https://www.ncbi.nlm.nih.gov/pubmed/38001462 http://dx.doi.org/10.1186/s12874-023-02098-x |
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author | Zhang, Xiangliang Wu, Kunpeng Pan, Yan Zhong, Wenfang Zhou, Yixiang Guo, Tingting Yin, Rong Chen, Wen |
author_facet | Zhang, Xiangliang Wu, Kunpeng Pan, Yan Zhong, Wenfang Zhou, Yixiang Guo, Tingting Yin, Rong Chen, Wen |
author_sort | Zhang, Xiangliang |
collection | PubMed |
description | The interrupted time series (ITS) design is widely used to examine the effects of large-scale public health interventions and has the highest level of evidence validity. However, there is a notable gap regarding methods that account for lag effects of interventions. To address this, we introduced activation functions (ReLU and Sigmoid) to into the classic segmented regression (CSR) of the ITS design during the lag period. This led to the proposal of proposed an optimized segmented regression (OSR), namely, OSR-ReLU and OSR-Sig. To compare the performance of the models, we simulated data under multiple scenarios, including positive or negative impacts of interventions, linear or nonlinear lag patterns, different lag lengths, and different fluctuation degrees of the outcome time series. Based on the simulated data, we examined the bias, mean relative error (MRE), mean square error (MSE), mean width of the 95% confidence interval (CI), and coverage rate of the 95% CI for the long-term impact estimates of interventions among different models. OSR-ReLU and OSR-Sig yielded approximately unbiased estimates of the long-term impacts across all scenarios, whereas CSR did not. In terms of accuracy, OSR-ReLU and OSR-Sig outperformed CSR, exhibiting lower values in MRE and MSE. With increasing lag length, the optimized models provided robust estimates of long-term impacts. Regarding precision, OSR-ReLU and OSR-Sig surpassed CSR, demonstrating narrower mean widths of 95% CI and higher coverage rates. Our optimized models are powerful tools, as they can model the lag effects of interventions and provide more accurate and precise estimates of the long-term impact of interventions. The introduction of an activation function provides new ideas for improving of the CSR model. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-02098-x. |
format | Online Article Text |
id | pubmed-10668529 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
spelling | pubmed-106685292023-11-24 Introducing activation functions into segmented regression model to address lag effects of interventions Zhang, Xiangliang Wu, Kunpeng Pan, Yan Zhong, Wenfang Zhou, Yixiang Guo, Tingting Yin, Rong Chen, Wen BMC Med Res Methodol Research The interrupted time series (ITS) design is widely used to examine the effects of large-scale public health interventions and has the highest level of evidence validity. However, there is a notable gap regarding methods that account for lag effects of interventions. To address this, we introduced activation functions (ReLU and Sigmoid) to into the classic segmented regression (CSR) of the ITS design during the lag period. This led to the proposal of proposed an optimized segmented regression (OSR), namely, OSR-ReLU and OSR-Sig. To compare the performance of the models, we simulated data under multiple scenarios, including positive or negative impacts of interventions, linear or nonlinear lag patterns, different lag lengths, and different fluctuation degrees of the outcome time series. Based on the simulated data, we examined the bias, mean relative error (MRE), mean square error (MSE), mean width of the 95% confidence interval (CI), and coverage rate of the 95% CI for the long-term impact estimates of interventions among different models. OSR-ReLU and OSR-Sig yielded approximately unbiased estimates of the long-term impacts across all scenarios, whereas CSR did not. In terms of accuracy, OSR-ReLU and OSR-Sig outperformed CSR, exhibiting lower values in MRE and MSE. With increasing lag length, the optimized models provided robust estimates of long-term impacts. Regarding precision, OSR-ReLU and OSR-Sig surpassed CSR, demonstrating narrower mean widths of 95% CI and higher coverage rates. Our optimized models are powerful tools, as they can model the lag effects of interventions and provide more accurate and precise estimates of the long-term impact of interventions. The introduction of an activation function provides new ideas for improving of the CSR model. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12874-023-02098-x. BioMed Central 2023-11-24 /pmc/articles/PMC10668529/ /pubmed/38001462 http://dx.doi.org/10.1186/s12874-023-02098-x Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) . The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/ (https://creativecommons.org/publicdomain/zero/1.0/) ) applies to the data made available in this article, unless otherwise stated in a credit line to the data. |
spellingShingle | Research Zhang, Xiangliang Wu, Kunpeng Pan, Yan Zhong, Wenfang Zhou, Yixiang Guo, Tingting Yin, Rong Chen, Wen Introducing activation functions into segmented regression model to address lag effects of interventions |
title | Introducing activation functions into segmented regression model to address lag effects of interventions |
title_full | Introducing activation functions into segmented regression model to address lag effects of interventions |
title_fullStr | Introducing activation functions into segmented regression model to address lag effects of interventions |
title_full_unstemmed | Introducing activation functions into segmented regression model to address lag effects of interventions |
title_short | Introducing activation functions into segmented regression model to address lag effects of interventions |
title_sort | introducing activation functions into segmented regression model to address lag effects of interventions |
topic | Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10668529/ https://www.ncbi.nlm.nih.gov/pubmed/38001462 http://dx.doi.org/10.1186/s12874-023-02098-x |
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