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Immediate level change estimates can be biased when interrupted time series analyses aggregate over time using segmented linear regression.

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Τίτλος: Immediate level change estimates can be biased when interrupted time series analyses aggregate over time using segmented linear regression.
Συγγραφείς: Turner SL; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia. Electronic address: simon.turner@monash.edu., Forbes AB; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia., Korevaar E; Faculty of Medicine, Dentistry and Health Sciences, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia., McKenzie JE; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia.
Πηγή: Journal of clinical epidemiology [J Clin Epidemiol] 2026 Oct; Vol. 198, pp. 112416. Date of Electronic Publication: 2026 Jul 13.
Τύπος έκδοσης: Journal Article
Γλώσσα: English
Στοιχεία περιοδικού: Publisher: Elsevier Country of Publication: United States NLM ID: 8801383 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1878-5921 (Electronic) Linking ISSN: 08954356 NLM ISO Abbreviation: J Clin Epidemiol Subsets: MEDLINE
Imprint Name(s): Publication: New York : Elsevier
Original Publication: Oxford ; New York : Pergamon Press, c1988-
Ιατρικοί όροι (MeSH): Interrupted Time Series Analysis*/methods , Interrupted Time Series Analysis*/statistics & numerical data, Linear Models ; Bias ; Humans ; Computer Simulation ; Time Factors
Περίληψη: Background and Objective: Interrupted time series (ITS) designs are commonly used to evaluate the impact of interventions in public health. In an ITS study, data are collected over time prior and post an interruption (eg, public policy intervention). Data are often aggregated over a time interval using the mean, and these means can then be analyzed using segmented linear regression with a continuous outcome. A commonly calculated effect measure from this model is the immediate level change (change in outcome immediately post-intervention). We investigated whether estimates of immediate level change can be biased depending on the time interval of data aggregation.
Methods: We developed an equation to estimate the magnitude of bias in the immediate level change parameter of a segmented linear regression model when data are aggregated over time intervals (eg weekly, monthly, quarterly, and yearly) using the mean. We validated the bias expression using a simulation study. We demonstrated through application to a real-world ITS how the bias can be removed via the simple formula.
Results: We found that the magnitude of bias in the immediate level change parameter is dependent on the time interval of data aggregation and the size of slope change. Longer intervals of aggregation and larger slope changes lead to larger bias. Our simulation study confirmed the validity of the expression for bias.
Conclusion: When aggregating ITS data over time using the mean, researchers need to be aware of the potential for bias in the estimate of the immediate level change parameter, so that they can mitigate its impact. Aggregating data over smaller time intervals, or removing the bias via a formula, provide simple solutions.
(Copyright © 2026 The Author(s). Published by Elsevier Inc. All rights reserved.)
Competing Interests: Declaration of competing interest None declared.
Contributed Indexing: Keywords: Bias; Interrupted time series; Quasi-experimental; Segmented regression; Statistical methods; Statistical simulation
Entry Date(s): Date Created: 20260713 Date Completed: 20260909 Latest Revision: 20260909
Update Code: 20260910
DOI: 10.1016/j.jclinepi.2026.112416
PMID: 42442488
Βάση Δεδομένων: MEDLINE
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  Data: <searchLink fieldCode="AU" term="%22Turner+SL%22">Turner SL</searchLink>; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia. Electronic address: simon.turner@monash.edu.<br /><searchLink fieldCode="AU" term="%22Forbes+AB%22">Forbes AB</searchLink>; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia.<br /><searchLink fieldCode="AU" term="%22Korevaar+E%22">Korevaar E</searchLink>; Faculty of Medicine, Dentistry and Health Sciences, Centre for Epidemiology and Biostatistics, Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Victoria, Australia.<br /><searchLink fieldCode="AU" term="%22McKenzie+JE%22">McKenzie JE</searchLink>; School of Public Health and Preventive Medicine, Monash University, 533 St. Kilda Road, Melbourne, Victoria 3004, Australia.
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  Data: Background and Objective: Interrupted time series (ITS) designs are commonly used to evaluate the impact of interventions in public health. In an ITS study, data are collected over time prior and post an interruption (eg, public policy intervention). Data are often aggregated over a time interval using the mean, and these means can then be analyzed using segmented linear regression with a continuous outcome. A commonly calculated effect measure from this model is the immediate level change (change in outcome immediately post-intervention). We investigated whether estimates of immediate level change can be biased depending on the time interval of data aggregation.<br />Methods: We developed an equation to estimate the magnitude of bias in the immediate level change parameter of a segmented linear regression model when data are aggregated over time intervals (eg weekly, monthly, quarterly, and yearly) using the mean. We validated the bias expression using a simulation study. We demonstrated through application to a real-world ITS how the bias can be removed via the simple formula.<br />Results: We found that the magnitude of bias in the immediate level change parameter is dependent on the time interval of data aggregation and the size of slope change. Longer intervals of aggregation and larger slope changes lead to larger bias. Our simulation study confirmed the validity of the expression for bias.<br />Conclusion: When aggregating ITS data over time using the mean, researchers need to be aware of the potential for bias in the estimate of the immediate level change parameter, so that they can mitigate its impact. Aggregating data over smaller time intervals, or removing the bias via a formula, provide simple solutions.<br /> (Copyright © 2026 The Author(s). Published by Elsevier Inc. All rights reserved.)
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  Data: Declaration of competing interest None declared.
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      – TitleFull: Immediate level change estimates can be biased when interrupted time series analyses aggregate over time using segmented linear regression.
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