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Sample size issues in time series regressions of counts on environmental exposures
BACKGROUND: Regression analyses of time series of disease counts on environmental determinants are a prominent component of environmental epidemiology. For planning such studies, it can be useful to predict the precision of estimated coefficients and power to detect associations of given magnitude....
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
BioMed Central
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6988321/ https://www.ncbi.nlm.nih.gov/pubmed/31992211 http://dx.doi.org/10.1186/s12874-019-0894-6 |
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author | Armstrong, Ben G. Gasparrini, Antonio Tobias, Aurelio Sera, Francesco |
author_facet | Armstrong, Ben G. Gasparrini, Antonio Tobias, Aurelio Sera, Francesco |
author_sort | Armstrong, Ben G. |
collection | PubMed |
description | BACKGROUND: Regression analyses of time series of disease counts on environmental determinants are a prominent component of environmental epidemiology. For planning such studies, it can be useful to predict the precision of estimated coefficients and power to detect associations of given magnitude. Existing generic approaches for this have been found somewhat complex to apply and do not easily extend to multiple series studies analysed in two stages. We have sought a simpler approximate approach which can easily extend to multiple series and give insight into factors determining precision. METHODS: We derive approximate expressions for precision and hence power in single and multiple time series studies of counts from basic statistical theory, compare the precision predicted by these with that estimated by analysis in real data from 51 cities of varying size, and illustrate the use of these estimators in a realistic planning scenario. RESULTS: In single series studies with Poisson outcome distribution, precision and power depend only on the usable variation of exposure (i.e. that conditional on covariates) and the total number of disease events, regardless of how many days those are spread over. In multiple time series (eg multi-city) studies focusing on the meta-analytic mean coefficient, the usable exposure variation and the total number of events (in all series) are again the sole determinants if there is no between-series heterogeneity or within-series overdispersion. With heterogeneity, its extent and the number of series becomes important. For all but the crudest approximation the estimates of standard errors were on average within + 20% of those estimated in full analysis of actual data. CONCLUSIONS: Predicting precision in coefficients from a planned time series study is possible simply and given limited information. The total number of disease events and usable exposure variation are the dominant factors when overdispersion and between-series heterogeneity are low. |
format | Online Article Text |
id | pubmed-6988321 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | BioMed Central |
record_format | MEDLINE/PubMed |
spelling | pubmed-69883212020-01-31 Sample size issues in time series regressions of counts on environmental exposures Armstrong, Ben G. Gasparrini, Antonio Tobias, Aurelio Sera, Francesco BMC Med Res Methodol Research Article BACKGROUND: Regression analyses of time series of disease counts on environmental determinants are a prominent component of environmental epidemiology. For planning such studies, it can be useful to predict the precision of estimated coefficients and power to detect associations of given magnitude. Existing generic approaches for this have been found somewhat complex to apply and do not easily extend to multiple series studies analysed in two stages. We have sought a simpler approximate approach which can easily extend to multiple series and give insight into factors determining precision. METHODS: We derive approximate expressions for precision and hence power in single and multiple time series studies of counts from basic statistical theory, compare the precision predicted by these with that estimated by analysis in real data from 51 cities of varying size, and illustrate the use of these estimators in a realistic planning scenario. RESULTS: In single series studies with Poisson outcome distribution, precision and power depend only on the usable variation of exposure (i.e. that conditional on covariates) and the total number of disease events, regardless of how many days those are spread over. In multiple time series (eg multi-city) studies focusing on the meta-analytic mean coefficient, the usable exposure variation and the total number of events (in all series) are again the sole determinants if there is no between-series heterogeneity or within-series overdispersion. With heterogeneity, its extent and the number of series becomes important. For all but the crudest approximation the estimates of standard errors were on average within + 20% of those estimated in full analysis of actual data. CONCLUSIONS: Predicting precision in coefficients from a planned time series study is possible simply and given limited information. The total number of disease events and usable exposure variation are the dominant factors when overdispersion and between-series heterogeneity are low. BioMed Central 2020-01-28 /pmc/articles/PMC6988321/ /pubmed/31992211 http://dx.doi.org/10.1186/s12874-019-0894-6 Text en © The Author(s). 2020 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. |
spellingShingle | Research Article Armstrong, Ben G. Gasparrini, Antonio Tobias, Aurelio Sera, Francesco Sample size issues in time series regressions of counts on environmental exposures |
title | Sample size issues in time series regressions of counts on environmental exposures |
title_full | Sample size issues in time series regressions of counts on environmental exposures |
title_fullStr | Sample size issues in time series regressions of counts on environmental exposures |
title_full_unstemmed | Sample size issues in time series regressions of counts on environmental exposures |
title_short | Sample size issues in time series regressions of counts on environmental exposures |
title_sort | sample size issues in time series regressions of counts on environmental exposures |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6988321/ https://www.ncbi.nlm.nih.gov/pubmed/31992211 http://dx.doi.org/10.1186/s12874-019-0894-6 |
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