Measurement error in time-series analysis: a simulation study comparing modelled and monitored data

BMC Medical Research Methodology

Massimo Vieno⁴  Ruth M Doherty²  Mathew R Heal⁵  Paul Wilkinson³  Richard W Atkinson¹  Ben Armstrong³  Barbara K Butland¹ 

[1] Division of Population Health Sciences and Education & MRC-PHE Centre for Environment and Health, St George’s, University of London, Cranmer Terrace, Tooting, London SW17 0RE, UK;School of GeoSciences, University of Edinburgh, Crew Building, West Mains Road, Edinburgh EH9 3JN, UK;Department of Social and Environmental Health Research, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH, UK;NERC Centre for Ecology & Hydrology, Bush Estate, Nr. Penicuik EH26 0QB, UK;School of Chemistry, University of Edinburgh, Joseph Black Building, West Mains Road, Edinburgh EH9 3JJ, UK

关键词: Ozone;    Nitrogen dioxide;    Mortality;    Time-series;    Epidemiology;    Measurement error;   

Others  :  866602
DOI  :  10.1186/1471-2288-13-136

 received in 2013-05-09, accepted in 2013-10-04,  发布年份 2013

【 摘 要 】

Background

Assessing health effects from background exposure to air pollution is often hampered by the sparseness of pollution monitoring networks. However, regional atmospheric chemistry-transport models (CTMs) can provide pollution data with national coverage at fine geographical and temporal resolution. We used statistical simulation to compare the impact on epidemiological time-series analysis of additive measurement error in sparse monitor data as opposed to geographically and temporally complete model data.

Methods

Statistical simulations were based on a theoretical area of 4 regions each consisting of twenty-five 5 km × 5 km grid-squares. In the context of a 3-year Poisson regression time-series analysis of the association between mortality and a single pollutant, we compared the error impact of using daily grid-specific model data as opposed to daily regional average monitor data. We investigated how this comparison was affected if we changed the number of grids per region containing a monitor. To inform simulations, estimates (e.g. of pollutant means) were obtained from observed monitor data for 2003–2006 for national network sites across the UK and corresponding model data that were generated by the EMEP-WRF CTM. Average within-site correlations between observed monitor and model data were 0.73 and 0.76 for rural and urban daily maximum 8-hour ozone respectively, and 0.67 and 0.61 for rural and urban log_e(daily 1-hour maximum NO₂).

Results

When regional averages were based on 5 or 10 monitors per region, health effect estimates exhibited little bias. However, with only 1 monitor per region, the regression coefficient in our time-series analysis was attenuated by an estimated 6% for urban background ozone, 13% for rural ozone, 29% for urban background log_e(NO₂) and 38% for rural log_e(NO₂). For grid-specific model data the corresponding figures were 19%, 22%, 54% and 44% respectively, i.e. similar for rural log_e(NO₂) but more marked for urban log_e(NO₂).

Conclusion

Even if correlations between model and monitor data appear reasonably strong, additive classical measurement error in model data may lead to appreciable bias in health effect estimates. As process-based air pollution models become more widely used in epidemiological time-series analysis, assessments of error impact that include statistical simulation may be useful.

【 授权许可】

   
2013 Butland et al.; licensee BioMed Central Ltd.

【 图 表 】

【 参考文献 】

• [1]Liu K, Stamler J, Dyer A, McKeever J, McKeever P: Statistical methods to assess and minimise the role of intra-individual variability in obscuring the relationship between dietary lipids and serum cholesterol. J Chron Dis 1978, 31:399-418.
• [2]Armstrong B: Effect of measurement error on epidemiological studies of environmental and occupational exposures. Occup Environ Med 1998, 55:651-656.
• [3]Reeves GK, Cox DR, Darby SC, Whitley E: Some aspects of measurement error in explanatory variables for continuous and binary regression models. Statist Med 1998, 17:2157-2177.
• [4]Zeger SL, Thomas D, Dominici F, Samet JM, Schwartz J, Dockery D, Cohen A: Exposure measurement error in time-series studies of air pollution: concepts and consequences. Environ Health Perspect 2000, 108:419-426.
• [5]Goldman GT, Mulholland JA, Russell AG, Strickland MJ, Klein M, Waller LA, Tolbert PE: Impact of exposure measurement error in air pollution epidemiology: effect of error type in time-series studies. Environ Health 2011, 10:61-71. BioMed Central Full Text
• [6]Lee D, Shaddick G: Spatial modelling of air pollution in studies of its short-term health effects. Biometrics 2010, 66:1238-1246.
• [7]Steenland K, Deddens JA, Zhao S: Biases in estimating the effect of cumulative exposure in log-linear models when estimated exposure levels are assigned. Scand J Work Environ Health 2000, 26:37-43.
• [8]Fung KY, Krewski D: On measurement error adjustment methods in Poisson regression. Environmetrics 1999, 10:213-224.
• [9]Anderson HR, Atkinson RW, Bremner SA, Carrington J, Peacock J: Quantitative systematic review of short term associations between ambient air pollution (particulate matter, ozone, nitrogen dioxide, sulphur dioxide and carbon monoxide), and mortality and morbidity. Report to Department of Health revised following first review; 2007. http://www.dh.gov.uk/en/Publicationsandstatistics/Publications/PublicationsPolicyAndGuidance/DH_121200 webcite
• [10]World Health Organisation: Air quality guidelines: global update 2005. Particulate matter, ozone, nitrogen dioxide and sulphur dioxide. Copenhagen: WHO Regional Office for Europe; 2006. http://www.euro.who.int/en/what-we-do/health-topics/environment-and-health/air-quality/publications/pre2009/air-quality-guidelines.-global-update-2005.-particulate-matter,-ozone,-nitrogen-dioxide-and-sulfur-dioxide webcite
• [11]Dominici F, Zeger SL, Samet JM: A measurement error model for time-series studies of air pollution and mortality. Biostatistics 2000, 1:157-175.
• [12]Sheppard L, Slaughter JC, Schildcrout J, Liu L-JS, Lumley T: Exposure and measurement contributions to estimates of acute air pollution effects. J Expos Anal Environ Epidemiol 2005, 15:366-376.
• [13]Szpiro AA, Paciorek CJ, Sheppard L: Does more accurate exposure prediction necessarily improve health effect estimates? Epidemiology 2011, 22:680-685.
• [14]Szpiro AA, Sheppard L, Lumley T: Efficient measurement error correction with spatially misaligned data. Biostatistics 2011, 12:610-623.
• [15]StataCorp: Stata Statistical Software: Release 10. College Station, TX: StataCorp LP; 2007.
• [16]Goldman GT, Mulholland JA, Russell AG, Gass K, Strickland MJ, Tolbert PE: Characterisation of ambient air pollution measurement error in a time-series health study using a geostatistical simulation approach. Atmos Environ 2012, 57:101-108.
• [17]Cox DR, Hinkley DV: Appendix 3 Second-order regression for arbitrary random variables. In Theoretical Statistics. London: Chapman and Hall; 1974:475-477.
• [18]Automatic Urban and Rural Monitoring Network (AURN) Data Archive: Automatic Urban and Rural Monitoring Network (AURN) Data Archive. http://uk-air.defra.gov.uk webcite
• [19]Simpson D, Benedictow A, Berge H, Bergström R, Emberson LD, Fagerli H, Flechard CR, Hayman GD, Gauss M, Jonson JE, Jenkin ME, Nyíri A, Richter C, Semeena VS, Tsyro S, Tuovinen J-P, Valdebenito Á, Wind P: The EMEP MSC-W chemical transport model - technical description. Atmos Chem Phys 2012, 12:7825-7865.
• [20]Vieno M, Dore AJ, Stevenson DS, Doherty R, Heal MR, Reis S, Hallsworth S, Tarrason L, Wind P, Fowler D, Simpson D, Sutton MA: Modelling surface ozone during the 2003 heat-wave in the UK. Atmos Chem Phys 2010, 10:7963-7978.
• [21]Carslaw D: Defra regional and transboundary model evaluation analysis - phase 1, a report for Defra and the Devolved Administrations. 2011. http://uk-air.defra.gov.uk/reports/cat20/1105091514_RegionalFinal.pdf webcite
• [22]Fagerli H, Gauss M, Benedictow A, Griesfeller J, Jonson JE, Nyíri Á, Schulz M, Simpson D, Steensen BM, Tsyro S, Valdebenito Á, Wind P, Aas W, Hjellbrekke A-G, Mareckova K, Wankmüller R, Iversen T, Kirkevåg A, Seland Ø, Vieno M: Transboundary acidification, eutrophication and ground level ozone in Europe in 2009. In EMEP Status Report 1/2011. Oslo: Norwegian Meteorological Institute; 2011.
• [23]Peng RD, Bell ML: Spatial misalignment in time series studies of air pollution and health data. Biostatistics 2010, 11:720-740.
• [24]Kim S-Y, Sheppard L, Kim H: Health effects of long-term air pollution: influence of exposure prediction methods. Epidemiology 2009, 20:442-450.
• [25]Sheppard L, Burnett RT, Szpiro AA, Kim S-Y, Jerrett M, Pope CA III, Brunekreef B: Confounding and exposure measurement error in air pollution epidemiology. Air Qual Atmos Health 2012, 5:203-216.
• [26]Strickland MJ, Darrow LA, Mulholland JA, Klein M, Flanders WD, Winquist A, Tolbert PE: Implications of different approaches for characterizing ambient air pollutant concentrations within the urban airshed for time-series studies and health benefit analyses. Environ Health 2011, 10:36-44. BioMed Central Full Text
• [27]Carrothers TJ, Evans JS: Assessing the impact of differential measurement error on estimates of fine particle mortality. J Air Waste Manage Assoc 2000, 50:65-74.
• [28]Carroll RJ, Gallo PP, Glesser LJ: Comparison of least squares and errors-in-variables regression, with special reference to randomised analysis of covariance. J Am Stat Assoc 1985, 80:929-932.