Impact of exposure measurement error in air pollution epidemiology: effect of error type in timeseries studies
 Gretchen T Goldman^{1},
 James A Mulholland^{1}Email author,
 Armistead G Russell^{1},
 Matthew J Strickland^{2},
 Mitchel Klein^{2},
 Lance A Waller^{3} and
 Paige E Tolbert^{2}
DOI: 10.1186/1476069X1061
© Goldman et al; licensee BioMed Central Ltd. 2011
Received: 3 January 2011
Accepted: 22 June 2011
Published: 22 June 2011
Abstract
Background
Two distinctly different types of measurement error are Berkson and classical. Impacts of measurement error in epidemiologic studies of ambient air pollution are expected to depend on error type. We characterize measurement error due to instrument imprecision and spatial variability as multiplicative (i.e. additive on the log scale) and model it over a range of error types to assess impacts on risk ratio estimates both on a per measurement unit basis and on a per interquartile range (IQR) basis in a timeseries study in Atlanta.
Methods
Daily measures of twelve ambient air pollutants were analyzed: NO_{2}, NO_{x}, O_{3}, SO_{2}, CO, PM_{10} mass, PM_{2.5} mass, and PM_{2.5} components sulfate, nitrate, ammonium, elemental carbon and organic carbon. Semivariogram analysis was applied to assess spatial variability. Error due to this spatial variability was added to a reference pollutant timeseries on the log scale using Monte Carlo simulations. Each of these timeseries was exponentiated and introduced to a Poisson generalized linear model of cardiovascular disease emergency department visits.
Results
Measurement error resulted in reduced statistical significance for the risk ratio estimates for all amounts (corresponding to different pollutants) and types of error. When modelled as classicaltype error, risk ratios were attenuated, particularly for primary air pollutants, with average attenuation in risk ratios on a per unit of measurement basis ranging from 18% to 92% and on an IQR basis ranging from 18% to 86%. When modelled as Berksontype error, risk ratios per unit of measurement were biased away from the null hypothesis by 2% to 31%, whereas risk ratios per IQR were attenuated (i.e. biased toward the null) by 5% to 34%. For CO modelled error amount, a range of error types were simulated and effects on risk ratio bias and significance were observed.
Conclusions
For multiplicative error, both the amount and type of measurement error impact health effect estimates in air pollution epidemiology. By modelling instrument imprecision and spatial variability as different error types, we estimate direction and magnitude of the effects of error over a range of error types.
Background
The issue of measurement error is unavoidable in epidemiologic studies of air pollution [1]. Although methods for dealing with this measurement error have been proposed [2, 3] and applied to air pollution epidemiology specifically [4, 5], the issue remains a central concern in the field [6]. Because largescale timeseries studies often use single central monitoring sites to characterize community exposure to ambient concentrations [7], uncertainties arise regarding the extent to which these monitors are representative of exposure. Zeger et al. [8] identify three components of measurement error: (1) the difference between individual exposures and average personal exposure, (2) the difference between average personal exposure and ambient levels, and (3) the difference between measured and true ambient concentrations. While the former two components of error can have a sizeable impact on epidemiologic findings that address etiologic questions of health effects and personal exposure, it is the third component that is particularly relevant in timeseries studies that address questions of the health benefits of ambient regulation [9].
Prior studies have suggested that the impact of measurement error on timeseries health studies differs depending upon the type of error introduced [8, 10, 11]. Two distinctly different types of error have been identified. One type is classical error, in which measurements, Z_{ t } , vary randomly about true concentrations, ; this can be considered the case for instrument error associated with ambient monitors. That is, instrument error is independent of the true ambient level, such that . Moreover, the variation in the measurements, Z_{ t } , is expected to be greater than the variation in the true values, . Therefore, classical error is expected to attenuate the effect estimate in timeseries epidemiologic studies. In contrast, under a Berkson error framework, the true ambient, , varies randomly about the measurement, Z_{ t } . This might be the case, for example, of a measured population average over the study area with true individual ambient levels varying randomly about this population average measurement. In this case, measurement error is independent of the measured population average ambient; that is, . Furthermore, the measurement, Z_{ t } , is less variable than the true ambient level, . A purely Berkson error is expected to yield an unbiased effect estimate, provided that the true doseresponse is linear [3].
Several studies have investigated the impact of error type on regression models. The simultaneous impact of classical and Berkson errors in a parametric regression estimating radon exposure has been investigated [12] and error type has been assessed in a semiparametric Bayesian setting looking at exposure to radiation from nuclear testing [13, 14]; however, no study to date has comprehensively assessed the impact of error type across multiple pollutants for instrument imprecision and spatial variability in a timeseries context.
Error type depends on the relationship between the distribution of measurements and the distribution of true values. Because true relevant exposure in environmental epidemiologic studies is not known exactly, determination of error type is challenging; thus, here we examine the impact of error modelled as two distinctly different types: classical and Berkson. First, we examine monitor data to assess whether error is better modelled on a logged or unlogged basis. Typically, researchers investigating error type have added error on an unlogged basis (e.g. [8, 11]); however, air pollution data are more often lognormal due to atmospheric dynamics and concentration levels that are never less than zero. It is plausible that true ambient exposures are distributed lognormally about a population average as well; therefore, measurement error may be best described as additive error on the log scale. We investigate the combined error from two sources that have been previously identified as relevant in timeseries studies: (1) instrument precision error and (2) error due to spatial variability [9]. We limit our scope to ambient levels of pollutants measured in accordance with regulatory specifications, disregarding spatial microscale variability, such as near roadway concentrations, as well as temporal microscale variability, such as that associated with meteorological events on subhour time scales. Here, building on a previously developed model for the amount of error associated with selected ambient air pollutants [15], we quantitatively assess the effect of error type on the impacts of measurement error on epidemiologic results from an ongoing study of air pollution and emergency department visits in Atlanta.
Methods
Air Pollutant Data
To assess error due to instrument imprecision and spatial variability of ambient concentrations, 19992004 datasets were used for the 12 pollutants with data completeness for this time period (2,192 days) ranging from 82% to 97%. Data from collocated instruments were used to characterize instrument precision error. Measurement methods and data quality are discussed in detail in our prior work [15]. Distributions of all air pollutant measures more closely approximate lognormal distributions than normal distributions ([19], see Additional file 1, Table S1); therefore, additive error was characterized and modeled on a log concentration basis so that simulations with error added to a base case timeseries would also have lognormal distributions.
Measurement Error Model
Here, ε_{ χt } is the modeled error in for day t, N_{ t } is a random number with distribution ~N(0,1) and σ_{ err } is the standard deviation of error added, a parameter derived from the populationweighted semivariance to capture the amount of error present for each pollutant, as described in the next subsection. Shortterm temporal autocorrelation observed in the differences between measurements was modeled using a threeday running average of random numbers for N_{t} [15].
Here, χ_{ t } is the standardized simulated timeseries (on the log scale) with type C error added and normal distribution . In this case of type C error, ε_{ χt } and are independent (i.e. ). For type B error, ε_{ χt } and χ_{ t } are independent (i.e. E[R(ε_{ χt }, χ_{ t })] = 0) and . It can be shown (see Additional file 2, eqs. S1S6) that simulations with type B error can be generated from the true timeseries by eq. 4.
For both error types, the simulated timeseries (Z_{ t } ) and true timeseries ( ) have the same log means (μ_{InZ}= μ_{InZ*}). For classicallike error (type C), the log standard deviation is greater for the simulated timeseries than the true timeseries (σ_{InZ}> σ_{InZ*}) because the simulated values are scattered about the true values. For Berksonlike error (type B), the log standard deviation is less for the simulated timeseries than the true timeseries (σ_{InZ}< σ_{InZ*}) because the true values are scattered about the simulated values.
Semivariogram Analysis
Thus, γ' represents the spatial semivariance scaled to a quantity indicative of the range of exposures over which health risk is being assessed; it is unitless and allows for comparison across pollutants. A scaled semivariance value of 0 corresponds to perfectly correlated observations (R = 1) and a value of 1 corresponds to perfectly uncorrelated observations (R = 0).
Populationweighted scaled semivariances, , Pearson correlation coefficients, , and model parameters used in the Monte Carlo simulations to simulate amount of error (σ_{ err }) and error type (σ_{InZ}/σ_{InZ*})
Pollutant 

 σ _{ err }  σ_{InZ}/σ_{InZ*} Type B  σ_{InZ}/σ_{InZ*} Type C 

1hr max NO_{2}  0.516  0.320  1.46  0.57  1.77 
1hr max NO_{x}  0.384  0.445  1.12  0.67  1.50 
8hr max O_{3}  0.051  0.903  0.33  0.95  1.05 
1hr max SO_{2}  0.517  0.319  1.46  0.56  1.77 
1hr max CO  0.411  0.418  1.18  0.65  1.55 
24hr PM_{10}  0.192  0.678  0.69  0.82  1.21 
24hr PM_{2.5}  0.100  0.819  0.47  0.90  1.11 
24hr PM_{2.5}SO_{4}  0.068  0.873  0.38  0.93  1.07 
24hr PM_{2.5}NO_{3}  0.140  0.754  0.57  0.87  1.15 
24hr PM_{2.5}NH_{4}  0.149  0.741  0.59  0.86  1.16 
24hr PM_{2.5}EC  0.337  0.495  1.01  0.70  1.42 
24hr PM_{2.5}OC  0.175  0.702  0.65  0.84  1.19 
Values of σ_{ err } and σ_{InZ}/σ_{InZ*}used here can be found in Table 1.
Sets of 1000 simulated timeseries with instrument and spatial error added for each pollutant for the scenarios of C and B error types were produced for the sixyear period 19992004. In addition, simulations of CO measurement error only were generated for a range of error types with σ_{InZ}/σ_{InZ*}values between error types C and B. Scatterplots demonstrate that C and B error types defined on a log basis (i.e. InZ  InZ*) are independent of InZ* and InZ, respectively (see Additional file 3, Figure S1).
Epidemiologic Model
Results
Distribution of Measurement Error Simulations
Impact of Error on Health Risk Assessment
Summarized epidemiologic model results with the magnitude of error representative of error associated with using a populationweighted average for each pollutant added to the base case (RR* = 1.0139, 95% CI = 1.00781.0201, pvalue = 0.000009, IQR = 1.00 ppm)
pollutant  RR per ppm (95% CI)  IQR (ppm)  RR per IQR (95% CI)  pvalue 

Error Type C simulations  
1hr max NO_{2}  1.0011 (0.99981.0023)  1.84  1.0020 (0.99971.0042)  0.0957 
1hr max NO_{x}  1.0024 (1.00031.0046)  1.51  1.0037 (1.00051.0070)  0.0251 
8hr max O_{3}  1.0114 (1.00601.0169)  1.05  1.0120 (1.00631.0178)  0.00004 
1hr max SO_{2}  1.0011 (0.99981.0023)  1.84  1.0019 (0.99971.0042)  0.0966 
1hr max CO  1.0021 (1.00021.0040)  1.57  1.0033 (1.00031.0063)  0.0342 
24hr PM_{10}  1.0063 (1.00251.0102)  1.20  1.0076 (1.00301.0122)  0.0013 
24hr PM_{2.5}  1.0094 (1.00451.0142)  1.10  1.0103 (1.00491.0156)  0.000157 
24hr PM_{2.5}SO_{4}  1.0107 (1.00541.0159)  1.07  1.0114 (1.00581.0170)  0.000066 
24hr PM_{2.5}NO_{3}  1.0079 (1.00351.0123)  1.14  1.0090 (1.00401.0141)  0.00040 
24hr PM_{2.5}NH_{4}  1.0076 (1.00331.0119)  1.15  1.0088 (1.00381.0137)  0.00050 
24hr PM_{2.5}EC  1.0032 (1.00061.0057)  1.42  1.0045 (1.00091.0081)  0.0140 
24hr PM_{2.5}OC  1.0068 (1.00281.0108)  1.18  1.0080 (1.00331.0128)  0.00090 
Error Type B simulations  
1hr max NO_{2}  1.0182 (1.00411.0325)  0.51  1.0092 (1.00211.0165)  0.0112 
1hr max NO_{x}  1.0169 (1.00561.0284)  0.61  1.0103 (1.00341.0172)  0.0034 
8hr max O_{3}  1.0142 (1.00751.0208)  0.94  1.0133 (1.00701.0195)  0.000027 
1hr max SO_{2}  1.0182 (1.00411.0325)  0.51  1.0092 (1.00211.0164)  0.0114 
1hr max CO  1.0172 (1.00531.0292)  0.59  1.0101 (1.00311.0171)  0.0044 
24hr PM_{10}  1.0152 (1.00681.0236)  0.78  1.0117 (1.00531.0182)  0.00030 
24hr PM_{2.5}  1.0144 (1.00731.0217)  0.88  1.0127 (1.00641.0190)  0.000074 
24hr PM_{2.5}SO_{4}  1.0143 (1.00741.0211)  0.92  1.0130 (1.00681.0193)  0.000039 
24hr PM_{2.5}NO_{3}  1.0147 (1.00711.0225)  0.83  1.0122 (1.00591.0186)  0.000152 
24hr PM_{2.5}NH_{4}  1.0148 (1.00701.0226)  0.82  1.0121 (1.00581.0185)  0.000175 
24hr PM_{2.5}EC  1.0165 (1.00601.0271)  0.65  1.0106 (1.00381.0174)  0.0021 
24hr PM_{2.5}OC  1.0150 (1.00691.0232)  0.79  1.0119 (1.00551.0183)  0.00030 
Discussion
In this study, in which quantification of error is based on the variability between monitors, error due to spatial variation is much greater than error due to instrument imprecision, particularly for primary air pollutants [15]. Conceptually, therefore, we speculate that this error is more likely of the Berkson type, with true values varying randomly about a populationweighted average represented by the base case. If spatial error is best described by the Berksonlike type defined on a log basis (our error type B) and the mean of the measurements is the same mean as the true values, we estimate there to be a 24% to 34% attenuation in RR per IQR estimates (Figure 4, right panel), and a 19% to 31% bias away from the null in RR estimates on a per unit of measurement basis (Figure 4, left panel), for the primary pollutants studied (SO_{2}, NO_{2}/NO_{x}, CO, and EC) when using a populationweighted average as the exposure metric. For the secondary pollutants and pollutants of mixed origin (O_{3}, SO_{4}, NO_{3}, NH_{4}, PM_{2.5}, OC, and PM_{10}), we estimate a 5% to 15% attenuation in RR per IQR estimates and a 2% to 9% bias away from the null in RR estimates on a per unit of measurement basis. We are currently investigating different methods for estimating actual error type based on simulated pollutant fields trained to have all of the characteristics, including the pattern of spatial autocorrelation, expected of true pollutant fields.
This study addresses error between measured and true ambient concentrations. Our results are consistent with previous finding that suggest that Berkson error, as defined on an unlogged scale (additive), produces no bias in the effect estimate [8, 11] as shown in Figure 5; however, Berksonlike error defined on a log basis (multiplicative) can lead to risk ratio estimates per unit increase that are biased away from the null (although with a reduction in significance). Thus, the direction and magnitude of the bias are functions of error type. With the multiplicative error structure used here in conjunction with a linear dose response, large "true" values of air pollution would likely be underestimated, resulting in an overestimation of pollution health effects. We have shown how multiple air pollution measurements over space can be used to quantify the amount of error and provide a strategy for evaluating impacts of different types of this error. The results suggest that estimating impacts of measurement error on health risk assessment are particularly important when comparing results across primary and secondary pollutants as the corresponding error will vary widely in both amount and type depending on the degree of spatial variability. These results are suggestive of error impacts one would have from timeseries studies in which a single measure, such as the populationweighted average, is used to characterize an urban or regional population exposure. The methodology used here can be applied to other study areas to quantify this type of measurement error and quantify its impacts on health risk estimates.
Conclusions
Health risk estimates of exposure to ambient air pollution are impacted by both the amount and the type of measurement error present, and these impacts vary substantially across pollutants. By modeling combined instrument imprecision and spatial variability over a range of error types, we are able to estimate a range of effects of these sources of measurement error, which are likely a mixture of both classical and Berkson error types. This study demonstrates the potential impact of measurement error in an air pollution epidemiology timeseries study and how this impact depends on error type and amount.
List of Abbreviations
 SO4:

sulfate
 NO3:

nitrate
 NH4:

ammonium
 EC:

elemental carbon
 OC:

organic carbon
 AQS:

US EPA's Air Quality System
 SEARCH:

the Southeastern Aerosol Research and Characterization Study
 ASACA:

Assessment of Spatial Aerosol Composition in Atlanta
 ED:

emergency department
 CVD:

cardiovascular disease
 RR:

risk ratio
 IQR:

interquartile range
 CI:

confidence interval.
Declarations
Acknowledgements
The authors acknowledge financial support from the following grants: NIEHS R01ES111294, NIEHS K01ES019877, EPRI EPP277231/C13172, EPA STAR R89291301, EPA STAR R83362601, EPA STAR R83386601, and EPA STAR RD83479901. The contents of this publication are solely the responsibility of the grantee and do not necessarily represent the official views of the USEPA. Further, USEPA does not endorse the purchase of any commercial products or services mentioned in the publication[19].
Authors’ Affiliations
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