Geocodes are geographic references for computer records that lack them [1]. In environmental health research, geocodes provide geographical references for people and environmental contaminants. While traditional environmental health research is often aspatial, it is becoming increasingly common to address environmental epidemiological questions through spatial analyses using finely geocoded data [1]. Attempts to establish relationships between environmental exposures and health depend on the accuracy of the geocodes. When health outcomes are sensitive to the magnitude of the exposures in question, any loss of accuracy can cause a loss in the ability to establish relationships between the two. Geocoding quality has become an issue in epidemiological and environmental health studies [1-15]. Different studies use different criteria to judge the quality of geocodes [1], although two measures of quality are widely recognized: positional accuracy and completeness in ascertaining a geocode for a given address. In most studies, the severity of these problems is related to the process that generates the geocodes.

The motivating question for the research in this paper is, how do errors in geocodes affect estimates of the relationship between environmental exposures and health outcomes? Statistical power in a model measuring the relationship between exposures and health is computed for different geocoding processes. The results are intended to help researchers decide whether a geocoding method under consideration in an environmental health study is adequate for risk assessment. A second motivating question asks whether it is possible to know the level of geocoding accuracy that is needed to establish the health risk of environmental contaminants in an area. We assume that the contaminant locations can be measured precisely and that the locations of persons exposed to the contaminants are subject to uncertainty. Our approach is similar to that taken by Rull and Ritz [16], who measured the loss in relationships between exposure and health outcomes due to exposure misclassification. We focus on a particular and common cause of exposure misclassification – the geometric inaccuracy of the geocodes. In this research, we analyze the positional inaccuracy of rural geocodes. There is evidence to show that rural geocodes are susceptible to larger inaccuracies than urban geocodes [4,10]. Geocoding inaccuracies are therefore a more pressing problem with rural geocoding than urban ones, although the method described in this paper can be easily adapted to urban situations.

We define a geocoding error as the difference in distance units between the Orthophoto geocode and the geocode (E-911, TIGER) for a given address. Analyses of the TIGER (G^T) geocoding errors and the E-911 geocode errors showed a median difference of 693 feet (211.23 m) for TIGER geocodes and 151 feet (46 m) for E-911 geocodes. Table 1 summarizes the errors between the orthophoto geocodes and other geocodes. Note that median error seems to be minimized at around 400 feet (122 m) offset for the TIGER geocodes. The largest errors with TIGER geocoding are in the range of 8 miles, which is caused by addresses in one part of the county being wrongly matched to a TIGER line file in another part of the county. These matching errors can be contrasted with the more frequent, but smaller offset errors. These errors (which are perhaps represented by the median) are in the range of 600 feet (183 m) for the TIGER geocodes. Earlier studies with a similar dataset have shown that if the outliers (represented by match errors) are removed then these errors can fit some well known distributions [3]. Contaminant values at E-911 geocoded locations and orthophoto map-based locations of addresses were highly correlated (Table 2). Figures 4 and 5 display the variation in errors with contaminant values. Note that while both E-911 (Figure 4) and TIGER (Figure 5) 19 geocoding have larger errors with increasing contaminant values, errors at smaller values seem to be more pronounced with TIGER geocoding. The outliers are addresses that are erroneously geocoded closer to the CAFOs than their true location. In fact these figures demonstrate that TIGER geocoding errors tend to introduce a pronounced positive bias in the contaminant values at address locations.

One exploratory method of comparing the effect of errors in contaminant values from geocoding errors is the method of calculating the attenuation of odds ratios [16] The odds of disease at a geocoded location for an address can be calculated as a function of the contaminant value as for example e(1.2/Δ)∗ZO, where Z^O is the contaminant value calculated using the orthophoto geocode for an address and Δ is the interdecile range (Z^o). Similarly the odds value of e(1.2/Δ)∗ZE would represent the odds calculated using the E-911 geocode. Z^O - Z^E would represent the bias or error in calculating the contaminant value and this bias would in turn affect the odds ratio e(1.2/Δ)∗ZO/e(1.2/Δ)∗ZE. The bias introduced by the error in contaminant values from geocoding inaccuracies could cause the odds of disease to be both greater or less than what we would expect it to be if the geocodes were accurate and there were no modelling error in the contaminant values. The ratio of odds calculated in the no error situation to that calculated with error would be 1 if this error were equal to zero, or so small that the ratio is equal to 1 when rounded to two significant decimal digits. To study the extent of the bias, odds ratios were calculated as odds (disease | Z^O)/odds (disease | Z^E) and odds (disease | Z^O)/odds (disease | Z^T). The results can be seen in Figures 6 and 7. In either of these figures, the more unbiased a given geocoding process is, the more we would expect the data points to cluster at odds ratio (OR) = 1. A larger proportion of the odds were unbiased (OR = 1) with E-911 geocoding (80.00%) than with TIGER geocoding with 0 offset (59.00%). Adding offset to the TIGER geocodes did not substantially improve the proportion of unbiased odds, with the mean being around 60%. There was also a bias towards detecting an association (OR < 1) with TIGER geocodes (≈20%), than with E-911 geocodes (10%). This is consistent with the observations made earlier from Figures 4 and 5.

We tested the robustness of the simulation by changing the value of the simulated odds. The results of this sensitivity analysis are summarized in Table 3 and Table 4. This was done for the 100% sample of 1581 addresses locations. Different values of simulated odds do not cause large differences in bias. The simulation program was tested with odds values of 1.01, 1.15, 1.2, 1.5 and 2.0 (with 1.2 being the value used in our main analyses). All these odds were recovered with reasonable accuracy by the geocoding processes (Table 3). However, as we might expect varying the odds value does have an effect on power (Table 4). An odds of 1.01 is successfully detected in only around 5% of the simulations by the various geocoding processes. In contrast an odds of 2.00 is detected with a power of 100%.

The relationships (odds) are recovered with almost no error across different sample sizes and geocoding processes (Table 5). The power is greater when E-911 geocodes were used than when TIGER geocodes were used, for a given sample size. TIGER geocoding provides very low power for the most part and it needs more than twice the sample size as that of E-911 or orthophoto geocoding to achieve the same power (Figure 8). The biased contaminant values (Figures 4, 5, 6, 7) at the TIGER geocodes contribute to this result. Table 6 compares odds recovered with varying TIGER offsets. Note that adding offset to the TIGER geocodes does increase power. The best power is obtained by using offsets in feet (meters) of 400 (121.92), 600(182.88) or 800(243.84) and the differences in power between the three are small. This can partly be explained by the fact that the median TIGER error is around 700 feet (213 m). It is therefore possible, that the 'optimal' TIGER offset is around this value. The higher offsets also result in an odds ratio which is slightly biased towards the greater than the true odds ratio. This could be because adding offset to the TIGER geocodes moves the address locations closer to the CAFOs, which are almost always located at an offset from the main street.

This paper investigated the degree to which the recovery of a known relationship between environmental exposure and health is affected by the geocoding quality of the subjects of the research. Power analyses showed that the quality associated with different geocoding processes affected the ability to recover the relationships. As with all power analyses the size of the sample as well as the variability in the contaminant surface and the location of the sample in relation to this surface also affected the ability to recover the relationship. Because state or local regulations often control the locations of CAFOs relative to the residences of people, the numbers of people living in areas of high exposure to CAFO contaminants is limited which, in turn, limits the ability to detect health effects in natural experiments as in this research [33]. Another limitation of this study is the spatial structure of the contamination surface. The structure of the surface we use is limited to the source of pollutants and the GIS model. A different source and a different model would result in a surface with a different structure. Thus the specific results obtained in these analyses are specific to the particular contaminant examined. Nevertheless, the methods used in this paper can be used for any contaminant surface of interest. The generality of the results described here lies in the methods of conducting the kind of the analyses we have described rather than the specific results.

The methods used in this paper can be adapted to other situations where the effect of environmental contaminants on health is the subject of study. Because linked social-spatial data [34-36] increase the risk of identifying the subjects of the research, institutions often limit the quality of the geocoding in order to mask the identity of the subjects. Such masks will severely limit the ability to recover relationships between contaminant exposures and health, especially when the health effects of such contaminants are sensitive to changes in short distances from the sources of exposure [17]. Pursuing such research in rural areas is doubly difficult because the most commonly used spatial mask which moves the location of the respondent from their true location to a masked location is most effective when used in urban areas where the number of other people with whom the respondent could be linked by location is large [35]. Also, large inaccuracies often occur in some geocoding processes in rural areas. It is easier to capture the variability in a contaminant surface in an urban area with the relatively dense settlement pattern of people there.

Our results suggest that studies of relationships between environmental contaminants and health may be better designed by using spatial sampling procedures that identify locations of residences that equalize the number of subjects for different estimated levels of the contaminant load. Random samples of subjects are unlikely to have such characteristics and power analyses based on such samples will be less effective. With the widespread availability in the U.S. and elsewhere of E-911 or similar master address lists, and the availability as in this study of spatially modelled contaminant surfaces, determining such spatially stratified random samples that parsimoniously identify respondent locations will improve the quality of analyses of effects of contaminants on health.

A common problem faced by researchers of this subject is that they cannot know a priori whether the quality of the geocoding process they have used is adequate for the purpose of finding a relationship between contaminant values and health. This study is a model of how they might proceed to determine the ability of their proposed research to determine the health effects of the contaminant they are studying by performing the same experiments described in our study. In these experiments they would control the size of sample, the location characteristics of their sample, and the degradation of the geocoding quality of the locations they examine. Some of the studies of geocoding quality include maps of expected geocoding error-rates. These too, when available, can be incorporated in these experiments. We expect that software that automates such experiments will become available in the future. It is needed and could be produced.

Analyses to predict the ability to detect relationships between contaminant values at given locations and health will generally need to incorporate known demographic covariates that are also predictive of a health effect. Power analyses can be designed to incorporate covariates. A recurring question in geographic information science is whether particular geospatial databases are sufficiently accurate for the purpose for which they are used. Determining "fitness-for-use" of a geospatial data set is difficult and has been the subject of research in GIScience [37-42]. An interesting case in point is a study by Lewis et al., [43] which estimated the effect of road traffic exposures to the prevalence of asthma in a sample of 11,562 UK children. The geocode used was the UK postal code which places each child in a relatively large area from the spatial centroid of which the distance to nearest main road was computed. Because of the errors in these estimates of distance from the child's home to the nearest main road, errors in exposure estimates were large, and probably large enough to question the conclusion of the study that asthma prevalence was not associated with proximity of the home to a main road.

Although spatial databases are becoming more accurate as GIS technology improves and efforts are made to improve the accuracy of geographic base maps, it is accepted that no single level of accuracy will meet the requirements of every purpose for which spatial data is used. For each use, there are accuracy requirements and the question we asked is which of three widely used measures of location is adequate for the purpose of assessing whether a relationship exists between exposure to environmental contaminants and health. While research in geocoding accuracy and environmental health problems has often focussed on the effect of inaccuracies on an observed prevalence or relationships [14,44,45], this is to our knowledge the first time the effect of geocoding inaccuracies on assessing the strength of an existing relationship has been addressed. Consideration of such inaccuracies in epidemiologic studies of environmental exposures can greatly improve confidence in the validity and accuracy of results.

An experimental method to investigate the effect of geocoding accuracy is proposed in this paper. The method of accuracy assessment takes into consideration the 'purpose of use' of the geocodes in an environmental health context. Since a goal of such research is to examine relationships between health and exposure, the proposed method focuses on estimation of disease risk in the presence of modelling errors introduced through geocoding inaccuracies. We examine three widely used geocoding processes. Health data are simulated using known odds from exposure to a contaminant. The contaminant values are calculated using a gold standard geocode. These odds are then detected using contaminant values calculated using two other (apart from the gold standard) geocodes. Of the three geocoding processes studied all were successfully able to recover the simulated odds, though the strength of the relationship varied from process to process. In these analyses E-911 geocoding came out superior to TIGER geocoding (with and without offset). More research is required to decide on an 'optimal geocode', since we have not evaluated all possible offsets of TIGER geocoding, E-911 with offsets and other geocoding processes such as GPS based or parcel based geocoding. Sensitivity analyses show relative robustness of the model at recovering the simulated odds. While the specific results obtained in this research may not be generalized to other situations the method can be applied in any situation where issues of geocoding accuracy are in question in an environmental epidemiological study. Our research extends the literature in geocoding quality analysis by placing it in the context of decision making in environmental epidemiological studies.

The author(s) declare that they have no competing interests.

SM proposed the experimental design for the paper, conducted the analyses and wrote sections of the paper. GR oversaw the GIS part of the research and wrote sections of the paper. BJS wrote the program for the simulation (in R) which SM modified for this research and extensively reviewed the paper. DZ reviewed statistical details of the paper and revised the statistical sections. KJD directs the research project to which this paper contributes. He wrote sections of the paper.