The neighbourhood concept is equivocal. Neighbourhood units are often defined as small-areas that share some predefined set of characteristics [1, 2]. Neighbourhood definition is an issue in many health studies at the intra-urban level that depend on this geographical concept. In Canada, the neighbourhood has been operationalized as the census tract in several studies [3–9], even if the use of this geographic unit is questionable. Only a few Canadian studies have specifically operationalized the neighbourhood in the context of health research [10–12]. As a consequence, exactly how place is conceptualized at the local scale is one of the weakest theoretical aspects of the way health studies, among others, are currently conducted [13]. The study of the relationship between exposure to criteria pollutants, such as nitrogen dioxide (NO₂) and health outcomes is no exception to this problem. Unfortunately, few health studies have focused on this issue [14], despite existing literature that demonstrates the feasibility of measuring different levels of association between health and space under different spatial zoning systems [15–18]. Considering that studies on the relationship between NO₂ and health outcomes are divided regarding the role of exposure to NO₂ on health, it is surprising that the study of the role of spatial representation in the analysis of this relationship has not received more attention.

Standard geographical units from the Canadian Census, especially the census tract, are often used to operationalize the neighbourhood concept. This method finds benefit in the readily available Census data for this zoning system [19]. In Canada, census tracts are delineated based on optimal population counts, the compactness of the shape, visible boundaries and input from local experts [20]. The census tract boundaries must follow visible features when possible, but in some cases, they are delineated by administrative boundaries and as such census tract definitions can be equivocal [21, 22]. Homogeneity in terms of socioeconomic status is not part of the boundary delineation criteria for census tracts or other standard geographical classification levels used in 2006 Canadian Census geography [21, 23]. However, neighbourhood units may be expected to be homogeneous along those socioeconomic dimensions related to a given health outcome(s) [1]. Consequently, the use of a census tract as a neighbourhood proxy becomes conceptually problematic. From an analytical viewpoint, using census tracts as the only spatial unit of measure is questionable when no other alternative spatial structure is used for sensitivity analysis, in which case, there can be no assessment of MAUP effects on results [16, 21].

The Modifiable Area Unit Problem (MAUP) can cause differences in the analytical results of the same input data compiled under different zoning systems [16, 24, 25]. Openshaw [16] explains that the MAUP is composed of a scale effect and a zoning effect. Herein, we use the term spatial structure to designate a particular combination of scale and zoning within a bounded region. The scale effect arises when the size of the spatial units of measure changes due to spatial aggregation procedures. Differing spatial aggregation schemes affect analytical results on the same dataset. The zoning effect arises when the number of the spatial units of measure remains the same, but changing their relative structure (changes in the unit boundaries and shape) generates different analytical results [14, 26]. According to some authors [23, 27], any study about the association between health and place will be influenced by the scale and zoning design used to conduct the study. Generally, the scale effect is recognized as the most troublesome component of the MAUP, while the zoning effect (effect of unit shape) matters to a lesser extent [23, 25]. However, the interplay between zoning and scale is complex because either effect can vary in weight due to the spatial scale of the process(es) being analyzed.

The MAUP impacts the results of univariate and multivariate regressions [25]. The MAUP can negatively affect regression model calibration and lead to unreliable results [26]. Some authors have provided insights as to the cause of the MAUP in regression analysis [28]. Accordingly, the MAUP "may be caused by the spatial non-stationarity of multiple predictors that together may be factors for a response variable" [29]. Because the health status of an individual is the result of multiple factors that vary at different spatial scales across a geographic region, health studies are at increased risk of being affected by the MAUP [29, 30]. One way to mitigate the impact of the MAUP on analytical results is to create a geographical structure with zoning units that possess "high internal homogeneity" and maintain a considerable amount of external or between-unit heterogeneity [31]. Such mitigation can also represent a solution to errors in the model building process that are induced by positive spatial autocorrelation [32]. Another proposed solution requires the evaluation of the association under different spatial structures (varying zoning and scale) as a way to conduct sensitivity analysis [26].

An automated zone design methodology was first developed for the study of zoning and scale effects on various analytical results [15]. These automated approaches, based on computer algorithms, regroup a set of spatial units into a number of zones so that each unique spatial unit is linked to one zone only [15, 33]. A contiguity/adjacency constraint is often used in these models [15]. Examples of other constraints include the compactness (shape), population count, area size and internal homogeneity. Automated zoning has been used for the study of the relationship between morbidity and deprivation [27]. Results of such experiments indicate that automatically delineated zoning systems that increase spatial aggregation tend to produce stronger correlations over smaller census zones [27]. Observations of increasing strength of statistical relationships with increasing spatial aggregation verify the work of Openshaw [15].

Since the main objective of this research is to determine the impact of the MAUP on the study of the relationship between exposure to NO₂ and respiratory health, three different spatial structures are incorporated into our framework: First, census tracts from the 2006 Canadian Census of population are used as small-scale basic administrative units; second, coarser natural neighbourhoods are delineated based on a homogeneity criteria in order to represent an optimal zoning design for the socioeconomic processes under consideration, and; third, an automated zoning structure is created through a continuity based aggregation of census tracts in order to present a different zoning structure with a scale equivalent to the natural neighbourhoods. By comparing analytical results from three spatial structures, we will improve our understanding of how scale and zoning influence the measured relationship between NO₂ and health.

Preliminary data analysis was first conducted to determine the role of spatial representation on summary statistics using global spatial autocorrelation and bivariate Moran's I. Bivariate Ordinary Least Squares (OLS) and multivariate OLS regressions where then applied to the three zoning systems to determine the impact of the MAUP on the relationship between the Respiratory health outcome rate and exposure to NO₂. Spatial regressions were not used in this research because a comparison between spatial regression and OLS has already been explored in another article in preparation by the same authors. SAS (version 9.2) [49] and GEODA [50] were used for statistical and spatial analysis of the data.

Numerous studies have concluded that increased exposure to NO₂ likely contributes to negative respiratory health but no positive and statistically significant association has been unequivocally found [43, 54, 55]. The main objective of this research was to examine the role of spatial representation, focusing on MAUP effects, in the study of the relationship between exposure to NO₂ and respiratory health. We find that the outcomes of this exposure/health relation are tied to the MAUP. The MAUP provides a method to learn how scale and zoning may affect the lack of consensus in studies that aim to expose the role that NO₂ has on overall health outcomes.

Some have recommended approaches to gain a better insight into how the MAUP can affect analytical results [16, 56, 57] but few published studies have incorporated any of these in their analyses. In our research, we implemented two of the recommended approaches [26]. The first approach is based on the use of an optimal zoning proposal, while the second suggests conducting sensitivity analysis using alternate spatial structures. In this study, the natural neighbourhoods delineated through a semi-automated method were used as the "optimal" zoning system. As mentioned, the main component of the delineation process was based on the concept of internal homogeneity along socioeconomic dimensions. Neighbourhoods were delineated in order to make homogeneous units in terms of SES. These units may not be suitable for all studies conducted in Ottawa, but they are assumed to represent many social processes associated with health. We also believe that these natural neighbourhoods could be used for research examining other health outcomes, aside from respiratory morbidity or even other social processes related to SES.

This research also used sensitivity analysis to mitigate the effect of the MAUP [16, 56, 57]. This study was conducted using three spatial structures: natural neighbourhoods, an aggregated structure of the same scale as the former but with a different zoning and census tracts with a different scale from the former structures. Using this sensitivity analysis method allowed us to address a number of questions related to the effect that the MAUP has on spatial autocorrelation and hence on univariate and bivariate and regressions.

The results obtained confirm the documented effect of the MAUP [58, 59] on summary statistics. The analysis of the summary statistics demonstrates that the MAUP does not have a strong effect on the mean of explanatory variables, confirming the previous results of other researchers [26]. Our results further substantiate the work of those authors who observed that the variance decreases with increasing aggregation. Likewise, we observe that the variance is affected when the same number of spatial units of study are used but with a different partitioning or zoning of space.

Global Moran's I was calculated for all the explanatory variables as well as for the dependent variable within three spatial structures. All the explanatory variables were characterized by positive spatial autocorrelation within the three zoning systems. Moran's I values tend to be lower for census tracts than the other two spatial structures. As aggregation increases, Moran's I is also expected to increase due to the "increased homogeneity in the landscape structure" [26]. While not definitive, our results concur.

The dependent variable Respiratory health outcome rate displays low levels of statistically significant spatial autocorrelation using census tracts and the aggregated structure. Using natural neighbourhoods, global Moran's I calculated for the dependent variable, reveals a non-significant value close to zero. In this case, instead of spatial autocorrelation increasing with aggregation, it is no longer statistically significant. By way of explanation, the natural neighbourhoods are internally homogeneous in terms of SES and adequately depict the spatial scale of the Respiratory health outcome rate, thus reducing spatial dependence between neighbourhoods. A zoning effect is also observed; levels of spatial autocorrelation using the natural neighbourhood structure are reduced when compared to the aggregated structure. These observations serve as a rationale for using custom geography delineated using processes known a priori to be associated with the dependent health outcome variable of interest.

Under the MAUP, we expected both the aggregated and neighbourhood structures (n = 95) to be characterized by stronger bivariate Moran's I values between the explanatory variables and the Mean NO ₂ concentration then under the census tract structure (n = 184) because aggregation is known to increase the strength of correlation [16, 27]. The use of an optimal zone design in the natural neighbourhoods based on minimizing internal homogeneity appears to be reducing the scale effect of the MAUP. For half of the explanatory variables, the correlation with Mean NO ₂ concentration is stronger at the census tract level than at the neighbourhood level or vice versa. On the other hand, the correlations measured using the aggregated structure are stronger (70% of the variables have stronger correlation) than under the census tract structure, which is the expected result [16]. Moreover, a relatively strong zoning effect is observed when comparing the bivariate Moran's I values for the correlation between NO₂ and health for the neighbourhood and aggregated structures. Similar results were obtained for the correlations between the explanatory variables and the Respiratory health outcome rate. This confirms that the natural neighbourhoods, which are internally homogeneous from a socioeconomic perspective, better capture the processes linked to respiratory health outcomes. We also found that the variable % retail trade industry has changed directions depending on the spatial structure, confirming that "correlation inference is not robust to the aggregation process" [60].

The use of an exploratory analytical approach in the context of sensitivity analysis can be seen as a tool to assess the role of the MAUP prior to conducting confirmatory data analysis. Exploratory analysis allowed us to obtain a more in-depth understanding of the potential effect of the MAUP on the results of statistical modeling used in the study of the relationships between area-level health and other variables [61].

The results of bivariate and multivariate regression suggest that using different spatial representations could contribute to the lack of consensus found in the literature regarding the NO₂ and health relation at the area-level. Bivariate regressions between the NO₂ concentrations and the dependent variable once again confirmed both the zoning effect and the scale effect of the MAUP. According to the census tract and aggregated structures, there is a low but statistically significant relationship between Mean NO ₂ concentration and Respiratory health outcome rate. As expected from earlier work on the MAUP, the R² value is higher when using an aggregated structure (coarser level of aggregation) then with the census tract [29]. The relationship measured between NO₂ and Respiratory health outcome rate cannot be confirmed using the neighbourhood structure in this study as it is not statistically significant. The OLS model for the neighbourhood structure is the only model not characterized by statistically significant positive spatial autocorrelation in the residuals and passes all tests for non-normality of the error term and heteroskedasticity, suggesting this model is correctly fitted.

The effect of the MAUP on multivariate analyses has been described as "complex and unpredictable" [26]. Considering that the health of an individual is the result of various factors apart from exposure to NO₂[62], the relationship is difficult to measure. The question of which variables are significant within our multivariate regression models is an essential element to be addressed; there was only one variable common to all three models (aside from Mean NO ₂ concentration which was forced into the models). The variable Educational attainment is an explanatory variable for variations in the morbidity rate for all three structures. In other words, scale and/or the zoning design considerations that may mediate this variable's inclusion/exclusion are being filtered out. The geographic scale of the variable Educational attainment is probably larger than the scale of the census tract. Another comparison to be made is between the variables used as input into the delineation of the optimal zoning design and the variables included in the different models. We observe that the census tract model includes both % occupied private dwellings built before 1946 and Average income, which were used in the delineation of the natural neighbourhoods. By creating an optimal zoning system based on these variables and other SES variables, housing and income covariates are no longer confounding variables in the relationship between exposure to NO₂ and health and hence are not found in the neighbourhood model.

The variable Mean NO ₂ concentration is not a statistically significant factor in any model and so allowed other variables to express their association with respiratory health. For example, % Lone-parent families, a measure of the economic structure, is part of the optimal zoning design model based on the natural neighbourhoods but not the census tract or aggregated structures. If the process of aggregation has the same impact on dependent and independent variables, then the effect of the MAUP is reduced in severity [25]. These results are demonstrated when the independent and dependent variables are spatially autocorrelated and averaged. Since the level of global spatial autocorrelation was found to be different for the dependent variable as a function of the spatial structure, the differences observed between the models are justified. Among the variables included in the neighbourhood model, two variables have a coefficient with a direction opposite to that suggested by bivariate Moran's I (Mean NO ₂ concentration and % Lone-parent families). Finally, the resemblance between the census tract and the aggregated structure; the aggregated structure is a complete subset of the census tract model. Aggregation can potentially generate collinearity between independent variables [29].

The MAUP implies that an OLS model developed using a specific spatial structure should not be transferred to another spatial structure with the same expectations. This finding has implications for research that may use index mapping techniques to estimate community vulnerability to air pollutants. Moreover, this finding has significant implications for studies that aim to propose morbidity pathways using variables that are found to be significant in models tested at only one scale. Thus, there is the prospect that different scales of analysis will deliver markedly different sets of explanatory variables induced by the MAUP. The sensitivity analysis conducted in this research clearly demonstrates that the explanatory factors of respiratory health will vary according to the geographical structure used to conduct the study. Since research relating exposure to NO₂ and health uses a variety of geographical units to conduct the analysis, the variability of the results of previous research may be caused by the MAUP. We believe the delineation of a custom geography that coincides with the spatial scale of the phenomenon under investigation can be justified because there is no prior reason to believe that administrative and statistical boundaries reflect the fundamental nature and scale of the economic and social phenomena measured within them [25]. The use of optimal zoning designs, like our natural neighbourhoods, becomes a way to resolve the consequences of geographic and methodological scale, the former describing the geography used to identify social processes and the latter the scale of data collection and aggregation [63].

The use of three different spatial representations confirms no measurable effect of NO₂ exposure on respiratory health in Ottawa. Under all three spatial structures, bivariate OLS regression between the Mean NO ₂ concentration and the Respiratory health outcome rate suggests that no significant relation is present. Based on the results obtained, we can confirm that in Ottawa, the lack of a significant statistical association is probably not induced by the use of a particular geography. The use of sensitivity analysis allows us to validate and conclude that the strength of the measured relationship is not produced by neighbourhood boundaries poorly reflecting "the ecological properties that shape" health processes [64].

Our methodological approach demonstrates that many factors could explain the observed differences in respiratory morbidity rates in Ottawa. Considering that respiratory health has already been associated with SES in several studies [65], our research serves as another example of the importance of the social and the environmental context on health.

There have been few studies on the role of spatial representation in air quality and health. To our knowledge, this is the first study specifically interested in the effect of scale and zoning on the relationship between exposure to NO₂ and health. However, our observations do agree with previous research on the subject. Of the limited research on the issue of scale and zoning, others have concluded that "the use of different specifications to assess spatial concentration, agglomerations economies, and trade determinants produces substantial variation in the estimated coefficients" [25]. A study on the relation between morbidity and deprivation showed that the use of spatial representations other than the census tract produced different analytical results [27]. On the other hand, some suggest that the method of neighbourhood definition does not significantly alter relationships and their strength [2, 11]. Additional studies on the impact of using different conceptualizations of the neighbourhood on analytical results are required to understand the role of spatial representation. In return, a thorough understanding of the role of MAUP on the study of the relationship between NO₂ concentration and health will allow decision-makers to develop interventions where they are the most needed. Policy makers' decision about how to improve the health of communities should be strongly influenced by the conclusions that neighbourhood quality affects health. This is particularly of interest in Canada where the population at large believes that the government has a responsibility for the health of citizens [66].

The use of an optimal zone design that has been reviewed and approved by city planners, public health practitioners, community health and resource persons as well as representatives from grassroots organizations is a strength of this research. These natural neighbourhood units have also been used for the Ottawa Neighbourhood Study (http://www.neighbourhoodstudy.ca) and have been updated since their production to reflect changes in Ottawa's communities. Another strong point of this research is the use of an automated zone design to create an aggregated structure that we could use to compare to the census tract structure and our natural neighbourhoods. However, our aggregated structure had to be created by grouping census tracts because of the availability of health data at that geographic level. As a consequence, we did not have as much flexibility when creating the aggregated structure as would be available if a smaller geographic set was used as the basic spatial unit for reporting census and health data. Moreover, our aggregation method produced a single boundary realization that is one of a finite number of possibilities when using a random seeding method that begins with a fixed tessellation defined by census tracts. Future work could provide tools to exhaust all possible aggregations and generate empirical frequency distributions of statistical estimates that could be used to evaluate the sensitivity of results to aggregation effects. Another feature that makes this study more complicated to administer is the fact the NO₂ concentration is not a statistically significant explanatory variable in the multivariate regressions. If the circumstances were different, we would have a better insight into how NO₂'s association with respiratory health varies at different scales. Finally, as a cross-sectional type study, we were limited in having only a few weeks of atmospheric sampling and our results do not preclude the future research with more environmental data through time from coming to different conclusions on the NO₂/Health connection on Ottawa.

The natural neighbourhoods used in this research can be viewed as "exposure areas" as they were delineated with the objective of creating homogeneous units from an SES perspective [67]. The use of area level data such as income, education and housing variables from the Canadian Census created units where environmental and social conditions are equivalent. There is increasing evidence that neighbourhood context affects the health of individuals living therein [68] and it is not unreasonable to assume that an appropriate delineation of neighbourhoods is essential to research outcomes and recommendations that may arise from such studies. Area units should be delineated with the purpose of representing the expected relationship between neighbourhood and health. If this relationship is well defined, the modifiable area units are not a problem [31]. This research confirms the conclusions of previous studies that more research on the role of spatial representation in health studies in general.