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Original Article: METHODS

An Attributable Risk Model for Exposures Assumed to Cause Both Chronic Disease and its Exacerbations

Künzli, Nino*†‡; Perez, Laura; Lurmann, Fred§; Hricko, Andrea; Penfold, Bryan§; McConnell, Rob

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doi: 10.1097/EDE.0b013e3181633c2f
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Many chronic diseases are a combination of our underlying chronic disease pathology superimposed with acute events or exacerbations. It is the underlying disease that determines the susceptibility to acute events triggered by environmental factors. This “chronic disease model” applies to conditions such as asthma, chronic obstructive pulmonary disease, or cardiovascular diseases. Risk factors that cause the underlying chronic pathology and also acute exacerbations (or complications) of the chronic condition require an expansion of the methods to derive the number of acute exacerbations that can be attributed to this risk factor.

Figure 1 shows this chronic disease model using asthma as an example. The underlying chronic pathology of asthma consists of hyperreactive airways and chronic inflammation, while acute deteriorations are characterized by episodes of wheezing and asthma attacks due to acute reversible obstruction of the airways.1Figure 1 assumes that exposure X is both a cause for the development of the underlying chronic disease and the triggering of acute events. Under this model, X would first increase the number of people with asthma (box A in Fig. 1) and thereby increase the pool susceptible to acute exacerbations of any etiology. Second, X would trigger acute events (boxes C and E) among all susceptible children (ie, all in boxes A and B). However, among children who developed asthma due to chronic exposure to X (box A), one may attribute all their asthma-related morbidities to factor X, including those exacerbations not directly caused by X (box D). This latter attributable burden has so far been neglected by risk assessors, and attributable cases of boxes C and E have not previously been distinguished.

The burden of asthma exacerbations in children attributable to some “exposure X,” assuming a causal role of X in both disease onset and exacerbation (or complication). Sizes of the boxes do not reflect the burden. The model starts with healthy children where some develop asthma due to X (A) or due to other causes (B). If X was the cause of asthma onset (A), all exacerbations among group A could be attributed to this factor X (C + D). (The text uses ambient air pollution as an example for “exposure X”.)

This article provides a model to derive the portions of the attributable burden shown in Figure 1, namely box A and boxes C, D, and E. We illustrate the method with an application using childhood asthma as the chronic disease and ambient air pollution as exposure (X). Evidence of a causal role of air pollution in asthma exacerbation is substantial.1 While not yet conclusive, there is an increasing number of studies suggesting that growing up close to busy roads (ie, in zones with high concentrations of traffic-related pollutants) may be a cause of onset of asthma during childhood.2–8

Public health researchers and regulatory agencies use air pollution risk assessments—or health impact assessments—to estimate either the current burden attributable to air pollution or the potential future impact of policies that will affect air quality.9–11 These health impact assessments often quantify acute effects of ambient pollution on cardiorespiratory hospitalizations, episodes of bronchitis symptoms, exacerbations of asthma or number of days with restricted activities. Given the emerging evidence of a contribution of ambient air pollution to both the development of chronic disease and its exacerbation,12 a more comprehensive approach to the total disease burden may be appropriate.


The proposed risk analysis model operates under the assumption that the burden of air pollution related to childhood asthma is a combination of effects on both onset of disease and acute exacerbations among those with asthma. For simplicity, we will focus on only one measure of exacerbations, namely episodes of bronchitis symptoms. However, the model can easily be expanded to other exacerbations such as wheezing, asthma attacks, increased need for medications, doctors’ or emergency room visits, hospitalizations, or school absences.

We demonstrate the approach for Long Beach, California, a community with high concentrations of primary air pollution. Long Beach air quality is heavily affected by traffic-related pollution due to activities in and around the adjacent ports of Los Angeles and Long Beach, one of the largest port complexes in the world.13 Long Beach school children participated in the southern California Children's Health Study. Results from the Children's Health Study cohort analyses demonstrate that (a) children living within 75 m of busy roads are more likely to have asthma than those living further away,2 and (b) asthmatics are more likely to suffer from bronchitis-symptom episodes during years with increased levels of ambient air pollution, characterized by small particulate matter (PM2.5 and PM10), nitrogen dioxide (NO2), or other markers.14 Our model integrates these 2 findings to present the combined burden of air pollution-induced asthma and asthma exacerbations.

As in most morbidity impact assessments, we express the burden of air pollution in terms of attributable fraction (AF) and attributable number (AN) of cases, using standard methods.15 We derive the total attributable risk under the model of both chronic and acute effects in 3 steps. First, we estimate the fraction of childhood asthma prevalence attributable to traffic-related pollution. This represents the fraction of chronic diseases attributable to traffic-related pollution (box A in Fig. 1). Second, we estimate the fraction of exacerbations of asthma symptoms triggered by air pollution among all asthmatics. This represents the fraction of acute diseases attributable to air pollution (C and E). Third, we quantify among those with asthma due to traffic-related pollution (box A) the number of exacerbations due to causes other than air pollution—for example resulting from a range of other nonspecified exogenous and endogenous triggers (box D). The quantification of these 3 components can be done as follows.

Attributable Cases of Asthma Due to Traffic Pollution (Box A)

The AF of asthma (ie, the chronic disease) due to traffic pollution among the total population of children in Long Beach (AFchron) is derived using the standard AF formula as shown below:

where pp is the proportion of the children living within 75 m of busy roads and RR is the relative risk (ie, the exposure-response function) observed in the Children's Health Study (see below).2

The attributable number of prevalent asthma cases (ANchron) due to traffic pollution is obtained as the product of the prevalence of asthma (Pchron), the total population of children in Long Beach (Poptot), and the above AFchron:

Accordingly, one can calculate the attributable number of cases of asthma in this population that are due to causes other than traffic pollution (AN(1−chron)) as is shown in Equation 3.

In other words, ANchron is the additional number of cases of asthma expected in Long Beach as compared with the expected (hypothetical) number if no children were living within 75 m of a major road. However, other points of reference could be chosen, and instead of a binary exposure term, one could use a continuous measure of exposure (see Equation 4, below).

Annual Exacerbations of Symptoms Attributable to Air Pollution (Boxes C and E)

The Children's Health Study reported associations between the year-to-year change in various markers of air quality and the year-to-year frequency in bronchitis-symptom episodes among children with asthma.14 We use ambient concentrations of NO2 as a marker of combustion-related pollution. The use of a continuous exposure (ie, NO2 annual means measured in ppb) requires some assumptions about the “reference level” to derive the attributable burden. We use an arbitrary 10 ppb contrast in the mean annual NO2 concentration; thus, we assume only 2 levels of exposure, namely the actual NO2 and an arbitrary level 10 ppb lower. In both cases we also assume that the proportion of children exposed to the respective pollution is 1.0, ie, we assume these concentrations to reflect the population-weighted average exposure.

The standard AF formula of the annual exacerbations of symptoms attributable to air pollution becomes:

where RRΔ is the concentration-response function (see below) for a specified change (Δ) in the ambient concentration (10 ppb in our example).

The burden of exacerbation of asthma has been quantified in several air pollution impact assessments.10,16 The attributable number of acute exacerbations (ANacute) can be derived by multiplying the population with the current condition (Popacute) with the fraction of annual exacerbations of symptoms attributable to air pollution (AFacute). Popacute is obtained through the frequency of the acute condition (Pacute) applied to the population with the chronic condition (Popchron = Pchron × Poptot). Depending on the definition of “exacerbation,” its frequency may be expressed with the incidence (eg, asthma attacks) or some measure of period prevalence (eg, chronic symptomatic episodes). Equation 5 shows the formula for ANacute using these parameters.

In Figure 1, ANacute is actually the sum of the 2 components, boxes C and E. By rearranging Equations 3 and 5, one can separate the 2 components into the attributable number of exacerbations due to air pollution among those for whom asthma is due to air pollution (AN1, box C) and the attributable number of exacerbations due to air pollution among those who have asthma due to other factors (AN2, box E) as shown in Equations 6 and 7:

Exacerbations Attributable to Causes Other Than Air Pollution Among Cases With Onset of Asthma Due to Air Pollution (Box D)

Exacerbations attributable to causes other than air pollution need to be considered “attributable to air pollution” if they occur among those who have asthma due to air pollution, ie, in our example, because they are living within 75 m of a major road (AN3, box D in Fig. 1). This quantity can be estimated with Equation 8.

Equations 6, 7, and 8 can be combined to calculate the total burden of asthma exacerbations (Tot ANacute) due to children living within 75 m of a major road and due to annual mean concentrations of NO2 being 10 ppb above the hypothetical reference value.


We applied the models to the population of asthmatic children who live in Long Beach, California using data and results of the Children's Health Study,2,14 as shown below. We used the 2000 Census Bureau data to derive the number of children living in Long Beach.

Based on Children's Health Study data, asthma prevalence among children in Long Beach was 12.8%. Asthma occurrence was defined as “doctor-diagnosed asthma” or, among children without doctor-diagnosed asthma, as severe wheeze in the previous 12 months to identify undiagnosed asthma due to poor access to medical care.2 We assumed that this estimate reflects asthma prevalence not only among the young age group of the study but in the population of Long Beach children up to age 17. This simplification is supported by California health survey data for Long Beach in which prevalence of doctor-diagnosed asthma was 11.7% and 12% among children aged 0–11 and 12–17, respectively.17

Episodes of Bronchitis Symptoms Among Asthmatics

In total, 38.7% of Long Beach children with asthma reported bronchitis symptom episodes (unpublished Children's Health Study data).14 In our study, a child was considered to have had chronic bronchitis symptoms during the previous year on the basis of the report of a daily cough for 3 months in a row, congestion, or phlegm for at least 3 months in a row or bronchitis.14

Number of Children Living Within 75 m of a Busy Road

The US Census block is the smallest geographical unit for which population data are available. Blocks vary in size from 104 to 106 m2 and represent 25 to 100 people. Spatial distribution of the population within each census block is not available. Because census blocks are generally surrounded by roadways, assignment of the population to the center of census blocks would underestimate the number of residents living close to roadways. Hence, we developed a method to spatially distribute the population and make more realistic estimations of the number of residences close to busy roadways.

Census block population (from the 2000 Census) was represented in discrete units corresponding to the Census block household density. For each census block, the area representing a single household was used to select a rectilinear spatial allocation grid with 20 m, 40 m, 60 m, or 100 m spacing. The population was assigned uniformly to the grids representing households in the census block. Residences were not placed in areas within 60 m from the centerline of interstate/freeways, 45 m of other highways, 30 m of major arterials, or 10 m of other roadways. Residences also were not placed in the portion of Census blocks that contained parks or water. Figure 2 shows an example of the population assignments to the grids representing households with the Census block.

Sample map of the population-spatial distributions within census tracts in relation to major roadways. Each number represents a household location and is the average number of residents per household in the census tract.

The distance from each population point to the nearest major road was calculated for all locations in Long Beach. A major road was defined as an interstate freeway, US highway or limited access highway, or other highway or arterial road (Tele Atlas functional roadway classes 0, 1, 3, and 4). The distance to the nearest major road was estimated using ESRI ArcGIS Version 9.2 (ESRI, Redlands, CA; Each direction of travel was represented as a separate roadway, and the shortest distance was estimated from the residence to the middle of the nearest side of the freeway or major road. Using this method, we estimated that 20% of children in Long Beach live within 75 m of major roads. This is slightly less than the observed 23% among the residences of the Children's Heath Study participants of Long Beach, which were clustered in a few areas of the city. We estimated the attributable cases of asthma assuming that 20% rather than 0% of children live within 75 m of a major road.

Exposure Assumptions Regarding Ambient NO2 Concentrations

As mentioned above, the burden of bronchitis exacerbations was expressed for a 10 ppb contrast in the population-weighted annual mean NO2. The long-term mean measured at the North Long Beach air quality monitoring station was 32 ppb (2002–2004); thus we calculated the burden of symptoms that may be prevented if the population-weighted mean concentration was assumed to be 22 ppb.

Exposure-Response Function

As shown in Equation 1, the quantitative association between exposure and health outcome is a key factor in the derivation of attributable risks using the risk functions published from the Children's Heath Study. The odds ratio (OR) for asthma prevalence among long-term residents (living since 2 years of age at the same home) given residential location within 75 m of a major road was 1.64 (95% confidence interval = 1.10–2.44).2 The OR for bronchitis symptoms for a 1 ppb increase in NO2 was 1.07 (1.02–1.13); thus, a 10 ppb increment in the annual mean NO2 levels translated into a 1.96-fold (1.22–3.39) change in bronchitis-symptom episodes.14 The original studies provided ORs. The larger an OR, the more it overestimated the true (unknown) RR. To take this into account, we corrected all ORs using the following standard formula:18

where Poutcome is the frequency of the outcome in the target population, namely 12.8% for asthma prevalence and 38.7% for the occurrence of bronchitis-symptom episodes among asthmatics.


Table 1 presents all input information used to derive the results. Table 2 shows the attributable number and fractions for all 3 steps of the model and its combination. As shown, approximately 9.3% of all asthma cases (ie, 1626 of the estimated 17,486 total number of children with asthma) would be attributable to living within 75 m of a busy road.

Summary of the Data Needed in the Application of the Combined Health Impact Assessment for Children Ages 0–17 Years, Long Beach, California
Comparison of Results, Nomenclature, and Formulas Using a Common Approach and the Expanded Combined Health Impact Assessment Approach to Estimate the Burden of Air Pollution on Exacerbations of Symptoms Among Asthmatic Children Ages 0–17 Years, Long Beach, California

Among these asthmatics (box A in Fig. 1) a total of 211 exacerbations are attributed to a 10 ppb contrast in NO2. These cases correspond to 3.1% of all exacerbations in Long Beach (box C). Another 418 exacerbations due to other causes (or 6.2% of all events) among these children with asthma would indirectly be attributable to air pollution (box D). The largest attribution is due to air pollution-related exacerbations occurring among those with asthma due to other causes (30.5%; box E). Therefore, as shown in Table 2, the total AF of exacerbations due to air pollution under the combined causal model is estimated to be 39.8% of all exacerbations.


Health impact assessment is a tool to translate research findings into quantitative information that is most relevant for public health professionals, policy makers, and the public. Participation of epidemiologists in risk assessment is crucial to appropriately translate epidemiologic research findings into Health impact assessment.15 We present a novel expansion of Health impact assessment methods for situations where an exposure of interest may affect the incidence or prevalence of a chronic condition and the exacerbation of acute events among those with the disease. While we use asthma as the chronic disease and air pollution as the exposure of interest to demonstrate the method, our approach can easily be applied to other chronic diseases characterized by acute events and to other risk factors, including genetic traits believed to affect both the development of chronic disease and the processes leading to exacerbations. Our exposure example is timely given the increasing evidence that air pollution may have a role in both the onset and the exacerbation of chronic diseases including asthma, chronic obstructive pulmonary disease, and atherosclerosis.12 As shown in Table 2, the common Health impact assessment that assumes a causal role of pollution on acute effects only, underestimates the burden as compared with a combined model. The latter results in a burden attributed to air pollution that is 16% larger than calculations based on the usual method (ie, 40% instead of 34% of all exacerbations attributed to air pollution).

While our approach leads to a larger burden than the traditional calculations, the size of this additional burden may vary substantially. It is affected by the size of the relative risks, the frequency of the disease and its exacerbations, and the choice of the pollution reference scenarios. Our model also comes with 3 assumptions and related uncertainties, namely a causal role of traffic-related pollution in the development of asthma, a causal role of air pollution in asthma exacerbations, and the assumption that those with asthma due to traffic-related pollution would not have developed asthma without this exposure, (ie, that all their asthma-related problems were attributable to air pollution). The evidence of a causal role of air pollution in the onset of asthma is less conclusive than for air pollution triggering asthma symptoms,1 so risk assessors may wish to consult formal assessments of the causal evidence that are beyond the scope of our methodologic focus. Uncertainties regarding causality may be integrated in uncertainty analyses. There is, to our knowledge, no study on whether traffic exposure competes with other causes of asthma, and whether the absence of traffic exposures would prevent or delay the onset of asthma. The model assumes that removal of one cause would reduce the number of children developing asthma. However, if removal of pollution only delays the onset of asthma among some children, our model would apply to some (unknown) time window rather than to the total period of childhood; in this case, we would be overestimating the attributable burden of box E.

Our approach presents an expansion of Health impact assessment methods traditionally dominated by mortality (ie, death or life time lost).19 Asthma is the most common chronic disease during childhood and a major source of reduced quality of life for children and their families.20 Our model integrates an additional element of the burden, and can be easily applied to other measures of acute exacerbations of asthma associated with air pollution, including medication, hospital admissions, and school absences.4,5,21–23 It is not necessary to simplify the asthma prevalence model by using a binary exposure at a distance of 75 m. This ignores the contribution to asthma prevalence of exposure at somewhat greater distances from major roads, out to approximately 150 m.2 As shown in Equation 4, an expansion of the AF and AN model to exposures with more than 2 categories can easily be adopted.15

Recent studies have suggested that living close to roads with high traffic density (a proxy measure for local exposure to traffic-related pollutants) may contribute to the development of asthma.2–7 While we use Children's Heath Study results because they include subjects from Long Beach, other studies would provide different risk functions for residential proximity to roads. Risk assessors face major challenges in evaluating the burden of “traffic proximity” because investigators have used a myriad of metrics to characterize proximity, and these preclude the use of a common exposure metric or the derivation of meta-analytic risk functions. However, the model is versatile enough to use different markers of exposure to air pollution (including the use of measured pollutants such as ultrafine particles) instead of proximity to roads, once such studies are available.

Partitioning attributable exacerbations (boxes C and E) may have a further advantage for risk assessors. Policies to prevent the onset of the disease (box A) may in some cases differ from those preventing exacerbations (boxes C and E). For example, in the above case of asthma, the pollutants near busy roads may require remedies other than curbing regional urban air pollution. The partitioning of attributable cases may, thus, be useful in source-specific risk assessments.

Knowledge of the population distribution of the exposure of interest is required. Such data are not routinely available for proximity to roads; thus, we had to develop a method. Our derivation of the “proximity” distribution for Long Beach uses the same definitions of distance and road types as used in the original Children's Heath Study studies. Therefore, our exposure distribution data are internally consistent. Risk assessors using other epidemiologic studies may have to adapt the procedures to derive exposure distributions of the target population.

Our asthma exacerbation model is based on urban background concentrations of NO2. However, other markers of regional traffic-related pollution could be used, given the correlations among various pollutants measured at fixed site monitors. Bronchitis symptoms are also associated with several other pollutants.14 Results of the burden estimates would be similar for other pollutants if comparable concentration contrasts were chosen. We expressed the burden for a 10 ppb contrast in the annual mean of NO2. This change is within the range of changes observed in the annual mean of NO2 in some of the Children's Heath Study communities on which the estimate of the exposure-response function is based.

A major issue for the validity of Health impact assessments relates to the expression of uncertainties.24 We do not provide the range of uncertainty around the estimate of attributable cases. While one may use the common formula to derive confidence intervals for attributable risks,25 we consider it more appropriate to integrate uncertainties more broadly, as uncertainties vary across the main assumptions (as noted above). Moreover, estimates of the exposure distribution and assumptions about the relevant time windows all play a role. We are developing risk assessment applications that integrate various sources of propagated uncertainties using Monte Carlo simulations. Regardless, uncertainties inherent to all risk assessments should not be used as an argument against choosing a conceptually more appealing model to derive the central estimate of attributable burden.

In conclusion, we have expanded the traditional health impact assessment model. The proposed risk assessment model may be applicable to endogenous or exogenous risk factors that play a role both in the development of chronic diseases and its exacerbations.


We thank our community-based participatory research partners, Long Beach Alliance for Children with Asthma, Center for Community Action and Environmental Justice, Environmental Health Coalition, and the Family Health Centers of San Diego. Their risk-assessment needs triggered this methods development.


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