ARCHIVED - Chronic Diseases in Canada


Volume 29 · Supplement 2 · 2010

Air Pollution

Nhu D. Le, Li Sun and James V. Zidek

Toxic air pollutants are continuously released into the air supply. Various pollutants come from chemical facilities and small businesses, such as automobile service stations and dry cleaning establishments. Others, such as nitrogen oxides, carbon monoxide and other volatile organic chemicals, arise primarily from the incomplete combustion of fossil fuels (coal and petroleum) and are emitted from sources that include car exhausts, home heating and industrial power plants. Pollutants in the atmosphere also result from photochemical transformations; for example, ozone is formed when molecular oxygen or nitrogen interacts with ultraviolet radiation.

An association between air pollution exposure and lung cancer has been observed in several studies. The evidence for other cancers is far less conclusive. Estimates of the population attributable risk of cancer has varied substantially over the last 40 years, reflecting the limitations of studies; these include insufficient information on confounders, difficulties in characterizing associations due to a likely lengthy latency interval, and exposure misclassification. Although earlier estimates were less than one percent, recent cohort studies that have taken into account some confounding factors, such as smoking and education amongst others, suggest that approximately 3.6% of lung cancer in the European Union could be due to air pollution exposure, particularly to sulphate and fine particulates. A separate cohort study estimated 5-7% of lung cancers in European never smokers and ex-smokers could be due to air pollution exposure. Therefore, while cigarette smoking remains the predominant risk factor, the proportion of lung cancers attributable to air pollution may be higher than previously thought.

Overall, major weaknesses in all air-pollution-and-cancer studies to date have been inadequate characterization of long-term air pollution exposure and imprecise or no measurements of covariates. It has only been in the last decade that measurements to PM2.5 become more widely available. A key weakness of many studies is using fixed-site monitoring data and assuming everyone in a region had the same exposure. This ignores spatial variability, and does not take into account how individuals’ exposures differ with pollution sources inside, outside, both at work, home and elsewhere. More recent efforts to model indicators of vehicular traffic, and residential distances to major roads and highway can allow for some of this spatial variability to be better controlled for. However, this still does not take into account differences in activity patterns. If the effect is small, these biases will compromise the ability to detect an association. In most situations, the resulting estimates tend to be biased toward the null (i.e., no effect). For misclassification of exposure the inability to adequately control for confounding variables may cause bias in either direction. Recent improvements in statistical methodology use measurements at fixed sites combined with residential histories to estimate individuals’ cumulative exposures. They also recognize measurement errors associated with covariates in the analysis to improve estimates of effects. Other challenges include the fact that measurements of exposure and confounders can change over time and long term data are needed due to the anticipated latency interval between harmful exposures and development of cancer


The London fog episode in 1952 played a pivotal role in spurring research into the effects of air pollution.1 This episode demonstrated dramatic short-term associations between very high levels of ambient particulate pollution and increases in mortality. Since then, the health impacts of air pollution have received increasing attention. This has spanned a large number of health outcomes and an examination of several constituents of both indoor and outdoor air and in workplace settings.

A US Environmental Protection Agency (EPA) preliminary inventory of toxic release estimated that about one billion kilograms of toxic air pollutants are released into the US air supply annually.2a Various pollutants come from chemical facilities and small businesses, such as automobile service stations and dry cleaning establishments. Others, such as nitrogen oxides, carbon monoxide and other volatile organic chemicals, arise primarily from the incomplete combustion of fossil fuels (coal and petroleum) and are emitted from sources that include car exhausts, home heating and industrial power plants. Pollutants in the atmosphere also result from photochemical transformations; for example, ozone is formed when molecular oxygen or nitrogen interacts with ultraviolet radiation. Table 1 describes commonly measured pollutants and their sources. A more detailed discussion on the sources of several air pollutants can be found in Fishbein.2b

Table 1
Commonly studied air pollutants and their exposure sources3b,4
Pollutant Source
Volatile organic compounds (VOCs) A large proportion of VOCs in Canada are from natural sources. Human sources include gasoline-fuelled vehicles and gasoline evaporation, solvents including oil-based paint, barbecue starter fluid, household cleaning products.
Total particulate matter Fine particulate matter (PM2.5) generally arise from combustion of fossil fuels in transportation, manufacturing, power generation and residential heating. Nitrogen oxides and sulphur dioxide combine with NH3 to form secondary airborne particles. Ground-level ozone and over half of PM are produced through the reaction of precursor gases, two of the key precursor gases are nitrogen oxides and VOCs. Ground-level ozone and airborne particles are two of the key components of smog.
Nitrogen oxides Nitrogen dioxide, the main component of nitrogen oxides is mainly related to motor vehicle emissions. Nitrogen oxides (NOx) and VOCs are two of the key precursor gases which react to form ground-level ozone and PM, sources of precursor gases include motor vehicles, smelters, homes, thermal power plants and other industries.
Sulphur oxides Non-ferrous smelters and coal-fired power plants are the principal sources of sulphur dioxide. Sulphur dioxide and nitrogen oxides are the main pollutants forming acid rain.
Carbon monoxide Transportation. CO is an air pollutant closely associated with harmful health effects and in high concentrations is fatal.
Ozone VOCs react with nitrous oxides in the presence of sunlight to form ground level ozone.

Annual concentrations of total suspended particulates (TSP), a measure of ambient air pollution, are very high in some parts of the world, much more so than in North America. For example, in the 1990s, TSP was higher than 400 µg/m3 in some Chinese and Indian cities.5 The 2005 Air Quality in Ontario report presents a comparison of air quality in 39 selected cities world wide.6 Since monitoring methods and locations may vary between cities, the comparisons were not intended to be used as a comprehensive ranking.

The Ontario Ambient Air Quality Criteria (AAQC) one-hour maximum ozone concentration is 80 parts per billion (ppb) and the United States National Ambient Air Quality Standard (NAAQS) is 120 ppb. Houston, Athens, Hong Kong and Sao Paulo recorded the highest one-hour maximums among the selected cities for 2005 at between 160 and 200 ppb and 9 cities (none in Canada) had values between 120 and 160 ppb. Windsor, Toronto, Montreal, and Ottawa had one-hour maximum concentrations between 80 and 120 ppb.

The United States NAAQS for the annual mean PM2.5, fine particulate matter 2.5 microns and less in diameter, is 15 µg/m3 and the World Health Organization (WHO) guideline is 10 µg/m3. Five cities, none in Canada, had annual means for 2005 from 15 to 26 µg/m3 and the means in Sao Paulo and Prague were over 20 µg/m3. Montreal had a level of 10 µg/m3 and the level in Windsor was slightly higher. Ottawa and Toronto had levels of approximately 7 and 9 µg/m3 respectively.

The United States NAAQS for the annual mean concentrations of NO2 is 53 ppb and the WHO guideline is 21 ppb. Eight cities had means for 2005 from 21 to 36 ppb including Toronto with a level slightly over the WHO guideline of 21 ppb. Windsor and Montreal had annual means of 17-18 ppb.

Levels of several air pollutants, such as carbon monoxide and nitrogen dioxide, have dropped markedly since 1990 in Canada and levels of several others, including volatile organic compounds, sulphur dioxide, nitrogen oxide and ground-level ozone stabilized between the mid 1990s and 2000.3a Annual mean concentrations of PM2.5 decreased at urban sites across Canada over the period 1990-1996 and have been relatively steady from 1996 to 2001, while annual mean concentrations of PM10 decreased at most urban sites.7 Using observations to 2005, a slight increase of 6% for PM2.5 is projected from 2000-2015.8 Canadian air pollution data, particularly for particulate matter, are scant before 1990.

There are several types of air pollution including: outdoor, indoor air pollution, occupational, and pollution arising from industrial point sources. The scope of this review is outdoor air pollution including industrial point sources. This chapter also includes a detailed discussion on the difficulties in measuring exposure along with some proposed solutions, as this is the focus of some of our ongoing research. However, this subject matter requires a more advanced mathematical background than the remainder of the monograph. We recommend that these sections be skipped by persons only interested in the review of outdoor air pollution and cancer.

The relationship between acute and chronic non-malignant pulmonary diseases and ambient air pollution is well studied, but which pollutants and which components of particulate matter are most harmful is uncertain. It is recognized that air pollution increases the incidence of these conditions (or exacerbates them). Increases in inhalable particles (airborne particles with a diameter of no more than 10 µm, commonly known as PM10) in the atmosphere have been associated with acute decrements in lung function and other respiratory adverse effects in children.9-11 There is evidence that mortality from respiratory and cardiac causes is associated with particle concentrations.12 Increases in concentrations of ambient ozone have been associated with reduced lung function, increased symptoms, increased emergency room visits and hospitalizations for respiratory illnesses, and possibly increased mortality; this extensive literature is reviewed elsewhere.13,14a More recent studies continue to show similar patterns.15,16 Some have posited that these increases may be due to preexisting disease in persons who are therefore more susceptible to harmful environmental exposures.

The important limitation of time-series studies is that they can only look at acute-type outcomes, not chronic exposures. Generally speaking, most of the health impact studies have concentrated on acute effects, such as emergency room visits, and the environmental relationships have been identified by correlating the rates of adverse effects with the levels of environmental pollution in a geographic region as measured over a short-term period. Chronic diseases with a long latency, such as cancer, generally require the measurement of chronic, long-term exposures.

As a consequence, air pollution risk has not been identified as clearly for cancer as for acute health problems, and the evidence for cancers other than lung cancer is limited. Since several excellent literature reviews on this subject have been published14b,17a-23 the intention here is to discuss key points and augment them with results from studies published recently.

Evidence of an association between air pollution and cancer

Biologic mechanisms

It is well-documented that air contains substances known to transform cells in culture,24 and known or suspected to cause cancer in humans.2c,23 A broad spectrum of potentially carcinogenic chemicals has been released into the air.25-27 Pollutants with a carcinogenic potential include benzo[a]pyrene, benzene, inorganic compounds such as arsenic and chromium, particulate matter, especially PM2.5, and possibly ozone.28a PM2.5 can penetrate deep into the lungs and are thought to pose a greater health risk than larger particles. Reactive oxygen species have been associated with the toxicological effects of ultrafine particles.29 PM2.5 also has higher concentrations of sulfates, nitrates, organic compounds, and transitional metals.30 Nielsen et al.,31 examining the pattern of a specific air pollutant – Polycylic Aromatic Hydrocarbon (PAH) – in a busy street in Copenhagen, Denmark, identified that the PAH levels followed the order ‘street > city background air > suburbs > village > open air’. The traffic contribution of PAH to street air was estimated to be 90% on working days and 60% during weekends. Its contribution to city background air was estimated to be 40%.

Lung cancer and urban residence

Some of the first studies of lung cancer and air pollution showed that lung cancer risks were lower in rural than in urban areas that, historically, have had higher air pollution concentrations due to traffic, industrial sources and home heating.32 Results from ecological studies indicate that the risk of developing lung cancer is greater in urban than rural areas by a factor of about 1.3 to 2.0, and generally is higher in men than women.33 However, these studies are of limited value as they lack information on important confounders such as smoking and occupational exposures at an individual level. It is well documented that smoking is the most important determinant of lung cancer, and that the smoking pattern is quite different between urban and rural populations.34a-35 Smoking has been estimated to cause 87% of all lung cancers.36-38 The estimation of air pollution associated risks for lung cancer should ideally be adjusted for several smoking characteristics including the number of smoking years and the quantity smoked. Other characteristics may also be important. For example, Doll discusses the role that the age a person initiates smoking may play on subsequent risk,34b and ETS also influences subsequent risk. Analytic epidemiological studies (case-control and cohort), where confounding factors such as smoking and occupational exposure, are taken into account, generally suggest slightly lower urban/rural risk ratios (1.2 to 1.5). However, it is possible that residual confounding for smoking may still persist, the assessment of occupational exposures are frequently crudely made and no information on radon exposure is available. It should be noted that confounding will only take place if individual-level smoking behaviours are correlated with the area-wide air pollution measures.

Case-control and cohort studies of outdoor air pollution and lung cancer

The American Cancer Society (ACS) and Harvard Six-Cities studies are key studies in the area, and form an intergral part of much of the US EPA’s air quality guidelines. The ACS cohort study enrolled approximately 1.2 million adults in 1982. Pope et al. found a 10 μg/m3 elevation in fine particulate air pollution was associated with an 8% increased risk of lung cancer.39a Measures of the coarse particle fraction (PM15-2.5) and total suspended particles were not associated with lung cancer mortality. The Harvard Six City Study included 8,111 adults with prospective follow-up for 14 to 16 years.40a Elevated lung cancer mortality in the most polluted city relative to the least polluted was not statistically significant (RR=1.37, 95% CI 0.81-2.31), whereas mortality for cardiopulmonary disease was significantly elevated.

In the Netherlands, Hoek et al41 found no association between lung cancer and exposure to fine particles (black smoke) and NO2; however, the study was limited by a relatively small number of lung cancer deaths (n=60). Another cohort study examined the relationship between air pollution and lung cancer and other causes of death among 16,209 Norwegian men.42 Yearly air pollution levels were linked with a participant’s home address. After adjustment for age, smoking and education, the RR for developing lung cancer was 1.08 (95% CI=1.02-1.15) for a 10 μg/m3 increase in nitrogen oxide. A Swedish cohort record-linkage study found an increased risk (RR=1.4) of lung cancer for those with high exposure to diesel emission.43

A study of 14,284 adults who resided in seven cities in France examined the relationship between outdoor air pollution and mortality.44 The study also collected information on smoking habits, educational level and occupational exposures to dust, gases and fumes. An increase of 10 μg/m3 was associated with an increased rate ratio of 1.48 (95% CI=1.05-2.06) of dying from lung cancer. This risk estimate is based on a total of 42 lung cancer deaths. Similar to other cohort studies, confounder information was collected only at one point in time, and air pollution exposures were measured over the course of three years. Therefore the risk estimates may be biased by an inability to take into account changes in the values of these characteristics over the follow-up interval. A notable strength of the study was the lengthy follow-up interval with some subjects followed for 25 years.

A cohort study among 6338 non-smoking southern California residents was carried out with lifetime exposure to air pollutants estimated for each member based on the zip code centroids of home and work location histories.45 For lung cancer mortality the RR associated with an increase in exposure equal to the interquartile range (IQR) of 24 μg/m3 in PM10 mean concentration was 3.36 (95% CI=1.57-7.19; 18 deaths) among men and 1.33 (95% CI=0.60-2.96; 12 deaths) among women. Among men, ozone was also significantly associated with lung cancer mortality (RR=4.19, 95% CI=1.81-9.69), although it was difficult to separate the effects of PM10 and O3 because of their correlation. For the subset of the cohort in which coarse and fine PM could be separated, the associations were best explained by the PM2.5 fine fraction.46

A review has identified ten case-control studies which included measurements on one or more of total suspended particulate matter, SO2 and NO2.47a Six studies reported significant associations with increases in risk of approximately 50%, although for one of these females had a lower and not significant RR. One study reported a negative association and three studies were not statistically significant. This review included a recent population-based case-control study of male residents in Stockholm, Sweden where the participants’ lifetime exposure was estimated using residential addresses and emission data created from road traffic and heating revealed a 40% increased risk of lung cancer for the highest relative to the lowest decile of NO2 exposure, adjusting for confounding factors and allowing for a 20-year latency period.48a

Studies of point sources of pollution and lung cancer

International studies of communities in the vicinity of large point sources of air pollution suggest such exposures increase the risk of developing lung cancer. A relative risk of around 1.5 to 2.0 was observed for people living close to arsenic-emitting smelters versus the reference group at the greatest distances, after controlling for smoking and other occupational exposures.49,50 A similar RR for lung cancer was associated with living near multiple industrial sources in northeast England, although patterns were different among men and women and at different ages.51 Ecological studies in Scotland have reported increased risks with residential proximity to steel and iron foundries even after adjustment for social class.52,53 A recent study of people living in the vicinity of a nonferrous metal smelter in Sweden found an elevated, but not statistically significant, risk for men exposed in the beginning of the operations (RR=1.51); no overall increased risk was observed for women.54 The geographic pattern of lung cancer incidence near a coke oven plant in Northern Italy suggested a role for industrial air pollution as a risk factor.55 Results from other studies, however, have not demonstrated excess risks.56,57 Misclassification of exposure may be more likely in such ecologic studies and the industrial sites differ.

Molecular epidemiology and toxicology

Molecular epidemiological and toxicological studies have provided evidence of relationships between air pollution exposure and lung cancer. One such study58 indicated various dose-response relationships between biomarkers and environmental exposures, such as polycyclic aromatic hydrocarbons and ambient indoor and workplace air pollution. The biomarkers included carcinogen-DNA and carcinogen-protein adducts, gene and chromosomal mutations, and polymorphisms in putative susceptibility genes. The study involved adults, infants and children, including cancer patients and controls exposed to varying levels of carcinogens. A cohort study in Italy found an association between living in an urban area and anti-benzo[a]pyrene diol epoxide DNA, a potential biomarker for lung cancer.59 Elsewhere, in a cohort of mothers and newborns living in an industrialized city in Poland, a dose-response relationship between ambient air pollution and PAH-induced DNA damage was observed.60 A recent in vitro study61 was the first to demonstrate that target cells of the lungs, when exposed to ambient particulate matter (a component of air pollution), initiate a cell signalling cascade related causally to aberrant cell proliferation and carcinogenesis. Cislaghi and Nimis62 studied the associations between cancer mortality and biodiversity of pollution-sensitive organisms, using the latter as a surrogate measure for air pollution. The results suggest an association between air pollution and lung cancer, although the weakness of the ecological design should be noted. These include individuals exposed in one area moving and developing the health outcome in another area, an inability to control for confounding factors, poor control for the latency period (particularly for cancer), and assignment of the same level of exposure over an entire area. The chapter on epidemiological methods in this monograph provides further discussion of the strengths/weaknesses of the different epidemiological designs (case-control, case- crossover, cohort, ecologic) and basic concepts in exposure assessment.

Cancers other than lung

Several epidemiological studies have included examinations for adult cancers other than lung. Increases in incidence and mortality have been observed often in urban areas for all cancer sites combined, or for sites other than the respiratory tract.20 The observed risks for other cancers are generally smaller than those for lung cancer, although some of the associations seen with childhood leukemia are stronger. For specific adult cancer sites, the results are quite inconsistent and below, some of the key findings are outlined.

A positive but not statistically significant association between living on roads with high traffic density and female breast cancer was reported for one of two counties in Long Island, New York.63 In a case-control study in Erie and Niagara Counties, New York, total suspended particulates (TSP), as a proxy for PAH exposure, was investigated as a risk factor. In postmenopausal women, exposure to high concentrations of TSP (>140 microgram/m3) at birth was associated with an adjusted odds ratio of 2.42 (95% confidence interval, 0.97-6.09) compared with exposure to low concentrations (<84 microgram/m3). However, in premenopausal women, where exposures were generally lower, the results were inconsistent with the hypothesis and in some instances were suggestive of a reduction in the risk of breast cancer.64

In a study along the border between Norway and Russia high levels of sulphur dioxide caused from industrial emissions was implicated in causing both environmental damage and an increased incidence of adverse health effects.65a Standardized mortality analysis revealed an increase in the number of deaths from cancer and cardiovascular disease in two cities with nickel refineries when compared to a control city.65b

In recent years, several studies have examined the cancer impact of exposure to air pollution due to motor vehicle emissions, focussing mainly on children and leukemia. Taken together the results are equivocal. Two childhood cancer case-control studies, one in Denver and one in northern Italy, found several-fold increased risks for leukemia in children with high exposure to traffic emissions.66,67 Elsewhere, paternal occupational exposure to exhaust fumes has been associated with an increase in childhood cancer in the offspring.68 Several studies however have found no association between living near high traffic areas and childhood leukemia.69-72 In one study, disparate findings were found between adults and children. Specifically, there was no association between residence along main roads and the development of adult cancers but an association was found with hematological malignancies in women and children.73

Population attributable risks

In summary, strong evidence exists for an association between air pollution exposure and lung cancer. The evidence for other cancers seems far less conclusive, though additional research is needed. Estimates of the population attributable risk of cancer has evolved over the last 40 years,17b,74 reflecting the limitations of studies, including insufficient information on confounders and latency, and misclassification of exposure. For example, Stocks and Campbell75 estimated that urban air pollution adds about 100 lung cancer deaths per 100,000 persons, while Doll and Peto35 estimated that less than one percent of lung cancer would be due to air pollution. In 1990, the US EPA estimated that, based on unit risks from known or suspected carcinogens found in ambient air, 0.2% of all cancer and less than one percent of lung cancer could be attributed to air pollution.76 In contrast, the population attributable risks for smoking and radon are considerably higher. Specifically, an estimated 87% of lung cancers can be attributed to smoking and 10-15% to radon.77

Recent cohort studies, however, reveal that up to 50% increases in the risk of lung cancer could be due to air pollution exposure, particularly associated with indices for sulphate and fine particulates.39b,40b,78 Based on a conservative estimate of 20% of the population in the low exposure group (RR 1.1), 4% in the medium exposure group (RR 1.3) and 1% in the high exposure group (RR 1.5) approximately 3.6% of lung cancer deaths in the European Union could be due to air pollution exposure.47b An estimated 5-7% of lung cancers among never and ex-smokers are due to air pollution in a multi-centre European study in which exposure to air pollution was assessed using concentration data from monitoring stations.79 Elsewhere, a review article by Nikic and Stankovic suggests that the estimate unlikely exceeds 2% based on applying unit risks of known or suspected carcinogens found in outdoor air.80 These studies suggest that while cigarette smoking remains the predominant risk factor, the widely-cited PAR estimates above may be low. These investigators used the prospective cohort approach in their studies in an attempt to overcome limitations associated with the ecological designs. Important confounding factors, such as smoking and education amongst others, were taken into consideration. However, most studies have been limited to using regional or neighbourhood fixed site exposure estimates which fail to take into account individual differences in activity patterns, or adjust for the effects of indoor radon or air pollution. Changes in time have largely not been controlled for.

Methodological difficulties in studying air pollution – cancer associations

This section on exposure assessment and measurement errors is included as part of the air pollution chapter since some of the methods have been developed as part of air pollution studies. Although some of the concepts represent advanced biostatistics, even a rudimentary understanding of them is helpful in assessing the literature on the association between cancer and air pollution.

Overall, a major drawback in all air-pollution-and-cancer studies to date has been the inadequate characterization of air pollution exposure. Generally speaking, air pollution exposure estimates for all individuals residing in a local area have been based on the average or median concentration levels from fixed monitoring stations in that area; that is, all individuals in the same area are assumed to have the same exposure. This is a limitation particularly given that for some pollutants associated with traffic (NO2 and ultrafine particles) variations within cities may exceed variations between cities.81,82 Moreover, even people living adjacent to each other may experience different exposures. Air pollution exposures are dependent on activity patterns, can vary seasonally, and certain occupations may be associated with different exposures. Lifetime residential histories have rarely, if ever, been taken into account. Also long-term attempts to characterize exposure would typically use annual exposure estimates, which are unable to capture potentially important long-term effects associated with very high and short term increases in exposure. Although individuals from the same area might have had similar exposures for a specified period, it is very likely that their lifetime exposures are very different due to the mobility of the population. In Canada, a recent census83 demonstrated that close to 25% of the population had changed place of residence during the previous five years. Personal monitoring devices are now used for some studies; however, given the latency involved for cancer and the need for retrospective exposure assessment, such methods are impractical for general population studies. In this situation, one would need to measure exposure in a cohort of 20,000 or more individuals prospectively over several decades. These devices may have some utility for occupational exposures. For studies of cancer, they can be useful for the purposes of creating retrospectively based job-exposure matrices; although such a study would either have to assume that current exposure were representative of past exposures, or have some means of making such an adjustment.

An approach that may become more widespread in the coming years is the use of satellite imaging data to estimate PM and NO2 levels. This approach can allow for pollution estimates to be obtained for rectangular grid areas on a 10 km by 10 km basis, and hence for all geographical areas (some better than other), not just areas in close proximity to fixed site monitoring stations.84

These limitations may create substantial misclassification of exposure and hence bias the estimated risks. In addition to a lack of data on other known or suspected risk factors, an important drawback comes from treating imprecise measurements of covariates as if they were measured accurately. In most situations, exposure misclassification will tend to bias the risk estimates towards the null (i.e., no effect) and model residual variance is increased. With an appreciable amount of exposure measurement error, as one might expect from the large scale of environmental epidemiological studies, the amount of bias can be substantial. Thus, an analysis which does not account for imprecision in covariates can mask the presence of a statistically important effect. These limitations have been recognized by several investigators.18,22,28b Measurement error in other risk factor data can bias the risk estimates in either direction. The potential for important sources of bias to arise is possible given that over a large follow-up interval, these confounding exposures (e.g., smoking) can change.

The remainder of this chapter focusses on methodological developments for estimating cumulative air pollution exposure using historical monitoring data and incorporating measurement errors into the analysis. The reason for the focus on cumulative exposure is because of the relevance of chronic pollution exposures to cancer.

Cumulative exposure assessment

The feasibility of estimating lifetime exposure to outdoor air pollution depends on the availability of information on residential histories of individuals and on historical air pollution data. These kinds of information are generally obtainable for residential history, but historical air pollution data are limited before 1990. For example, in a recent large Canada-wide study on environmental risk factors – initiated by Health Canada and the provincial partners, and called the Enhanced Cancer Surveillance Initiative (ECS)85a – residential histories and information on important confounding factors, such as smoking, diet, and occupational histories, were collected for over 20,000 cancer patients and 5,000 controls from the general population. A database of potential exposures was also established. The pollutants modelled included PM10, O3, CO, NO, NO2, and SO2. Historical air pollution measurements from fixed monitoring stations are generally available from government-administered environmental networks; some stations have been in operation for over 20 years, although startup dates vary greatly.

Even with the availability of residential histories and historical air pollution data, the difficulties associated with lifetime exposure estimation remain. Cost prohibits having air pollution measurements at all locations of interest, such as residential locations. Therefore, the basic problem is to predict the concentration level at an unmonitored location using the observed concentrations at the monitoring locations. The predictions at individual residential locations can then be aggregated to estimate the cumulative exposure level. However, even such methods may not be accurate as they fail to take into account differences in the activity patterns, and hence, can misclassify exposure to outdoor air pollution at an individual level.

Such so-called spatial interpolation problems arise in diverse fields, including engineering, geology, soil science, hydrology and mining. Analysts commonly tackle such problems with the well-known method of Kriging, introduced in the 1960s by Matheron.86 The Kriging method predicts the concentration levels at a location of interest using a weighted average of all observed concentration levels at the monitoring stations where the weights are proportional to the inverse distances between the location of interest and the stations. The predictions have an appealing optimality, that of being from the best linear unbiased estimator, when the covariance between the locations (or equivalently the variogram) is known. Kriging requires a reasonably dense network of monitoring stations (10-100), depending on the type of analysis.87 The method has been extended to incorporate additional information from covariables to improve the interpolator. This is called co-Kriging.88

These approaches implicitly assume isotropy for the air pollution field in the study region; that is, that the closer the distance between two locations, the more similar the concentration levels are. This assumption is generally unrealistic for environmental data due to potential differences in geographic setting and meteorology. For example, the concentration levels at two locations located on opposite sites of a mountain may not be very similar regardless of how geographically close they are. On the other hand, two locations far apart may have very similar levels if they are on the direction of the prevailing wind.

These methods also fail to incorporate uncertainty about the covariance structure of the pollution field into their measure of interpolation error, leading to unwarranted confidence in the interpolated values. Several authors have since recognized these limitations and have proposed modifications to adjust for them.89,90 These modifications, although overcoming the problems to a certain extent, still assume isotropy for the pollution field.

Recently, a new theory for the spatial interpolation of air pollution was developed that avoids the limitations described above.91a,92a The approach, which is a Bayesian alternative to Kriging and co-Kriging, does not assume either isotropy or a known covariance structure. The theory permits temporal and spatial modelling to be done in a convenient and flexible way. At the same time, model misclassifications, if any, can be corrected by additional data – if and when they become available. The developed model is hierarchical Bayesian in character, where the spatial covariance is left completely unspecified in the first level. Uncertainty about the covariance structure is incorporated through the second level prior, and hence unrealistically small credible regions for the interpolants are avoided. The covariance structure is non-parametrically modelled through the powerful approach of Sampson and Guttorp,93a thus avoiding the isotropy assumption.

This theory has been extended to encompass not only univariate but also multivariate responses measured at ambient monitors. Thus these can be used in predicting responses at unmeasured sites, e.g., individual residences. The further extension 94a,95a deals with situations where not all monitoring stations measure the same suite of pollutants and not all stations started operation at the same time. The extended theory allows for the use of all available data for different pollutants and from different sources in the estimation process. In other words, it permits “borrowing strength” to provide more accurate estimate exposures to air pollutants. This development is very relevant for environmental data where, commonly, over time stations and pollutants may have been added to or dropped from the networks due to financial considerations and additional knowledge.

Validation studies96a indicate that the method performs very well. It has been used successfully in several health impact studies of air pollution,97a,98a including one in British Columbia, using the ECS case-control data. In this study, the spatial and temporal predictive distributions of specific pollutants were calculated for each month between 1975 and 1995 using historical concentration levels. Figure 1 displays contour levels for the estimated monthly mean ozone concentration field (June 1985) over a region.

Figure 1
Contour levels for the estimated monthly mean ozone concentration field (μg/m3) for June 1985, southern British Columbia

Contour levels for the estimated monthly mean ozone concentration field for June 1985, southern British Columbia
Text equivalent, Figure 1

Figure 1
Contour levels for the estimated monthly mean ozone concentration field (μg/m3) for June 1985, southern British Columbia

Through the predictive distributions, the estimates for monthly concentrations and their corresponding uncertainties can be obtained for specific locations in a region. Thus, for a given residential history, it is possible to trace the individual locations of residence through these distributions and aggregate the corresponding monthly estimates to get the cumulative exposure estimates, along with their uncertainties. Figure 2 displays the estimated monthly ozone levels from 1975 to 1995 at three different locations where a study participant resided. It is quite clear that the exposure patterns and levels vary substantially, suggesting that cumulative personal exposure estimates based on short time periods may not be appropriate. Furthermore, the observed levels at the nearest station are quite different from those estimated at the location of residence, confirming the need for spatial interpolation. The new theory is developed with the assumption that the random fields follow a gaussian distribution. This assumption may not be realistic for air pollutants and so transformations of the fields are usually required. In some cases, however, this may not be possible.

Figure 2
Estimated monthly ozone levels (μg/m3) from 1975 to 1995 at three different locations where the study participant resided, southern British Columbia

Estimated monthly ozone levels from 1975 to 1995 at three different locations where the study participant resided, southern British Columbia
Text equivalent, Figure 1

Figure 2
Estimated monthly ozone levels (μg/m3) from 1975 to 1995 at three different locations where the study participant resided, southern British Columbia

The vertical dash lines separate the three locations, while the dotted line on the right is the observation series of the monitoring site that is the nearest to location 3.

Another approach for estimating the exposure levels at individual residential locations is to use a dispersion model in conjunction with emission databases and the geographical information system. This approach has been used in a case-control study in Sweden48b and found to provide estimates consistent with ambient measurements for NO2 at various locations.99a The emission databases are generally not readily available and may have to be constructed for individual studies. Such constructions could be a major undertaking, eg. requiring data on the growth of urban areas, the development of district heating systems and local industrial sources, as well as road traffic patterns.99b It may also be impossible to construct retrospective emission estimates.

Land use regression methods are also increasing in popularity. These methods predict pollution concentrations at a given location based on surrounding land use and traffic characteristics. The pollution concentrations are modelled as the dependent variable. These methods have been used in Europe to model exposures at an intra-urban level. Jerrett et al.100a provide background for types of exposure assessment methods.

Measurement error


The large scale of studies in environmental epidemiology makes error in the measurement of individual subject attributes and exposures inevitable – a fact that has long been recognized. A large body of work has been developed and much of the work in occupational exposure assessment measurement error applies here. In recent years, advances in computer simulation have provided some opportunities to look at the extent of these errors. The observation that many researchers do not take account of this pervasive problem may well derive from complacency inspired by “… a common perception that the effect of measurement error is always to attenuate the line”.101a That view encourages misplaced confidence in findings that reject the null hypothesis on the basis that, if anything, the measurement error will have “attenuated” the slope of regression, that is, reduced it toward the null value. In other words, the correct p-value would be even smaller if it were not for the measurement error.

Recent increasing reliance on non-linear regression models in epidemiology may have helped kindle interest in the problem. That reliance can be explained by a combination of computing technology and methodological advances like Generalized Linear models, and GEE (generalized estimating equations).102a GEE methods are a mechanism to adjust for correlations in the data so that the standard errors are more accurate (larger errors). The complexity of the newer models may have challenged simplistic views borne of simple linear regression models.

Those same advances may also explain why investigators have been willing to turn to the so-called “errors in variable (EIV)” problem. The errors in variable model differs from classical regression in that the “true” explanatory variables are not observed exactly, but rather are imprecisely measured. Undoubtedly, Fuller’s fundamental treatise on the problem103a stimulated that work, for it convincingly demonstrated the truly complex and pernicious character of measurement error. Since the publication of Fuller’s book, great advances have been made by several authors.101b,104a In this section, a very selective overview of the problem is given, particularly as it relates to the authors’ contributions.

Types of measurement error

For exposure variables, measurement error is generally characterized as either of “classical” or “Berkson” type, “differential” or “non-differential”, “structural” or “functional” (Appendix I). Different categories of error have seen the development of different methodological tools. Some involve errors of mixed type.105a

However, the taxonomy of error is redundant if error is treated within a Bayesian framework. All its elements and more are automatically subsumed by treating all uncertain quantities (including those measured with error) as random variables that can be incorporated in any analysis through the appropriate joint distribution. The Bayesian framework is thus natural for the treatment of measurement error. Subsequently, in this review the Bayesian methods developed will be showcased.

In spite of the increasing reliance upon Bayesian methods in modern statistical science, much current and recent theory for treating measurement error has been developed within the framework of the repeated sampling paradigm. For completeness, the developments from that perspective will also be described.

Error effects and their mitigation

Little of a general qualitative nature is known about the effects of measurement error, even though a substantial methodological base for handling errors exists. By using that base, the implications of error can be assessed in particular contexts. However, some general results are known, and those are summarized in this subsection.

In the case of binary exposure variables, Thomas et al105b showed for analytic studies that quantities like relative risk are attenuated by non-differential misclassification. Analogous results for matched case-control studies have also been obtained by Greenland.106a In fact, Greenland showed the surprising result that non-differential misclassification can have more detrimental effects in matched than unmatched designs, the size of the detriment growing with the closeness of the match. This is of note for investigators planning a case-control study.

However, these results reverse in cluster-based i.e., ecological studies. In this case, the populations are partitioned into groups and group attribute measures, rather than those of individuals, enter the analysis; for example, ecological studies where the group exposure is measured by the proportion of those exposed are considered.107 With non-differential misclassification, estimates of rates (slopes) for individuals, based on group-level analysis, will generally be inflated rather than deflated (attenuated) towards the null, as in the case of the classical error model and simple linear regression. Thomas et al.105c noted the complexities introduced by multi-level (discrete) exposure variables that make the effects on ecological estimates quite unpredictable.

For continuous variables, the classical non-differential measurement error model leads, in simple linear regression, to attenuation toward the null of the apparent effect of exposure. This does not occur in the case of the Berkson error model, however, where the apparent effect remains unbiased. This result has recently been proved for more general settings than just simple linear regression by Gustafson and Le.108a

In general, ignoring measurement error can lead to a myriad of problems apart from the bias resulting from attenuation discussed above.109a Further descriptions can be found in examples given in Appendix II. In the space available here, it is difficult to completely survey the array of other problems attributable to measurement error. Instead, the reader is referred to comprehensive surveys available in the literature.101c,104b

Thomas et al.105d give a good brief survey of mitigating strategies within the framework of exposure measurement error, and Appendix III contains a brief summary of those most directly relevant to environmental cancer epidemiology. A longer general review may be found in Carroll et al.101d Comprehensive discussion on the Bayesian developments for case-control settings can be found in Gustafson104c and Gustafson et al.114,115

Environmental cancer epidemiology

In this section, an approach to cancer epidemiology within the context of environmental health in a general setting is described. The assessment of environmental risk in this setting proves challenging. One expects the relative risks of cancer from environmental factors to be subtle and hard to detect. In addition, for some health conditions, the time between exposure and disease onset can be lengthy.

To gain realistic power to detect environmental effects, investigators of environmental health studies may rely on quasi-experimental control populations or “quasi-controls”. In other words, they target subjects from high as well as low exposure sub-populations i.e., “clusters”. These clusters may be determined by geographic sub-regions, as in the multi-level longitudinal study of children’s lung function and disease now being carried out in southern California by Duncan Thomas and his co-investigators.116,117 Here the exposure of primary interest is air pollution and the clusters are sub-populations of school children in a number of regions of southern California. Some regions with low air pollution levels, as well as some with high levels, have been randomly selected into the study. Salient data on other risk factor data are collected from both “cases” and “controls”.

However there is a potential difficulty. The grading of prospective clusters for level of exposure must be done largely on a priori (heuristic) grounds. If subjects are then followed over time, it may well turn out that the between-cluster contrasts are insufficiently large to enable meaningful comparison. In cancer epidemiology, following subjects in this manner would not be realistic, since latency times are typically long. This forces purely retrospective analysis. If administrative records are used, investigators may by forced to incorporate an ecological component into their design that comes with it all the difficulties that can hinder characterizing risk at an individual level. Paramount among these is the inability to collect information on the changes in these risk factors over time.

Noting the difficulties associated with ecological studies, Johnson et al.85b advocated instead a case-control study for trying to elucidate environmental causes of cancer in a population based sample of Canadians. Their case-control design matched cases only rather loosely to controls (using frequency matching) with respect to age and area of residence, a desirable feature in their design if one recalls the work of Greenland106b cited above. The authors give a comprehensive summary of co-factors (“diet”, “exercise”, “SES”, “smoking” and “occupation”) for which, ideally, the analysis needs to be adjusted. Nevertheless, the case-control design is not void of limitations, particularly recall bias, and participation bias. Participation bias may essentially yield controls that are not representative of the population that gave rise to the cases, while recall bias can affect the risk estimates in instances where cases and control differ in their remembering past exposures. These are important limitations that lead some to rely more on findings derived from prospective (cohort) studies.

Johnson et al.85c also point to the need to account for “residential mobility”, since this is an important factor in determining environmental exposures. The anticipated gains from using quasi-control clusters may well be eroded by uncontrolled variation due to facts such as subjects moving between clusters, thereby effectively creating “misclassification error” in either analytic or ecological studies. The activity levels for each individual are also important.

Johnson et al.85d proposed using the “Environmental Quality Database” in their study of the role of environmental factors in the development of cancer. However, they provided little discussion on the likely impact of the inevitable error in the measurement of exposure. Because of cancer’s long latency period, and the difficulty in reconstructing historical exposures, the size of such error is likely large. In fact, it can be large even in prospective studies because of the impracticality of measuring individual, as opposed to ambient, exposure levels. To yield convincing results, any statistical analysis must, therefore, recognize at a fundamental level and incorporate measurement error. Moreover, incorporation of that error will entail backcasting existing space-time series for environmental hazards for varying lengths of time, depending how long individual stations have been monitoring the environmental factors. Error can arise not only in the environmental database that is based on objective determination of exposure, but in confounding variables from the reliance on self-reported data (inaccurate recollection, recall bias, etc).

One statistical strategy for environmental risk analysis that incorporates measurement error and concerns a chronic health outcome such as cancer is described in Appendix IV. Basically the cumulative exposures are estimated using the recently developed Bayesian method94b,95b as outlined in the previous section. The exposure estimates come with the associated measure of uncertainties, including measurement errors, that can be directly incorporated in the health impact analysis through the generalized estimation equation method.98b,102b,105e The strategy involves a space-time series of environmental covariates including the risk factors. Both individual and ecological studies are embraced by the abstract formulation of the problem. This breadth is achieved by taking “cluster” as the fundamental building block. The cluster can represent either a single individual followed prospectively or retrospectively over time or a cluster of individuals, each with an associated series of exposure measurements. A more detailed survey on this statistical strategy can be found in Zidek.109b

Concluding remarks

In this chapter, the evidence on the relationship between cancer and air pollution is examined. Methodological issues affecting the precision of the evidence are reviewed, particularly the inadequate characterization of air pollution exposures and the failure to account for their potential misclassification. The discussion specifically concerns the association, if any, between air pollution and cancer, although it is applicable to general chronic diseases. Studying the relationship between risk factors and chronic health outcomes proves difficult, namely because subjects, being mobile, will have resided in areas where pollution levels were unmeasured, leading to potential measurement error. The deleterious and unpredictable effects of such error and the consequent need to mitigate those effects using predictors of the unmeasured exposures are discussed. A new general approach that may be taken in environmental epidemiology to overcome these difficulties to a certain extent is described. More research into methods such as those discussed here is needed since, in environmental epidemiology, identifying the risk factors for chronic morbidity has proven much more challenging than for acute morbidity. A more detailed description and recent developments will be available in the forthcoming book by Le and Zidek.127.

Appendix I. Taxonomy of measurement error

Classical measurement errors obtain in “analytic” studies i.e., studies of individuals; the exposure measurement W = X + U where X denotes the “true exposure” and U independent “noise”. The Berkson type arises, for example, when all members of a sub-region are assigned a single sub-regional value W obtained from an ambient monitor for that region and X = W + U, U representing an independent deviation ascribable to individual differences. Carroll et al.101e used instead “error calibration” and “regression calibration” respectively to describe these two classes of error models. These two seemingly similar models are actually very different in their implications for practice.

The mixed model of Thomas et al.105f arises when W = X + U (classical) while X = Z + V (Berkson) where Z is an extraneous environmental variable and V represents an additive Berkson residual variable.

Non-differentiable measurement error obtains when the health response Y and W are independent random variables when X, the true exposure, is given. In other words, the measurement has no information about the response other than that contained in the true exposure itself. In this case, unlike that of “differential” error, W serves merely as a “surrogate” for the true exposure and nothing more. Carroll et al.101f suggested that many situations are best described by non-differential models. In particular, this approach should be applied in the study of the acute health effects of environmental exposures.

Structural measurement error refer to the case where the true exposure is random whereas functional means it is treated as fixed (but unknown).

In the technically elementary case of binary exposure variables (0 = “low” and 1 = “high” say) measurement error is called “misclassification”. Although conceptually relevant, the classical-Berkson dichotomy cannot be formally used. To see this, note that the mathematical expectation E(W | X) cannot equal X (which is 0 or 1 except in degenerate cases) as it must if the classical model were to obtain. However, the concepts can be expressed through a reformulation of the measurement error model in terms of probabilities and conditional probabilities.

Appendix II. Some problems associated with ignoring measurement error

Zidek109c demonstrated, in the case of non-differential structural measurement error, that the “curvature” of non-linear regression models can pick-up the covariance of the measurement error’s covariance structure.

To see, in a simple setting, some of the complexities ahead, consider just a trivariate response vector (Y, X, Xg) having a joint multivariate normal distribution. Assume the commonly used “impact model” E[Y | X] = exp[β X]. Inference concerns β, and (X, Xg) has a bivariate normal distribution. Now E[Y | Xg]= E{exp[β X] | Xg} if Y and Xg are conditionally independent, given X. Thus E[Y | Xg]= exp[ββX,Xg Xg+β2σX,Xg/2]. As in the linear case, bias induced by measurement error expresses itself through βX,Xg. However the “curvature” of the model now draws in a measure of how precisely the surrogate Xg represents X through the residual variance σX,Xg. If the latter were 0, one could fit the naive model Y= exp[b Xg] and then correct for bias in the estimator b of β exactly as in the linear case. However, if σX,Xg is non-zero, there is a competition between the need to inflate b to compensate for bias and also to deflate b to compensate for lack of precision. To be precise, if one has a large residual variance and fits the Y on Xg model above, the fitted value of β will be close to 0.

The effect can thus dominate the attenuation that leads to bias. The effect of the error can, therefore, not be predicted without detailed analysis; the coefficient that transfers exposure to health impact can be either inflated or deflated by the error.

Zidek et al.110a described a more subtle problem that can arise when both non-differential structure measurement error and collinearity obtain. The authors assume in a hypothetical situation, that a response count has a Poisson distribution with conditional mean exp(α0 + α1 x). Here x is a realization of X, the “cause” of Y. A second predictor covariate, w has been observed, but both x and w are measured with error according to a non-differential classical model to yield X and W. It is shown, by means of a simulation study, that if an investigator were to fit exp (α0 + α1 x + α2W) when the measurement error in X is sufficiently large compared to that of W, while X and W are sufficiently strongly correlated, the analysis may well show α1 and α2 to be non- and significant respectively. Thus, although X represents the causative factor, that represented by W inherits the role. Causality has thus been “transferred” through a combination of measurement error and collinearity. This phenomenon is noted for linear regression models by Fuller.103b While hypothetical, the result raises serious concerns for practice. Can any significant finding from a multi-variable environmental health impact study be due to such a simple collusion among the variables? That concern is further re-enforced by Fung and Krewski111a who extended and confirmed the analysis of Zidek et al.110b by considering both Berkson and classical error models.

Appendix III. Measurement error coping strategies most relevant to environmental cancer epidemiology

In the setting of structure measurement error, Carroll et al.101g call the most general approach to dealing with measurement error (outside of that offered by the Bayesian paradigm itself) “regression calibration”. That approach consists of replacing the erroneously measured variable X with E(X | Z,W) in the regression model where W represents the measured value of X , and Z other covariates or predictors measured without error. The result will be the “correct” regression model for regression of Y on Z and W. That conditional expectation will involve unknown parameters that would then need to be estimated, possibly by weighted least squares or maximum likelihood methods. In any case, the resulting estimates of the effect of X, as expressed through those parameters, will be corrected for the measurement error.

Pierce et al.112 advocate this approach. Moreover, they advocate its use in the setting of functional measurement error and suggest how an appropriate distribution for the nonrandom X variable can be constructed and interpreted.

A “complementary approach” (in the terminology of Carroll et al.101h) is given by Cook and Stefanski.113 This so-called SIMEX method uses the erroneous model for a succession of data sets created by adding independent random error of successively greater variance to the W values. The resulting regression coefficient estimates can then be plotted and the plot extended backwards to the case of zero variance to estimate the coefficient estimate that would have been obtained had X been measured instead of W.

The SIMEX method looks promising and has much intuitive appeal. However, Fung and Krewski,111b on the basis of their simulation study, favour the regression calibration method over SIMEX. Their detailed findings about the performance of these readings will be valuable to investigators confronting the measurement error problem in practice.
Carroll et al.101i describe likelihood, Bayesian and semi-parametric approaches to handling measurement error. They also discuss methods specifically available for use with functional measurement error.

Appendix IV. A statistical strategy for environmental risk analysis incorporating measurement error

Suppose K clusters and T times are considered. For a given pair (k,t), k = 1, … ,K, t = 1, …, T, Ykt denotes an observable health response. At the same time Xkt is the vector of covariates, some random and some fixed. These may include cumulative exposures over time. Let Yk be the vector of all responses for cluster k and Y that obtained by combining clusters.

Consider the following example to fix ideas. Burnett et al.118a explored potential health effects of air pollution by examining the association between respiratory morbidity and designated risk factors. Summer days t (from 1983 to 1988) formed the time-period of their study and sub-regions of Ontario k the “clusters”. Health responses were random daily hospital admission counts {Ykt }. Covariates (including their lagged values) were daily pollution concentrations and meteorological variables, Xkt. Thus pairs (Ykt Xkt ) entered into their regression analysis for association.

However, the covariates in Xkt were not actually measured for most k. Thus Burnett et al.118b were forced to impute unmeasured values as those obtained from the ambient monitors in closest proximity to the sub-regions in which the admitting hospital was located. At the same time, they ignored the imputation (measurement) error of Berkson type thereby introduced.

Zidek et al.119a revisited that study using promising new methods that involve imputed measurements but formally admit imputation error into the analysis. Because of their possible applications in cancer epidemiology, these methods are now described. First a brief description of the construction of an imputation methodology for unmeasured explanatory variables is given. That approach, described in detail by Zidek et al.98c adapts the theory of Le and Zidek,91b as refined and assessed by Brown, Le and Zidek,92b Sun,120 Sun121 and Sun, Le, Zidek and Burnett.96b That theory admits a fixed set of covariate vectors shared by all sites: {zt}, for example, time of year or temperature. Then, conditional on model parameters, it is assumed that E(Xt |zt ) = B zt. Conditionally on {zt} and those same parameters, the {Xt} are assumed to be a sequence of independent random vectors with a joint multivariate normal distribution. Furthermore, a hierarchical Bayesian framework is adapted to incorporate uncertainty about model parameters that are, in fact, unknown. To achieve a reasonable level of tractability, a conjugate prior distribution is adopted for the model parameters. The predictive distribution for the unmeasured {Xkt}, conditional on those measured at existing monitors, can then be obtained as the marginal distribution from the joint distribution of all uncertain quantities, including model parameters and unmeasured responses.

However, additional parameters, called “hyperparameters”, enter into the problem through the hierarchical prior distribution. To fit these new parameters, the two-stage approach of Brown, Le and Zidek92c may be used. That approach first uses the EM algorithm (in the manner of Chen122) to estimate the hyperparameters associated with measurable covariates. Next the method of Sampson and Guttorp93b is used to extend estimated hypercovariances to include those for pairs of sites, at least one of which does not have a monitor. To make the data conform to model assumptions, the data must be “pre-whitened”.

How can the predictive distribution described briefly above now be used? One approach to answering this question may be found in the work reported by Duddek et al.97b They extend the methods of Burnett and Krewski123 and Lindstrom and Bates.124 That method is further extended in Zidek et al.119b to overcome a technical deficiency in the earlier theories. Davidian and Giltinan125 provide a recent general reference to the subject of this section, although that work does not discuss advances to be described here.

In fact, the re-analysis of Zidek et al.98d uses the generalized estimating equation (GEE) methodology (c.f. Liang and Zeger102c) as adapted by Zidek et al.119c An advantage of that approach lies in its requirement of just moments of order, at most two. Thus one needs only E(Xkt) = zkt and Cov( Xkt1,Xkt2 )=Gkt1t2 from the joint distribution of the explanatory vectors. To construct a ‘working’ covariance matrix, Duddek et al.97c and Zidek et al.98e take Gkt1t2=0 when t1t2. Another well-known advantage of the GEE approach stems from its capacity to “adjust” the working covariance matrix and estimate the “true” covariance estimates.

To finish implementing the method of Zidek et al.98f moments for the conditional distribution of daily hospital admissions need to be specified. To that end E (Ykt| Xkt) = mkt exp(β’ Xkt) can be considered. In that model for health responses, mkt incorporates day-of-the-week and population size effects of cluster k (as well as low frequency components such as seasonality or trend). So mkt is regarded as a known correction factor that acts as a high-pass filter on the Y series. The conditional covariance of Ykt is Cov( Ykt1, Ykt2|bk, Xkt1,Xkt2 )= δkt1t2 φ  mkt exp(β’Xkt) where δ denotes the Dirac delta function and  φ is an unknown scalar called the overdispersion parameter.

Using the model above, the approach of Zidek et al.119d adopts the predictive distribution for the Xkt described above. In particular, a student’s matric-t distribution gives the expected value and the covariance structure for the unmeasured Xkt. These moments then enter the adapted GEE approach of Zidek et al.119e described above to estimate parameters like δ above.

However, for constructing the historical data series needed for a long latency disease like cancer, a further extension of the spatial predictive distribution is needed. The problem that must be solved stems from the irregular manner in which ambient monitors are added to the existing networks. They come on-stream at widely varying times. Thus results from the oldest monitors must be used to help impute exposures over the whole grid in which subjects are deemed to have moved during their latency period.

Such an extension has, in fact, been made by Le, Sun and Zidek.95c In particular, they use a new conjugate prior distribution for the hypercovariance matrix, the Generalized Inverted Wishart distribution of Brown, Le and Zidek.126 This gives much more flexibility in choosing the degrees of freedom in that conjugate prior for the spatial covariance matrix. Thus varying degrees of certainty can be attached to covariances for data from monitoring stations in different subregions.


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