During last decades, a growing number of studies concerning the relationship between outdoor air quality and its impact on pregnancy outcomes have been published , where an increasing incidence of preterm births and low birth weight among this group of population has been reported [2–4]. These outcomes have been associated to air pollutants such as ozone, particulate matter, carbon monoxide or sulfur dioxide [5–14]. Studies concerning air quality assessment in the Alentejo Litoral highlighted evidences of an association between the degradation of air quality and the industrial air pollutants emitted [15–18]. It is now important to assess if there is an association between outdoor air pollution mixtures and pregnancy outcomes, because this association is not yet investigated in the region.
Semi-ecological design studies are widely used to assess effects of air pollution in humans . In this type of analysis, health outcomes and covariates are measured in individuals and exposure assignments are usually based on air quality monitoring stations data. Therefore, estimating individual exposures are one of the major challenges when investigating these relationships with a semi-ecologic design.
To assess human exposure to outdoor air pollution in an ecological study, measurements are frequently collected from a set of known pollutants in air quality monitoring stations placed in sites previously selected for regulatory purposes. Besides the fact that these sampling sites tend to be selected for their expected relatively high concentrations, the obtained data are time series of instantaneous concentrations values measured on a continuous basis for few pollutants and are sparse in space. In this way, it is difficult to obtain data regarding the exposure to mixtures of pollutants (known and unknown) with high sampling density. In the last years, these constraints have been overcome using lichen diversity biomonitoring programs [20, 21]. Lichens (symbiotic organisms consisting of fungi and algae or cyanobacteria) are available almost everywhere on the planet, and have been used to monitor air pollution by several pollutants, particularly sulphur, nitrogen, fluoride, metals, radionuclides, dioxins, PAHs, and also particulate matter [22–26]. As they are long-lived organisms, lichens accumulate pollutants over time, reflecting a long-term exposure (from months up to several years); moreover, lichen diversity tend to decline in polluted areas, as a consequence of the harmful effects of the persistence of pollutants on the lichen physiology. Lichen diversity provides an overall measurement of the air quality, since lichens are exposed to the same complex mixture of pollutants that humans have been exposed to in the previous years. This is of critical importance for health studies, since one of the most difficult tasks is to relate the low pollution levels with medium or long-term effects on health . This was shown by the work of Cislaghi and Nimis , where lichen diversity value, used as indicator of air pollution, showed a good correlation with lung cancer mortality in north-east Italy; these authors found that the lung cancer mortality was higher in the areas where the lichen diversity was lower. Furthermore, lichen diversity biomonitoring programs allow the adoption of cost-effective sampling strategies with relatively high density of sampling locations, thus generating more spatially detailed data in order to obtain high resolution maps for outdoor pollution . These spatially detailed data are important to assess the different levels of exposure to pollution between individuals living and/or working at different areas inside the same region.
To assess uncertainty of individual exposures to outdoor air pollution, not much work have been yet published . Standard errors of estimated exposure are one way of assessing exposure uncertainty, however it is difficult if not impossible to derive by analytical methods the effect of this uncertainty on the estimated risk of an health outcome and associated confidence intervals, since the amount of uncertainty varies from location to location . Spiegelman  recommends exposure validation methods to assess uncertainty. These methods adjust exposure measurements errors collecting simultaneously data on the exposure surrogate and on a gold standard method of exposure assessment collected within a subsample of the main study population. Baxter and co-authors  also use a validation study to reduce traffic-related air pollution exposure misclassification (using indoor concentration measurements in a subset of the study population as gold standard method) to estimate the degree of misclassification and correct for it. A different approach followed in recent years is based on geostatistical simulation. Waller and Gotway  used this methodology to a case-control study on association between Very Low Birth Weight (birth weight <1500 gr) and pollution from industrial emissions, and found no significant differences between exposed and unexposed groups. This approach assumes a model for spatial autocorrelation of exposure data and uses Monte Carlo simulations to provide a distribution of exposures in each site and to determine personal variability of the exposure. The set of simulations produced have the same statistical and spatial properties as the original exposure data, which means they reproduce the spatial covariance and histogram, and they honor the observed exposure values. The use of simulations as input to further statistical analysis with multivariate regression models provides therefore a mechanism for quantifying the sensitivity of complex systems to spatial variability .
In our study we assess spatial uncertainty of individual exposures using this last approach. This method provides multiple realizations (simulations) of observed data, with reproduction of the observed histogram and spatial covariance while matching for conditioning data (observed values). Each simulation yields a unique value for each location and represents a measure of personal exposure, and the distribution of all values in each location, provides a measure of uncertainty at each location. In the end of the simulation process, we use all simulations as input for statistical analysis with multivariate logistic regression. We assess exposure parameter uncertainty using the empirical distribution of the exposure odds ratio parameters, where its mean and empirical confidence intervals are used as point and interval estimates of true odds ratio. The mean odds ratio represents the factor by which being exposed to air pollution compared to not being exposed, changes the odds of the outcome of interest (low birth weight, preterm birth).