**1. Introduction**

Adverse birth outcomes are important public health issues including preterm birth (PTB) and low birthweight (LBW). Over the past 20 years, the literature confirmed that, in developed countries, PTB remains a risk factor of adverse health outcomes including neonatal mortality and short- and

long-term morbidity [1–8]. PTB is also recognized as a risk factor for LBW, delayed motor and social skills, as well as learning disabilities [9].

Various contextual determinants, characterizing place where people live, have been reported to be associated with births outcomes, including socio-economic, demographic characteristics and environmental factors such as exposure to environmental contaminants. Several studies concluded that prenatal development is a window of high susceptibility to the adverse impact of environmental nuisances, in particular ambient air pollution [10–17] More specifically, studies revealed that maternal air pollution exposure such as particulate matter ≤10 and ≤2.5 μm in diameter (PM10 and PM2.5) and nitrogen dioxide (NO2) reduced birth weight and increased the odds of low birth weight and preterm birth, [11,12,18]. While findings for PTB remains inconsistent in the literature (depending, in particular, on the study design, exposure assessment, pregnancy periods and adjustment for confounders [12,18–21]), experimental studies support plausible biological mechanisms explaining, for instance, how air pollution exposure could reduce gestational age via placental inflammation linked to oxidative stress [22].

In addition, some studies suggested that the adverse health effect of maternal environmental exposure may be influenced by other contextual or individual characteristics (such as sex, socioeconomic position and psychological factors [12,23–25]). Many authors concluded that health risk related to environmental exposure may be different according to the socioeconomic level of populations [26–30]. For instance, Yi et al. in 2010 found a three-fold increase in the PTB risk for an increase in PM10 concentrations among babies born in low-income groups [27] and Carbajal-Arroyo et al. in 2011 revealed a significant increase in the risk of all-cause mortality only among infants with low and medium SES [31]. These social inequalities in air pollution exposure of pregnan<sup>t</sup> women and newborns are a public health issues. Additional studies are needed in Europe to improve our level of understanding concerning the underlying mechanisms explaining the existence of environmental inequality and to tackle this public health issues [32].

In epidemiological studies, quantifying the strength of the association between risk factors and health outcomes constitute pivotal information to document causality. However, these measures provide limited guidance for effective policies aimed at improving population health and reducing health inequalities. Spatial approaches may bring, in complement, useful information to help policymakers to elaborate on the choice of intervention.

To our knowledge, few epidemiological studies investigated the spatial distribution of PTB. For instance, in Philadelphia, using a descriptive geographic-spatial approach conducted at census tract level, Boch et al. investigated the geographical patterns of the prevalence of PTB and examined its relationships with race, poverty, crime, and natality [33]. Today, the use of geographical information system for mapping adverse birth outcomes and maternal addresses, while more and more popular, is not sufficient to highlight areas that exhibit a higher risk. Additional spatial analyses are required to explore the spatial pattern of adverse birth outcomes and the spatial implication of neighborhood characteristics that may explain it. In Worcester, Ogneva-Himmelberger et al. in 2015 studied the spatial distribution of preterm births by racial groups to identify spatial clusters using mother's residence address such as point location. Using two different spatial clustering methods, they analyzed associations between PTB and neighborhood characteristics including distance to major roads, exposure to hazardous air pollutants from stationary sources, access to vendors of healthy food, and access to green space and parks [34].

To our knowledge, no study has investigated the geographical distribution of PTB and its spatial association with the level of deprivation and the concentrations of air pollution measured at a small spatial scale. Indeed, to assess spatial patterns of health outcomes and its risk factors, fine spatial scale has been recommended in order to increase the homogeneity of specified variables within each area (such socioeconomic characteristics in this present study) and maximized differences between areas [35,36]; it is particularly important, when the study area, as in Paris city, presents a high population density per km<sup>2</sup> with contrasted socioeconomic profiles. In addition, investigations of the

spatial distribution of health events and risk factors conducted at the state or county level may not provide useful results for development of local policies or local decisions aiming to tackle social and environmental inequalities [37]. Small- spatial scale analyses appear to be an appropriated statistical unit to identify areas of high risk of PTB for targeted interventions and for reduction of inequalities in PTB.

In our study, spatial approaches appear to be the most appropriated to examine the spatial distribution of health risk and neighborhood characteristics. Using Kulldorf methods, we sought to perform clustering analysis to map the spatial distribution of the relative risks and to investigate the spatial implication of neighborhood characteristics. Unlike more traditional epidemiological studies which implement logistic regression to estimate impact of air pollution on the risk of preterm birth, with our approach we aim to answer to the same objective with an additional constraint related to spatial distribution of the health event. For example, Sabel et al. revealed that the relative risk (RR) of the pneumonia and influenza cluster adjusted for age, sex and deprivation is 1.92 whereas, the relative risk for the age, sex, deprivation and air pollution adjusted cluster is 1.99, respectively. However, these two clusters were not located in the same part of the territory and include different numbers of Census Area Unit (CAUs) while the risks estimated were similar [38]. More recently, Kihal et al. in France, found that the RR of end-stage renal disease (ESRD) incidence adjusted for sex, age and rural typology was 1.5, whereas the RR adjusted for age, sex and socioeconomic deprivation was 1.44. However, even estimated RR were similar; the two clusters were located at different part of the region: the first in the South-western part and the second in the extremely western Bretagne) and contained also different numbers of census blocks [39].

In this context, the localization of small geographical areas that exhibit a high PTB risk and their fine description may facilitate actions closely targeted towards areas most at risk: it is precisely the objective of this study. This work is not intended to reveal any causal pathway between neighborhood characteristics and PTB risk, an objective that requires other study designs [40,41].
