Modeling Spatial Risk of Diarrheal Disease Associated with Household Proximity to Untreated Wastewater Used for Irrigation in the Mezquital Valley, Mexico

We conducted three rounds of surveys in the Mezquital Valley between November 2016 and November 2017 to longitudinally measure diarrheal prevalence in children. Participants were recruited and surveyed during in-home visits by trained interviewers. Households were sampled from four municipalities in the Mezquital Valley that are characterized by high levels of agricultural activity and wastewater reuse: Tula de Allende, Atitalaquía, Tetepango, and Tlahuelilpan. We sampled specific localities (towns) within those four municipalities that were known to have substantial agricultural activity based on our previous work in the area (Contreras et al. 2017). A large reservoir is located between one study locality and the wastewater canal system. Because participants in this locality do not face the same exposure to wastewater canals, they were excluded from this study before analysis. The remaining localities varied by degree of rurality, including peri-urban communities around the larger city of Tula as well as more rural communities, but each locality was located near wastewater canals and engaged in agricultural activity.

Eligible households were those with at least one child younger than 4 y old in which a parent or legal guardian was present. We used the criterion of 4 y to ensure that children could be followed for 1 y while still under age 5, which is the age of interest for the diarrheal disease outcome, but respondents were asked to report on all children under 5 y old in the household. At the baseline visit, a parent or legal guardian in participating households completed a survey with questions related to sociodemographics, agricultural activities, household characteristics, hygiene practices, caregiving practices, and diarrhea in children. Follow-up surveys included questions that may change over time, including select sociodemographics and diarrhea. Diarrheal disease was recorded for children under 5 y old and defined as passing three or more loose stools in a day within the past 7 d (WHO 2017). Survey data were recorded on cellphones using the Qualtrics offline application (version 2019; Qualtrics LLC).

At the baseline visit, interviewers logged the coordinates of each household with a handheld GPS recorder. For consistency, interviewers logged coordinates while standing as close to the front door of the household as possible. Geographic Information Systems (GIS) shapefiles for the Mezquital Valley wastewater canal system were provided by the Instituto Nacional de Estadística y Geografía (INEGI) of Mexico. These files describe the entire canal system around these study communities but exclude the smallest canals that bring water directly to fields. These excluded canals could be a missed source of exposure to households, but they are generally used only during irrigation periods and do not contain water at other times. The shortest distance between each household and any point along a wastewater canal was calculated in meters using ArcMaps (version 10.6) and serves as the primary exposure variable (ArcGIS). This exposure variable did not consider how many canals were near a household. If households were equally close to more than one canal segment, the exposure variable remained a single value for the closest point to any canal.

The outcome for our analysis, diarrheal disease within the previous 7 d, was recorded for each child under age 5 in participating households at each survey round. The primary exposure, household distance to a canal, was treated as continuous in meters. For descriptive analyses, the prevalence of the outcome and proportions or mean values of potential covariates were calculated across quintiles of household distance. In addition, we applied a smoothing function to the prevalence of diarrhea over household distance among all observations to visualize the unadjusted relationship between diarrheal prevalence and distance (Figure 2). This analysis indicated that the relationship between distance from a canal and diarrheal prevalence was nonlinear, with a sharp decline in prevalence over the first $250\mathrm{m}$. The rate of decay slowed significantly after this point.

The exponential decrease in crude diarrheal prevalence with increasing distance suggests that changes in exposure to wastewater occurring nearest to canals are more important than changes at farther distances. This implication matches theories of pathogen transport through aerosolization, one proposed spatial route of exposure. Aerosolized pathogens are dispersed through the wind and die off or settle over distances. Pathogen die-off and dispersal of aerosols are generally modeled with exponential functions (Courault et al. 2017; Brown and Mohr 2016). We assume that risks from other spatial routes of exposure, such as contact with contaminated animals, follow a similar decay. To capture this relationship, we modeled the natural log of distance between a household and a canal as the primary exposure variable. This transformation of distance treats relative increases in distance as more important for diarrhea than absolute increases. For example, the expected difference in risk between 10 and $100\mathrm{m}$ is greater than the expected difference between 100 and $190\mathrm{m}$.

We fit hierarchical logistic regression models via Markov chain Monte Carlo (MCMC) using RStan (version 2.19.2; Stan Development Team). We estimated the change in odds associated with a single meter increase in household distance from a canal and used that model coefficient to estimate the change in odds associated with a 10-fold and a 100-fold increase in distance. Random intercepts specific to each locality (town) were introduced to control for residual correlation in diarrheal prevalence within communities that is independent of the effects of distance to a canal. Due to the small number of households from certain communities, some spatially contiguous localities were combined into a single unit, resulting in nine locality groups. Random intercepts for each household also were included to account for repeated observations of households through multiple survey rounds.

Households that are close to each other, and thus share a similar distance exposure, also could share similar characteristics or exposures that are related to disease status. To account for that possibility, we included a spatial autocorrelation model that considered potential spatial clustering of diarrheal disease risk unrelated to canal exposure. Specifically, we estimated the household random intercepts using a Gaussian process (GP) prior, specific to each locality group, which considered covariance with nearby households. The GP was a parameterized with a Matérn covariance function that had a smoothness parameter fixed to 3/2, with the ratio of the length-scale (rate at which household correlation decays with distance) and signal amplitude learned from the data (Stein 1999; Banerjee et al. 2014). To ensure that the spatially structured random effect specifically captured clustering of risk between nearby households, the household GP was constrained using an informative prior for the length-scale parameter that favored a spatial correlation of 0.5 at a distance of $60\mathrm{m}$, declining to nearly zero at $400\mathrm{m}$ (Banerjee et al. 2014). Nevertheless, inferences were robust to changes to the prior selected for length-scale (Table S1). Final models were run with eight chains of 4,000 iterations each, and convergence was assessed using the Gelman-Rubin statistic (Gelman and Rubin 1992).

Model covariates were potential confounders of the relationship between household distance from a canal and diarrheal disease [socioeconomic status (SES) and access to sewerage], a predictor of diarrheal disease that is not related to distance but may increase precision (ages of children), and study factors to control for potential heterogeneity between surveys (survey round and season). We selected these covariates based on prior knowledge of their causal relationships with diarrheal disease and our understanding of their possible association with household proximity to wastewater canals in the Mezquital Valley. After assessing the relationship between each covariate and the primary outcome and exposure variables through bivariate descriptive analyses, we decided to include each variable as covariates in our final model.

SES factors included caregiver education level in total years completed, a binary indicator of occupation in agricultural or pastoral fieldwork, and an overall wealth indicator comprising seven household ownership questions (presence of a refrigerator, cellular telephone, vehicle, washing machine, microwave, computer, and flat-screen television). Households were asked about three additional assets. Those three assets were not included in our analysis because they were owned by almost all households in the study (electricity and any television) or by almost no households (Internet access in the household). The remaining seven ownership questions were used to construct a wealth index using principal component analysis (PCA) (Abdi and Williams 2010). The calculated principal components (PCs) did not account for much variation in the questions, resulting in a wealth index that was highly correlated with the sum of the seven binary ownership variables ($\text{correlation coefficient}=0.99$). Tertiles of the wealth index were calculated and used in adjusted models. Households that reported a connection to the public sewage network or to a private septic tank were considered to have access to sewerage. This operationalization assumes that private septic tanks protect household members from fecal exposure to a degree similar to that of the public system, although we did not confirm that the septic tanks in our study were safely constructed and emptied to protect health. The age of each child was calculated in months using the date of survey completion. After descriptive analyses indicated a nonlinear association between age and diarrhea, age was modeled using a categorical variable with eight age groups (0–9, 10–15, 16–21, 22–27, 28–33, 34–39, 40–45, and 45–59 months). The rainy season was defined as May through October based on statewide rainfall data from the National Meteorological Service of Mexico for the years from 2004 to 2017. However, each round took place fully in either the rainy or dry seasons, resulting in complete collinearity of the two variables. The baseline survey took place during the dry season, and the first and second follow-up surveys took place during the rainy season. We included study round in adjusted models, which accounts for any potential differences between the rainy and dry season but precludes estimation of an independent effect of season.

After estimating the adjusted association between household distance from a canal and diarrheal disease, we next estimated the proportion of risk at each household location that was attributable to canal proximity. The attributable risk proportion was defined as the proportion of risk that would be prevented if a household were minimally exposed to a wastewater canal (Suzuki et al. 2012). Minimal exposure was defined as the exposure faced at the distance of the farthest household within each locality group. We estimated the attributable risk proportion by comparing the modeled prevalence at the observed distance of a household with an estimated prevalence as though the household were at the minimal-exposure distance in its locality group, holding all else constant. The attributable risk proportion (ARP) was calculated for each household as:

The population ARP was calculated as the mean ARP across households. Population ARPs were calculated using all households in the study. To understand the risks among the most intensely exposed households, we also summarized the population attributable risk for the subset of households within $100\mathrm{m}$ of a canal using the same counterfactual distances. In addition, ARPs were calculated along one canal segment to visualize an example of the spatial decay of attributable risk. We divided a map of the canal segment into a grid of $10\text{-m}$ by $10\text{-m}$ cells and computed the attributable risk for each cell in the grid. The counterfactual maximum distance used for calculation was the maximum distance to the canal across all grid points, which was $415\mathrm{m}$.

A total of 568 households completed the baseline survey. Of those, 550 (97%) completed the first follow-up, and 546 (96%) completed the second follow-up survey. Four households were excluded due to missing covariates, resulting in 1,664 total interviews for analysis. Seventy-nine of these households had more than one child under age 5 during at least one survey round. A total of 646 children were observed at one or more survey rounds, resulting in a total of 1,856 child observations. Furthermore, 596 (92%) of those children were recorded in all three rounds, 18 (3%) were recorded at two rounds, and 32 (5%) were recorded at only one round, including children born between rounds. The average distance from a household to a wastewater canal was $327\mathrm{m}$ (range: $2\mathrm{m}–\mathrm{1,181}\mathrm{m}$). There were no clear trends across distance quintiles for any wealth indicator variable measured (Table 1). The quintile of households closest to a canal had the lowest proportion of households engaged in fieldwork (19%) and with access to sewerage (80%). The same quintile had the highest proportion of households that reported diarrheal disease at least once during the study (25%).

A total of 105 children were reported to have diarrhea during any survey round (6%). These included 46 cases (7% of 633 children measured in the baseline survey) at baseline, 37 (6% of 608 children) during the first follow-up, and 22 (4% of 615 children) during the second follow-up. Households that reported at least one case were less likely to include a field worker (19% vs. 32%) and were more likely to have a vehicle, a microwave, and a computer (Table 2). Children with diarrhea were younger than noncases (21.4 vs. 27.9 months old) and fewer children had diarrhea during the rainy season compared with during the dry season (56% vs. 44%; Table 3). The average distance from a canal was shorter for households that reported a case of diarrhea during any survey compared with those that never reported a case ($\text{mean}=278$ vs. $337\mathrm{m}$). SES indicators, household distance, and diarrheal prevalence varied among locality groups as expected, given general background differences among localities (Table S2).

After considering model covariates individually and in combination, the final model was adjusted for age of the child (using eight age groups: 0–9, 10–15, 16–21, 22–27, 28–33, 34–39, 40–45, and 45–59 months), survey round, caregiver education in total years completed, tertile of wealth based on PCA, and presence of a field worker. The adjusted posterior median odds ratio (OR) for a 10-fold increase in distance to a canal (e.g., $100\mathrm{m}$ vs. $10\mathrm{m}$) in the adjusted model was 0.55 [95% credible interval (CI): 0.33, 0.91; Table 4]. Based on the same estimate, the OR for a 100-fold increase in distance to a canal (e.g., $1000\mathrm{m}$ vs. $10\mathrm{m}$) was 0.30 (95% CI: 0.11, 0.82; Figure 3). The odds of diarrhea were lower among older children and those living in households with a fieldworker.

The proportion of cases of diarrheal disease in all households attributable to proximity to wastewater canals was 24% (95% CI: 5%, 38%). Of the 105 cases that occurred in our study, 25 (95% CI: 5, 40) were potentially attributable to canal exposure using this estimate. Among diarrheal cases occurring in households within $100\mathrm{m}$ of a canal, the population attributable risk proportion was 50% (95% CI: 11%, 71%), indicating that 16 (95% CI: 4, 23) of the 32 cases occurring in this group were potentially attributable to canal exposure. Figure 4 demonstrates the spatial decay of attributable risk as household distance increases along an example canal segment.