A mass-balance model to assess arsenic exposure from multiple wells in Bangladesh.

BACKGROUND: Water arsenic (As) sources beyond a rural household's primary well may be a significant source for certain individuals, including schoolchildren and men working elsewhere.
OBJECTIVE: To improve exposure assessment by estimating the fraction of drinking water that comes from wells other than the household's primary well in a densely populated area.
METHODS: We use well water and urinary As data collected in 2000-2001 within a 25 km2 area of Araihazar upazila, Bangladesh, for 11,197 participants in the Health Effects of Arsenic Longitudinal Study (HEALS). We estimate the fraction of water that participants drink from different wells by imposing a long-term mass-balance constraint for both As and water.
RESULTS: The mass-balance model suggest that, on average, HEALS participants obtain 60-75% of their drinking water from their primary household wells and 25-40% from other wells, in addition to water from food and cellular respiration. Because of this newly quantified contribution from other wells, As in drinking water rather than rice was identified as the largest source of As exposure at baseline for HEALS participants with a primary household well containing ≤50 µg/L As. SIGNIFICANCE: Dose-response relationships for As based on water As should take into account other wells. The mass-balance approach could be applied to study other toxicants.

Introduction

Arsenic (As) contaminates groundwater in many regions of the world, including much of South and Southeast Asia, posing a health threat where people rely on well water. In Bangladesh, more than 50 million people have been chronically exposed to concentrations above the World Health Organization (WHO) guideline of 10 μg/L [1, 2]. Chronic exposure to As can induce skin lesions and cancers of the skin, bladder, and lung, but the current leading cause of adult deaths related to As exposure is cardiovascular disease [3, 4, 5, 6, 7]. Exposure of pregnant women to As also increases the risk of stillbirth and infant mortality, and exposure of children to As in well water has been related to reduced intellectual function [8, 9, 10, 11, 12].

A number of studies have quantified the relationship of various health outcomes to urinary As concentration or drinking water As concentration [3, 7, 8, 9, 10, 12, 13, 14]. Drinking water As concentrations are usually assigned to participants based on the concentration measured at the primary source of water identified by that participant, in some cases considering additional water sources as well. Few such studies, however, display, or examine closely, the relationship between urinary As and drinking water As. When the data span several orders of magnitude, they are often displayed on a log-log plot or linear regressions are conducted using log-transformed data. One reason may be that these comparisons often show considerable scatter and seem only partly determined by As concentrations in the primary water source [15, 16, 17, 18, 19]. This scatter has been been attributed to variable As intake from food and/or to participants drinking water from multiple sources containing different levels of As. Previous studies have already pointed out that schoolchildren [20] and men who work away from home [21] drink a large portion of their water from wells other than their household well. For individuals with low levels of As in their primary water source, both food and water from other sources could contribute the majority of As exposure. While urinary As concentration may be a good metric of overall As exposure in relation to health effects, understanding the cause of the mismatch is important because regulations set standards in terms of concentrations of As in drinking water rather than As in urine. In some situations, a well-constrained measure of As intake from water may also provide a more reliable assessment of long-term exposure than the occasional urine sample that reflects recent intake only [22].

El-Masri et al. [23] recently applied a highly detailed physiologically-based pharmacokinetic (PBPK) model [24] to drinking water and urinary As data from two distinct populations, one in rural Bangladesh and the other in the US, both of which were exposed to a wide range of As levels in drinking water [25, 26]. El-Masri et al. [23] concluded from their analysis that dietary sources of As had to be included for the PBPK model predictions to match the observations, while recognizing that the improvement from making this adjustment was greater at the low end than at the high end of the range of exposures.

On the basis of a reanalysis of the urinary and water As data for the same Bangladesh cohort the PBPK model was applied to, we apply a much simpler model for both water and As intake and loss to show that the mismatch between the PBPK model and the urinary As data can instead be explained by participants drinking from more than one source of water. This explanation reduces the mismatch at both ends of the range in exposure. We estimate the contributions by sources of water and As other than an individual’s primary well by enforcing a mass-balance for both water and As in our analysis. The mass balance constraint equates the mass of water entering the body to the mass of water leaving the body and, similarly, the mass of As entering the body to the mass of As leaving the body. We also consider the possibility of loss of As to a permanent deep compartment, or “sink” in the body. The benefit of introducing mass balance as a constraint for interpreting the available data, along with other reasonable assumptions, is that we can formulate and solve equations for the average fraction of total water intake that participants consume from their primary household wells.

The mass-balance framework provides a useful tool for the general class of problems in which a contaminant is conservative in the human body and data are available on both the sources of the contaminant to, and the sinks from, the body. The approach is similar the integrated exposure uptake biokinetic (IEUBK) model that relates various sources of lead exposure to lead concentrations in blood using mass-balance [27]. Since mass must be conserved, the approach leads to estimates of total dose that rely on estimates of both input and output: the approach reduces uncertainty on either side of the balance by considering data from the other side. For this reason, the tool is particularly useful for discovering what may be missing from an analysis.

We use the mass balance approach to test two additional hypotheses about sources of water consumption in Araihazar. We hypothesize, based on self-reports of water consumption and gendered patterns of behavior, that women drink a higher proportion of water from primary household wells than men do. We test this hypothesis by applying the mass balance separately for men and women and comparing the resulting estimates of the fraction of water consumed from primary wells. We also hypothesize that people drink more water from wells near their primary household wells. We test this hypothesis by including a term in the mass balance model for water consumption from nearby wells.

Methods

Health Effects of Arsenic Longitudinal Study (HEALS)

We use well As data, well location data, urinary As data, and gender information collected for 11,197 participants in the Health Effects of Arsenic Longitudinal Study (HEALS). The collection of the HEALS data used in this paper is summarized here. Ahsan et al. [26] provide a more detailed description. Data were collected in a 25 km2 area in Araihazar, Bangladesh. In 2000–2002, the field team conducted a blanket survey of wells in the study area, recorded their GPS coordinates, and collected water samples to measure As concentrations in the laboratory.

HEALS participants at recruitment were aged 18 years or older, had lived in the study area for 5 or more years, and had used their primary well for at least 3 years. Towards the end of baseline recruitment, the residency requirement was relaxed to a minimum of 3 years. During baseline surveys from October 2000 to May 2002, each participant provided a urine sample and told interviewers which well they used as their primarydrinking water source. The participant’s gender was also recorded. Only about 3% of participants in HEALS had independently tested their wells for As prior to the beginning of the study [28]. Previous independent well testing is therefore unlikely to substantially impact our results.

We report new total As measurements in 814 rice samples, both uncooked (408) and cooked (406), obtained directly from a subset of 410 HEALS households between February and July 2016. Some of this rice was grown by the household on their own land and some was purchased by households from local markets, but the distinction was not recorded. The rice was digested in a microwave and analyzed for total As either directly by inductively-coupled plasma mass spectrometry or by summing all As species determined by high performance liquid chromatography-ICPMS [29]. Rice flour (SRM 1568b) from the National Institute of Standards and Technology with a certified total As concentration of 285±14 μg/kg was analyzed along with the samples. The concentrations obtained for this standard averaged 312±10 μg/kg and 325±18 μg/kg by ICPMS and HPLC-ICPMS, respectively.

Model of arsenic and water mass balance in the bodies of participants

Simplest version:

A linear regression model based on the volume balance of water and mass balance of As for study participants is used to estimate the fraction of water excreted via urine and the fraction of water consumed from the primary household well. The key features are first illustrated with the most tractable version of the model. The effect of considering additional processes and terms is evaluated subsequently.

The volumetric water balance for an individual is to a first approximation be described by where Q and Q represent water input from the individual’s primary household well and other wells, respectively, and where Q and Q represent water output through urination and evaporation (perspiration and respiration). Rewriting the equation in terms of the fractions of water gained or lost gives Even if some As may be lost through the skin by sweating, this loss is likely to be small compared to urination [30, 31]. The As mass balance for an individual can therefore be described by where [As] is the As concentration in the primary household well, [As] is the As concentration in other wells, [As] is the As concentration in urine, and M is the mass of As consumed per time in food (Figure 1). The expected value for urinary arsenic of an individual can be calculated as a function of the primary household well arsenic [As] for that individual i by assuming statistical independence with and among the other variables, taking expected values, and rearranging the equation (3) to solve for . For the other variables, a single average representative of the entire population is used. Substituting f with 1 – f and rearranging eq. (3) yields: According to this equation, urinary arsenic is a simple linear function of primary well arsenic [As] with a slope determined by the proportion of water intake from the primary household well and an intercept that reflects the contribution of As from food and the concentrations of As in other wells (Figure 1). The entire expression for is also inversely proportional to the fraction of water intake excreted as urine.

Figure 1.

Average urinary arsenic as a function of average well-water arsenic for well-water data binned into 15 equally-sized bins shown with examples of linear relationships of urinary arsenic as a function of primary well arsenic predicted by the distributed wells model by changing one parameter at a time based on eq. (4) with: (a) reference case without arsenic intake from food and all water intake excreted as urine, (b) with half the water intake excreted as urine, (c) with arsenic intake from food, and (d) half the water intake from non-primary wells.

In the simplest version of this model, referred to hereon as the “distributed wells” model, we assume that individuals get some of their water from their primary wells and for the rest of their water consumption they are equally likely to drink well water from any of the other wells in the study area. Under this scenario, [As] in the equations above is 95 μg/L, the average well water As concentration from a blanket survey of all wells in the study area conducted at the beginning of the study in 2000–2001.

Without attempting to fit the data at this point, a few examples illustrate the key features of the distributed wells model. Not surprisingly, urinary arsenic [As] equals primary well arsenic [As] if the contribution of As from food is negligible, all water is consumed from the primary well, and all water intake is excreted as urine (Figure 1A). If only a fraction of the water intake is excreted as urine and the rest is lost through evaporation, the concentration of As in urine increases in inverse proportion (compare Figure 1B to Figure 1A).

El Masri et al. [23] estimated the dietary intake of As of the HEALS cohort to be 64 μg/day, mostly from eating 410 g of rice containing 150 μg/kg As. The As content of rice samples obtained from a subset of 410 HEALS households ranged very widely (50–1200 μg/kg), with averages of 244±150 and 235±180 μg/kg (1-sigma) for uncooked and cooked rice, respectively, that are indistinguishable. The model is therefore also applied to the HEALS data using the higher corresponding local estimate of dietary intake of 96 μg/day based on rice only. We estimate drinking water consumption as 3±1 L/day, the average reported for HEALS [23, 26].

Applying these values to the model illustrates how the dietary contribution creates a positive intercept without changing the slope of the relationship between urinary and well-water As (compare Figure 1C to Figure 1A). More to the point of this paper, even the most basic version of the model shows that another way to obtain a positive intercept, and in this case without any contribution from food, is by drinking from other wells (compare Figure 1D to Figure 1A). In other words, a positive intercept in the relationship of urinary As as a function of water As does not necessarily indicate a contribution from food according to this model. In addition, drinking from other wells reduces the slope of the relationship between As in urine and the primary well.

Distributed well model with additional terms:

A more realistic version of the mass-balance model considers additional sources and sinks of water and As which, as it turns out, only modify the coefficients of the basic model. With the added terms shown in red, the volumetric water balance for an individual is now described by where the additional terms Q and Q correspond to water input from food and cellular respiration (a process that converts food molecules into energy for cells and produces water as a byproduct), respectively, and where Q represent water output through defecation. Rewriting the equation in terms of the fractions of water gained or lost gives Assuming again negligible As loss through evaporation, the As mass balance on an individual is now described by for the distributed well model, where M is the mass of As lost per time to defecation and M is the mass of As lost per time to a sink in the body (Figure 2). A term for As buildup in the body is included since it is possible for As to accumulate in bones and teeth [32]. The mass loss of As via defecation M and the loss of As to a sink in the body M are modeled to be a fixed proportion of the total mass of As input or loss (which on average must balance each other). This fixed proportion is an assumption, but it is plausible and widely used in other contexts. If m is the mass fraction of As lost to defecation and m is the mass fraction of As lost to a deep compartment in the body, this total loss T is expressed as Therefore Substituting T with this expression in M and M and f with 1 – f – f – f in equation mass-balance equation (7) yields: Rearranging the equation again to solve for yields Which simplifies to This is a similar expression for urinary arsenic as a function of primary well [As] as before with the exception of two sets of terms: a multiplier of both the slope and the intercept that reduces as due to loss to defecation and a deep compartment in the body, and an adjustment to the fraction of water from other wells that multiplies [As] to account for the additional contribution of water from food and cellular respiration to the total water intake. Other potential loss terms for As, for instance sweating, flaking skin, or loss of hair, could also plausibly be modeled to be proportional to the total As flux through the body and would in that case be represented by additional terms following m and m. For loss of As to the body, the formulation represents an upper bound, since it treats the body as an infinite sink for As.

Figure 2.

Average urinary arsenic as a function of average well-water arsenic for well-water data binned into 15 equally-sized bins shown with examples of linear relationships of urinary arsenic as a function of primary well arsenic predicted by the distributed wells model by changing one parameter at a time based on and based on eq. (9) with: (a) a third of water intake from food and cellular respiration and (b) a fifth of arsenic intake lost by defecation.

Two examples for the distributed wells models illustrate the sensitivity of the model to the additional terms. The fraction of water consumed via food f is estimated as 0.2 ± 0.1 from studies conducted in the United States [33], since no such estimates are available for Bangladesh. The fraction of water produced from cellular respiration f is estimated as 0.12 ± 0.06 [34]. One implication is that the total water intake needs to account for water contributions other than Q drinking well-water. In the case of HEALS, the average water consumption determined from detailed interviews of 3 L/day is therefore increased by 1/(1 – f – f), i.e. to 4.4 L/day to account for water intake from food and cellular respiration (Table 1). In the simple case of drinking from a single well and excreting all water intake as urine, which is unrealistic especially in a hot climate, the slope of the relationship of urinary As as a function of primary well As would be about 2/3 (compare Figure 2A to Figure 1A).

Table 1.

Estimated parameters used to solve the arsenic mass balance equations.

Variable	Description	Estimated Value	Reference
ff	Fraction of water consumed via food	0.2 ± 0.1	Popkin et al. 2011
fc	Fraction of water produced from cellular respiration	0.12 ± 0.06	Gomella and Haist 2007
fp	Fraction of water from primary well
fo	Fraction of water from other wells
fu	Fraction water lost to urination
fe	Fraction of water lost to evaporation
fd	Fraction of water lost to defecation
md	mass fraction of arsenic loss via defecation	0.06 ± 0.03	Pomroy et al. 1980
mb	Mass fraction of arsenic lost to deep compartments in the body	0
Mf	Mass of arsenic consumed via food	64 ± 4 μg/d96 ± 6 μg/d	El-Masri et al. 2018New HEALS rice data
Q	Total water intake	4.4 L/d	Dividing HEALS wellwater intake of 3 ± 1 L/d by [1 – (ff + fc)]
[As]o	Average As of all wells in the study area	95.2 ± 1.4 μg/L	van Geen et al. (2003)

The mass fraction of As loss via defecation m has been estimated at 6 ± 3% from experiments involving the ingestion of radioactive 74As by volunteers [22]. At the end of this 7-day experiment, over two-thirds of the ingested dose of 74As had been expelled in urine (62%) and feces (6%). The loss of ingested As to deep compartments in the body m is unlikely to be as high as the loss to feces because it would lead to the build-up of unreasonably high concentrations of As in some tissues such as the liver over time. Losing As to a sink other than urine, either by defecation or accumulation in a deep compartment, is functionally equivalent and has the effect of reducing the slope of the relationship of urinary As as a function of primary well As (compare Figure 2B to Figure 1B).

Self-reports of water consumed from primary household wells and other wells

In the HEALS study, participants were directly asked about the sources of their drinking water at home, at work, and elsewhere. For participants who reported that they bring water from home to drink at work, we assumed that this water was from their primary household well. Interviewers were instructed to ask questions about water consumed at work only of participants who work outside home and drink water from outside their home on a regular basis. If no sources of work water were reported for a participant, we assumed that they consumed no water at work. Most individuals surveyed (93% of women and 89% of men) provided a breakdown of their consumption into water from primary household wells and water from other wells.

Results

Water consumption from primary household wells and other wells

The distributed wells model describes participants as drinking from their primary wells and from wells throughout the study area. Conducting a simple linear regression on [As] as a function of [As] (Figure 3a,b) for all 11,197 HEALS participants, we obtain a slope S of 0.69 ± 0.01 and an intercept I of 68 ± 2, respectively (Table 2). From eq. (10), and Solving these two equations for two unknowns yields Setting for now the fraction of As intake lost to a deep compartment to zero, the two equations yield f = 0.67 ± 0.02 and f = 0.50 ± 0.01 using our local estimate of As intake of 96 μg/day from rice (Table 2). The listed errors for f and f reflect only the maximum compounded effect of the uncertainty (1-sigma) in the slope and intercept.

Figure 3.

The empirical relationship between urinary arsenic and primary well arsenic for all 11,197 HEALS participants. (a) Fitted (red, simple linear regression, [As] = (0.69 ± 0.01) [As] +68 ± 2) and observed (black) values of urinary arsenic as a function of primary household well arsenic (b) and average arsenic for data binned into 15 equally-sized bins. Eleven data points fall outside the axis limits used in panels (a) are not shown in the figure.

Table 2.

Regression parameters and model estimates from fitting the mass balance model to all 11,197 HEALS participants with different assumptions for the rate of consumption of arsenic via food.

		Distributed well model
		All	Male	Female
	n	11197	4843	6354
	R 2	0.26	0.24	0.27
	Radj2	0.26	0.24	0.27
	I	68±2	74±3	64±2
	S1	0.69±0.01	0.65±0.02	0.72±0.02
Mf = 96 μg/d	fu	0.67±0.11	0.68±0.12	0.67±0.11
	fp	0.50±0.08	0.47±0.08	0.52±0.08
	fo	0.18±0.08	0.21±0.08	0.16±0.08
Mf = 64 μg/d	fu	0.60±0.10	0.60±0.10	0.60±0.10
	fp	0.44±0.07	0.42±0.07	0.46±0.07
	fo	0.24±0.07	0.26±0.07	0.22±0.07

An additional compounded uncertainty for f of ± 0.06 and for f of ± 0.06 derives from the uncertainty in the fractions of water gained from food and from cellular respiration of f = 0.20 ± 0.10 and f = 0.12 ± 0.06. Varying the term m accounting for loss of As to defecation between 0.03 and 0.09 affects f by only ± 0.01 and does not affect f at all (equation 15). By the same token, the model indicates that a loss of As to a deep compartment expressed by the term m does not affect the estimate of the proportion of water obtained from the primary well either. Combining the additional errors, the uncertainties on f and f are therefore on the order of ± 0.11 and ± 0.08, respectively. From and f = 1 – f – f – f, the corresponding proportion of total water gain from other wells is 0.18 ± 0.08 (Table 2).

Assuming the lower As intake from food of El-Masri et al. [23] of 64 μg/day does not affect the slope or intercept of the regression but lowers f from 0.67 to 0.60 and f from 0.50 to 0.44. By the same token, a lower food As intake increases f from 0.18 to 0.24 in order to account for a larger portion of the intercept that cannot be explained by food As (Table 2).

Gender differences in consumption of water from primary wells

We hypothesized that women drink a higher proportion of water from the primary household well than men do. Applying the mass balance method separately to all 4,843 male and 6,354 female HEALS participants reduces the estimate of f for men to 0.47±0.08 and increases it to 0.52 ±0.08 for women for the distributed well model, using the local estimate of As intake from rice of 96 μg/day (Table 2). The error ranges overlap but the trend is consistent with a gender difference in the proportion of water consumed from primary versus other wells.

Model-derived values of f have to be divided by 0.68, the proportion of water obtained from drinking only, for comparison to direct reports of water consumption from primary wells in the HEALS survey. According to the distributed well model, men are therefore estimated to consume 69±12% of water from primary wells, in close agreement with the 70% reported in interviews. Women are estimated to consume 76±15% of water from primary wells, which is lower than the average of 91% reported in interviews but not inconsistent (Figure 4).

Figure 4.

Proportion of water consumed from wells other than the primary household well for men (blue) and women (red) based on self-reports.

Discussion

Variation in urinary arsenic

The regression of urinary As as a function of primary household well As for study participants indicates an underlying relationship. However, the relationship has a large amount of scatter, as can be observed visually (Figure 3) and from the regression coefficient indicating that about a quarter of the variation in urinary As is explained by the concentration of As in participants’ primary wells (Table 2). Comparable scatter in the relationship between urinary and drinking water As has been reported by other studies, including several conducted in Bangladesh [18, 19, 21]. Some of these studies attribute a higher proportion of the variance in urinary As to primary well As but this is at least in part because the data were log-transformed, adjusted for urine dilution based on urine density or creatinine, and other covariates were included in the regression. In the case of HEALS, for instance, the regression coefficient for urinary As as a function of well-water As increases from 0.26 (Table 2) using concentrations, as in the present study, to 0.36 for log-transformed concentrations and 0.51 for creatinine-normalized log-transformed concentrations [26].

The source of the variation in urinary As likely reflects individual-level differences in behavior in the specific setting of this study. As indicated by the greater variance accounted for after normalizing to creatinine in HEALS, a participant’s urinary As may vary because the amount of water they lose via sweat varies over time, affecting how concentrated or diluted As and other solutes are in their urine. We used arsenic concentrations directly rather than normalizing by creatinine because actual arsenic concentrations are required to perform a mass balance analysis. Whereas our analysis focuses on the average amount of As consumed from primary wells relative to other wells, different individuals within the study population consume different proportions of water from their primary well as, for instance, demonstrated by our exploration of gendered patterns of drinking water consumption (Table 2). Combined with the extremely large spatial variability of As concentrations in the study area, even for neighboring wells [35], such differences in individual behavior will impact urinary As concentrations. Additionally, urinary As concentrations were observed from a single spot urine sample from each participant. Previous work in a setting where the source of water was relatively constant showed little differences in repeated urinary As measurements over the course of a day, however [17].

While these individual-level differences contribute to the variation in urinary As, none of them are expected to correlate with an individual’s primary household well As concentration. Thus, while they add noise to the observed relationship between urinary As and primary well As, they do not affect the estimates of the regression slope and intercept.

Plausibility of water balance estimates

As a check on whether the estimates produced by the As mass balance models are reasonable, we compare the estimated water loss to urination to prior observations of human water balance. A 70 kg man taking in 2.5 L/day of water, including food water and cellular respiration, typically loses about 0.8–1.5 L water to urination, 0.25 L to stool, and 0.6–0.9 L to insensible water loss, which does not include sweat [34]. This corresponds to a range of 0.7–1.0 in the proportion of total water intake lost to urination in the absence of sweat. During exposure to high temperatures, water loss to sweat increases while loss of water to urine declines, and thus individuals may lose a lower fraction of their water to urination [36, 37]. This may explain why the proportion of total water intake excreted as urine f ranging from 0.6–0.7 inferred from the model is at the low end of the expected range (Table 2). Sweating also helps explain the considerably higher well-water consumption of 3 L/day (i.e. 4.4 L/day total intake) reported for the HEALS population on the basis of detailed interviews at baseline.

Robustness of model results

As another check, we constructed a slightly more complex model with an additional term in the mass-balance equation that allows for individuals to drink some water from their primary wells, some from wells distributed throughout the study area, and some from wells located within a distance of 20 m or more of their compound (Supplemental Material). We refer to this version as the neighboring wells model. It reduces the fractions of water consumed from the primary well f and from other wells f from 0.50 to 0.40 ± 0.06 and from 0.18 to 0.07 ± 0.07, respectively (Tables S1–S2, Figure S1). These reductions are compensated by a new sizeable contribution from neighboring wells f of 0.20 ± 0.03 but the fit to the data improves only marginally (=0.27 compared to the =0.26 for the distributed well model).

Both the distributed well and the neighboring well models suggest that women more consistently drink from their primary well than men, even if less so than indicated by self-reports obtained at baseline. The men in our study cohort were primarily manual laborers, while the women were primarily homemakers [26], consistent with the traditional division of labor throughout Bangladesh [38]. Under this division of labor, we expect men to drink from a wider array of wells beyond their primary household well, and our observations are consistent with this expectation. Our observations are also consistent with the prior findings of Sohel et al. [21], who observed higher agreement between urinary As and the reported main source of drinking water for women compared to men in Matlab, Bangladesh.

The model results are sensitive to the estimate of As intake from food, primarily rice, but not extremely so (Table 2). The As content of uncooked rice is unlikely to have changed between urine sampling in 2001–02 and rice collection in 2016, but the As content of cooked rice may have been higher before over half of HEALS households switched to lower As wells in response to well testing [39]. The HEALS rice data are closer to the average As content of rice in Bangladesh measured by 17 different studies summarized by Javed et al. [40] than the estimate used by El-Masri et al. [23]. For the remainder of the discussion, we use parameters obtained from the distributed wells model for 11,197 HEALS participants and assume the higher local estimate of As intake from rice of 96 μg/day (Table 2).

Throughout this analysis, intake and excretion of arsenic are assumed to be independent of arsenic metabolism. At the individual level, there is undoubtedly variability in arsenic excretion related to arsenic metabolism, which is influenced in turn by variations in the level of arsenic exposure, speciation of the ingested arsenic, diet, genetics, and other factors. We average all these effects in the study by assuming a long-term mass balance for arsenic at the population level instead of incorporating them explicitly in the model.

Implications of arsenic exposure model for sources of arsenic exposure

The mass balance model suggests that, on average, individuals with low concentrations of primary household well As receive most of their As exposure from wells other than their primary well. For example, an individual with 10 μg/L primary household well As is estimated to receive 14% of their As exposure from their primary well, 47% from other well water, and 39% from food (Figure 5). As primary household well As increases, primary household well water is predicted to make up an increasing fraction of an individual’s As exposure. Individuals with 50 μg/L primary household well As are estimated to receive 44% of their As exposure from their primary well, 31% from other wells, and 25% from food.

Figure 5.

Predicted contribution of primary household well arsenic (blue), other well arsenic (orange), and food arsenic (green) to total arsenic exposure as a function of primary household well arsenic concentration, based on the distributed wells model for a distance of 20 m (f = 0.50, f = 0.20, and f = 0.19; Table 2). The x-axis has been scaled by primary well arsenic concentration percentile, so that equal numbers of study participants are represented by equal distances along this axis. The dashed line indicates the primary household well arsenic concentration at which the primary well begins to contribute the majority of a study participant’s arsenic dose.

These estimated contributions to As exposure represent a population average and do not capture the variability between individuals in the study population. A model of As exposure at the individual rather than population level would require knowledge of the As content and amount consumed for each water source, as well as As intake from food, for each individual.

Implications of our arsenic exposure model for dose-response relationships

The mass-balance model for As indicates that the actual range of water As exposure in the two Bangladesh study population was probably narrower than originally reported. This is because participants with low primary household well As, on average, drink from other wells with higher As concentrations than their primary household wells and, similarly, participants with high primary household well As, on average, drink from other wells with lower As concentrations than their primary household wells.

By applying the distributed well model to the entire HEALS cohort, the recalculated well water As concentrations for the lowest exposure category averages 31 rather than 5 μg/L and for the highest exposure category averages 210 rather than 270 μg/L, respectively (Table 3). There is no obvious reason to believe a similar correction does not apply to the other all-cause mortality study conducted in Matlab [7], even if the variance of the urinary As data accounted for by well-water As did not increase markedly when neighboring wells were included [21]. In HEALS, the effect of neighboring wells and the intake As from food was integrated by referring instead to urinary As concentrations [3], but this relationship is more difficult to relate to regulatory standards for As concentrations in drinking water.

Table 3.

Comparison of well water As exposure estimated from primary household wells (Argos et al. 2010) to well water As exposure estimated when other wells are included, using parameters f = 0.50, f = 0.20, and f = 0.19 (Table 2) derived from the model applied to all 11,197 women and men, regardless of whether they were informed of their well arsenic status.

N	As (μg/L) in primary household well water	Average As (μg/L) in primary household well water	Average As (μg/L) in all water consumed
2835	0.1–10	5.45±0.02	31.2±0.4
2389	10.1–50	29.7±0.2	53.6±0.6
3303	50.1–150	95.3±0.5	97.2±0.7
2665	150.1–864	268.1±2.0	212.4±2

When interpreting findings for the population exposed to low-arsenic (e.g., ≤10 μg/L) water from the primary household well, it is important to consider that average water arsenic exposure from secondary well sources could be higher. This misclassification source in water arsenic exposure could result in an overestimation of the impact of exposure levels on health effects at low water arsenic levels and an underestimation at high water arsenic levels, when absolute measures of disease were used.

Two large studies conducted in Bangladesh have modeled all-cause mortality as a function of water As in the primary well at baseline [3] or a reconstructed history of As exposure from drinking water [3, 7]. Related studies have considered As exposure from secondary wells based on interviews and proximity, but these modified measures were not incorporated in the all-cause mortality models [21, 26]. Hazard ratios for all-cause mortality in the highest exposure categories (>150 μg/L) relative to the lowest (≤10 μg/L) in primary well As water range from 1.4 to 1.7 in the two studies [3, 7]. Due to the misclassification source in water arsenic exposure, the hazard ratios comparing higher levels to lower levels could have been underestimated, whereas the abolute risk of death due to arsenic at lower levels could have been overestimated.

In summary, HEALS participants on average consumed at baseline about 25–40% of their water from wells other than their primary well, mainly wells located within walking distance from their primary well. These other wells therefore comprise a significant fraction of total As exposure, particularly for participants whose primary household well As concentrations are low. For example, participants with primary household well As concentrations at the WHO drinking water standard of 10 μg/L are estimated to get 47% of their As exposure from other wells, and participants with primary household well As concentrations at the Bangladesh drinking water standard of 50 μg/L are estimated to get 31% of their As exposure from other wells, with the remainder coming from their primary household wells and food. These findings suggest that use of solely primary household well As concentrations results in under-estimating exposure at the low and over-estimating exposure at the high end. To our knowledge, the assumption of long-term mass-balance of water and As has not been applied previously. The approach could potentially increase our understanding of uptake and release by the human body when applied to other toxicants in drinking water.