{"paper_id":"04cbacc5-cf93-459c-a218-b4ad6707ff3e","body_text":"1 \n \nTitle: A mechanistic modeling approach to assessing the sensitivity of outcomes of water, \nsanitation, and hygiene interventions to local contexts and intervention factors \nAuthors (tentative order): Andrew F. Brouwer1, Alicia N.M. Kraay2, Mondal H. Zahid1, Marisa \nC. Eisenberg1, Matthew C. Freeman3,†, Joseph N.S. Eisenberg PhD1,†  \n†: these authors contributed equally \nAffiliations \n1. Department of Epidemiology, University of Michigan, Michigan, USA \n2. Institute for Disease Modeling, a program within the Global Health Division of the Bill and \nMelinda Gates Foundation, Seattle, Washington, USA \n3. Rollins School of Public Health, Emory University, Atlanta, GA, USA \nCorresponding author: Andrew F Brouwer; Department of Epidemiology, University of \nMichigan, 1415 Washington Heights, Ann Arbor, MI 48109; brouweaf@umich.edu; 734-764-\n7373 \nDeclaration of conflicts of interest: ANMK’s contributions were directly funded by the Bill and \nMelinda Gates Foundation and not as part of the foundation grant to the authors. ANMK is an \nemployee of the Bill and Melinda Gates Foundation; however, this study does not necessarily \nrepresent the views of the Bill and Melinda Gates Foundation. \n  \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \nNOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice.\n\n2 \n \nAbstract \nBackground: Diarrheal disease is a leading cause of morbidity and mortality in young children. \nWater, sanitation, and hygiene (WASH) improvements have historically been responsible for \nmajor public health gains by reducing exposure to enteropathogens, but many individual \ninterventions have failed to consistently reduce diarrheal disease burden. Analytical tools that \ncan estimate the potential impacts of individual WASH improvements in specific contexts would \nsupport program managers and policymakers to set targets that would yield health gains. \nMethods: To understand the impact of WASH improvements on diarrhea, we developed a \ndisease transmission model to simulate an intervention trial with a single intervention. We \naccounted for contextual factors, including preexisting WASH conditions and baseline disease \nprevalence, as well as intervention WASH factors, including community coverage, compliance, \nefficacy, and the intervenable fraction of transmission. We illustrated the sensitivity of \nintervention effectiveness to the contextual and intervention factors in each of two scenarios in \nwhich a 50% reduction in disease was achieved through a different combination of factors \n(higher preexisting WASH conditions, compliance, and intervenable fraction vs higher \nintervention efficacy and community coverage).  \nResults: Achieving disease elimination depended on more than one factor, and factors that \ncould be used to achieve disease elimination in one scenario could be ineffective in the other \nscenario. Community coverage interacted strongly with both the contextual and intervention \nfactors. For example, the positive impact of increasing intervention community coverage \nincreased non-linearly with increasing intervention compliance. Additionally, counterfactually \nimproving the contextual preexisting WASH conditions could have a positive or negative effect \non the intervention effectiveness, depending on the values of other factors. \nConclusions: When developing interventions, it is important to account for both contextual \nconditions and the intervention parameters. Our mechanistic modeling approach can provide \nguidance for developing locally specific policy recommendations. \nKeywords: water, sanitation, and hygiene; randomized controlled trial; intervention; disease \ntransmission model; simulation  \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n3 \n \nIntroduction  \nDiarrheal disease is a leading cause of morbidity and mortality in young children, with an \nestimated 500,000 children under 5 years dying from diarrheal disease each year.1–3 Diarrheal \ndisease is primarily caused by enteropathogens spread by fecal–oral pathways through \ncontaminated environments, such as water, food, and fomites. Much of this burden is in low- \nand middle-income countries (LMICs) and among people living in poverty.\n4 Most \nenterpathogens are not good vaccine candidates, and those that are (e.g., rotavirus) can be \nhard to administer in the field (e.g., because of cold-chain requirements\n5) or suffer from \ndifferential effectiveness.6 Thus, preventive approaches for reducing enteric infections \ninterventions are essential.  \nHistorically, large-scale WASH improvements have been responsible for major public health \ngains by greatly reducing exposure to fecal pathogens, demonstrating the potential \neffectiveness of WASH in reducing the burden.7,8 Yet many trialed interventions, especially in \nthe most disadvantaged areas where enteric infections are endemic, have failed to consistently \nreduce the burden of diarrhea disease.\n9–15 A recent meta-analysis of WASH intervention \nrandomized controlled trials (RCTs) demonstrated that while WASH interventions can reduce \ndiarrhea in children in low-resource settings overall,16 the heterogeneity across the aggregated \ntrials is substantial, with many of the more recent, large-scale trials finding modest-to-null \nresults.\n9–15  \nDifficulties in achieving consistent reduction of diarrheal burden are caused by multiple factors. \nFirst, local contexts can vary widely in terms of preexisting WASH conditions (i.e., WASH \ninfrastructure in place prior to the intervention) and disease prevalence, among other factors. \nThese differences have made it difficult to apply the results from studies conducted in one \nlocation to other locations. Second, interventions are imperfect. For example, 1) they may not \nblock transmission along all transmission pathways (e.g., a water chlorination intervention will \nnot reduce disease from exposure to animal feces or contaminated food), 2) the intervention \ncoverage within the target population may not be sufficient to confer indirect protection, 3) the \nintervention may provide access to improved WASH but not ensure compliance, or 4) the direct \nefficacy of the provided interventions on reducing transmission to the users may be limited.\n17,18 \nOther factors are important as well, such as bias and inconsistency in reporting diarrhea and \ndifferences in the pathogens and taxa responsible for diarrheal disease in different locations.\n19 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n4 \n \nAnalytical tools that can dynamically estimate the potential impacts of individual WASH \nimprovements would support program managers and policymakers to set targets for \ninvestments to yield anticipated health gains. For example, with a given budget, should a \nprogram aim for greater coverage of an intervention or higher compliance, if the goal is health \nimpact? Mechanistic transmission models can be enhanced to help implementors design \noptimal intervention strategies by accounting for location-specific contextual factors. One \nimportant strength of mechanistic approaches is their ability to generalize from available \ncontext-specific epidemiological findings to other contexts and counterfactual scenarios, and \nthere is a need for tools that can generalize WASH trial results to other contexts.  \nOur objective was to develop a model to dynamically simulate diarrheal disease outcomes \nunder various contextual and WASH intervention factors to understand which had the greatest \nimpact on resulting disease burden. We previously developed a mechanistic model to simulate \nWASH trials and applied it to the WASH Benefits Bangladesh trial.\n20 Here, we aim to 1) \ndemonstrate and estimate interactions between each of the contextual and intervention WASH \nfactors and their impact on intervention efficacy and 2) increase the accessibility of the modeling \nframework for trialists and policymakers. This work will build our understanding of WASH \ninterventions and improve the design of future trials. \nMethods \nWASH factors. In this analysis, we explore how effectiveness of a single intervention depends \non six contextual or intervention WASH factors. \n• Preexisting WASH conditions. We account for the fraction of the population that already \nhas water, sanitation, and hygiene infrastructure comparable to that provided by the \nintervention. \n• Disease transmission potential. We summarize disease transmission potential using the \nbasic reproduction number \n/g1844 /g2868 . Note that because the baseline disease prevalence is \ndetermined by /g1844 /g2868  (given the values of other the other factors), we will not independently \nvary the baseline disease prevalence in this analysis. \n• Intervention compliance. We account for the fraction of participants assigned to an \nintervention that are actually using it. Compliance includes both fidelity (whether the \nintervention was delivered) and adherence (whether participants used the intervention).  \n• Intervenable fraction of transmission. Diarrheal disease pathogens are transmitted along \nmultiple pathways, often summarized by an “F-diagram”: fluids, food, flies, fields, fauna, \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n5 \n \netc. Any individual intervention typically targets one or a few of these pathways, but not \nall of them, and each pathway is responsible for a different fraction of the total disease \ntransmission potential. We account for how much transmission the intervention could \nprevent if it were perfectly efficacious and fully adopted. For trials that combine multiple \ninterventions, the intervenable fraction can be thought of as the fraction of transmission \nthat a combination of interventions could block. \n• Intervention efficacy. Interventions do not perfectly prevent transmission along the \npathways that they impact. We account for how much transmission (or shedding into the \nenvironment) the intervention prevents.   \n• Community coverage. In many trials, not everyone in the community is provided the \ninterventions. We account for the fraction of the population that is enrolled in the trial. \nEach of these factors is specifically accounted for in our transmission model, described below. \nModel \nOur compartmental transmission model, denoted SISE-RCT, is a susceptible-infectious-\nsusceptible (SIS) model with transmission through environmental (E) compartments. To \napproximate the outcomes of a RCT, we solve for the model’s steady state in an endemic \nsetting.\n20 The SISE-RCT model accounts for the six mechanistic WASH factors outlined above \nthat underlie WASH RCT results. In the case of a single intervention, the population is \npartitioned into individuals with regular exposure (those not enrolled or included in the \nintervention and those not compliant), and those with exposure or shedding attenuated by the \nintervention (those compliant with the intervention or an equivalent preexisting WASH \ncondition). Susceptible and infectious individuals with regular exposure are designated \n/g1845 /g2879  and \n/g1835 /g2879 , and those with exposure or shedding attenuated by the intervention are designated /g1845 /g2878  and \n/g1835 /g2878 . The intervention and control arms are simulated separately, and both the regular and \nattenuated exposure populations are modeled in both simulations, accounting for the fraction of \npopulation not enrolled in the study (\n/g2033/g4667 , the fraction of the population with preexisting WASH \nconditions (/g2025 /g2868 /g4667 , and intervention compliance (/g2025/g4667 . Individuals with regular exposure are either in \nthe study but not compliant to the intervention (/g2033 /g4666 1/g3398/g2025 /g4667 ) or are not in the study and do not have \npreexisting WASH conditions (/g4666 1/g3398/g2033 /g4667/g4666 1/g3398/g2025 /g2868 /g4667 ). Individuals with attenuated exposure are either \nin the study and compliant to the intervention (/g2033/g2025 ) or are not in the study but have preexisting \nWASH conditions (/g46661 /g3398 /g2033/g4667/g2025 /g2868 ). Hence, the population fractions of the attenuated and regular \nexposure populations are given by  \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n6 \n \n/g1840 /g2878 /g3404/g2033 /g2025/g3397 /g4666 1/g3398/g2033 /g4667 /g2025 /g2868 ,# /g4666 1 /g4667  \n/g1840 /g2879 /g3404/g2033 /g4666 1/g3398/g2025 /g4667 /g3397 /g4666 1/g3398/g2033 /g4667/g4666 1/g3398/g2025 /g2868 /g4667 ,  \nrespectively. \nOnce infected, individuals clear the infection at rate /g2011 . An environmental compartment is \ncharacterized by the shedding into the environment /g4666/g2009/g4667 , the decay of pathogens in the \nenvironment /g4666/g2022/g4667  , and the transmission of pathogens from the environment to susceptible \nindividuals /g4666/g2010/g4667.  For the single-intervention model, the environment is partitioned into the \nenvironmental pathway that is affected by the intervention /g1831 /g2869 , either in terms of shedding into or \ntransmission from the environment, and the environmental pathway that is not affected by the \nintervention /g1831 /g2870 , with the same subscripts on /g2009 , /g2022 , and /g2010 . For example, /g1831 /g2869  could be pathogens in \nwater for an intervention that targets water, with /g1831 /g2870  representing all other potential transmission \npathways (e.g., fomites, food, etc). The relative magnitude of shedding into /g1831 /g2869  and relative \ntransmission from /g1831 /g2869  for the attenuated compared to the exposed populations are given by /g2038 /g3080 /g3117 \nand /g2038 /g3081 /g3117, respectively. \nThe SISE-RCT parameters are given in Table 1, and a model diagram is given in Figure 1. The \nfull equations are given below (Eqs 2). The two transmission terms \n/g2010 /g2869 /g1831 /g2869  and /g2010 /g2870 /g1831 /g2870  denote \ntransmission from the environmental pathway attenuated by the intervention (/g1831 /g2869 /g4667  and from the \nenvironmental pathway not attenuated by the intervention (/g1831 /g2870 ), respectively. The transmission \nterm /g2010 /g2869 /g1831 /g2869  is attenuated by /g2038 /g3081 /g3117only for people in the attenuated exposure group (/g1845 /g2878 /g4667 , and \ncontamination of that environmental pathway is attenuated by /g2038 /g3080 /g3117 only for infectious people of \nthat same group (/g1835 /g2878 /g4667 . There is no attenuation of transmission to or shedding from the \nenvironmental pathway not affected by the intervention (/g1831 /g2870 ). Parameters /g2033,  /g2025 , and /g2025 /g2868  do not \nshow up in these equations but are accounted for in the constraints, as discussed below. For \nbrevity, we omit the \n/g3031/g3020\n/g3031/g3047  equations, each of which is given by \n/g3031/g3020\n/g3031/g3047 /g3404 /g3398\n/g3031/g3010\n/g3031/g3047   for the corresponding \nsubpopulation. \n/g1856/g1835 /g2878\n/g1856/g1872 /g3404/g4666 /g2038 /g3081 /g3117/g2010 /g2869 /g1831 /g2869 /g3397/g2010 /g2870 /g1831 /g2870 /g4667/g1845 /g2878 /g3398/g2011 /g1835 /g2878 , ##/g46662/g4667 , \n/g1856/g1835 /g2879\n/g1856/g1872 /g3404 /g4666 /g2010 /g2869 /g1831 /g2869 /g3397/g2010 /g2870 /g1831 /g2870 /g4667 /g1845 /g2879 /g3398/g2011 /g1835 /g2879 ,  \n/g1856/g1831 /g2869\n/g1856/g1872 /g3404/g2009 /g2869 /g4666/g2038 /g3080 /g3117/g1835 /g2878 /g3397/g1835 /g2879 /g4667/g3398/g2022 /g2869 /g1831 /g2869 , \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n7 \n \n/g1856/g1831 /g2870\n/g1856/g1872 /g3404/g2009 /g2870 /g4666 /g1835 /g2878 /g3397/g1835 /g2879 /g4667 /g3398/g2022 /g2870 /g1831 /g2870 . \nTo find the steady state values (denoted by *) for the human compartments in the intervention \narm, we set the above equations equal to 0 and simplify out the environmental compartments, \n0/g3404/g4666 /g2030 /g3081 /g1844 /g2868,/g2869 /g4666/g2030 /g3080 /g1835 /g2878\n/g1499 /g3397/g1835 /g2879\n/g1499 /g4667/g3397/g1844 /g2868,/g2870 /g4666/g1835 /g2878\n/g1499 /g3397/g1835 /g2879\n/g1499 /g4667/g4667/g1845 /g2878\n/g1499 /g3398/g1835 /g2878\n/g1499 ,# /g4666 3 /g4667  \n0/g3404/g4666 /g1844 /g2868,/g2869 /g4666/g2030 /g3080 /g1835 /g2878\n/g1499 /g3397/g1835 /g2879\n/g1499 /g4667/g3397/g1844 /g2868,/g2870 /g4666/g1835 /g2878\n/g1499 /g3397/g1835 /g2879\n/g1499 /g4667/g4667/g1845 /g2879\n/g1499 /g3398/g1835 /g2879\n/g1499 .  \nHere, /g1844 /g2868,/g3036 /g3404 /g2009 /g3036 /g2010 /g3036\n/g2022 /g3036 /g2011/g3415  is the pathway-specific reproduction number for transmission through \nenvironment /g1831 /g3036 . For this specific model, the overall basic reproduction number is /g1844 /g2868 /g3404/g1844 /g2868,/g2869 /g3397\n/g1844 /g2868,/g2870 , denoting the sum of the transmission potential through the pathway affected by the \nintervention (/g1844 /g2868,/g2869 ) and the pathway not affected by the intervention (/g1844 /g2868,/g2870 ). The intervenable \nfraction (based on the strength of the transmission pathway targeted by the specific \nintervention) is \n/g1844 /g2868,/g2869 //g1844 /g2868 . \nTo get the steady states solutions for our four state variables (/g1845 /g2878\n/g1499 , /g1835 /g2878\n/g1499 , /g1845 /g2879\n/g1499 , /g1835 /g2879\n/g1499 ), we solve the \nnonlinear system of equations (Eqs (3)) subject to the constraints /g1845 /g2878\n/g1499 /g3397/g1835 /g2878\n/g1499 /g3404/g1840 /g2878  and /g1845 /g2879\n/g1499 /g3397/g1835 /g2879\n/g1499 /g3404\n/g1840 /g2879 , where /g1840 /g2878  and /g1840 /g2879  are given in Eqs (1). We solved this system using the nleqslv package \nin R. This approach is more computationally efficient than the differential equation simulation \napproach we used previously.20 We solve for the steady state in the control arm with the same \nparameters as the intervention arm except that /g2025/g3404/g2025 /g2868 .  \nThe prevalence of disease in the population is denoted /g2024 /g1499 /g3404/g1835 /g2878\n/g1499 /g3397/g1835 /g2879\n/g1499 . The prevalence in the \nintervention arm /g2024 /g1499  is compared to the prevalence /g2024 /g3030\n/g1499  in the control arm. Then, intervention \neffectiveness (the RCT outcome) is defined as /g2013/g3404/g4666 /g2024 /g3030\n/g1499 /g3398/g2024 /g1499 /g4667//g2024 /g3030\n/g1499 , namely the fractional reduction \nin prevalence in the intervention arm relative to the control arm.  \nWe investigated the sensitivity of the intervention effectiveness to each WASH factor. We first \nsolved for the steady state solution for each of two scenarios with different sets of parameters, \nas listed in Table 1. Scenario 1 is characterized by a greater fraction of preexisting WASH \nconditions, compliance, and intervenable fraction, while Scenario 2 is characterized by a greater \nintervention efficacy and community coverage. The specific parameters in both scenarios were \nchosen to have 50% intervention effectiveness \n/g2013  but largely different values of the WASH \ncontextual and intervention factors. The transmission potential was the same in both scenarios \nbut the resulting baseline disease prevalence in Scenario 1 (6.4%) was much lower than that of \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n8 \n \nScenario 2 (20.9%) because of the differences in the other factors (particularly the preexisting \nconditions). The scenarios were chosen to demonstrate how sensitivity to the WASH factors \nmight be different in different, plausible scenarios and are not intended to be representative of \nany specific intervention trial.  \nWe varied each factor one at a time across the range of values given in Table 1, calculating the \nvalue needed to achieve disease elimination in that scenario. We also varied each pair of \nfactors together (e.g., varying coverage and compliance together) to investigate potential \ninteractions between factors. Only simulations with /g2025/g3408/g2025 /g2868  and /g2024 /g3030\n/g1499 /g34080  were included to avoid \nsimulation of situations where the intervention reduced use of WASH or in which an intervention \nwas applied to a system with no disease. This model has been made publicly available as a \nweb app at https://umich-biostatistics.shinyapps.io/sise_rct/\n and is included as supplementary \nmaterial. \nNote that the contextual factors, i.e., the preexisting WASH conditions and the transmission \npotential, are not modifiable in a real-world setting. In this analysis, changing these parameters \nrepresents the changing the location of the hypothetical trial and can help to reveal how the \nfinds of a trial might generalize to other locations. While the sensitivity of intervention \neffectiveness to these parameters may be less relevant for trial planning in a specific location, it \nis important for developing a better understanding of the heterogeneity between trials and may \nalso help to identify contexts where certain intervention approaches may be more effective than \nothers. \nResults \nThe intervention effectiveness outcome \n/g2013  in Scenario 1, given by the parameters in Table 1, \nwas 50%, with a steady-state prevalence of 6.4% in the control arm and 3.2% in the intervention \narm. Disease elimination would have been achieved in this hypothetical intervention if 1) we \nincreased the preexisting conditions so that 31% rather than 25% of the population already had \ncomparable WASH infrastructure; 2) we reduced the disease potential transmission potential \nfrom \n/g1844 /g2868 =1.25 to /g1844 /g2868 =1.20, which is equivalent to reducing the baseline disease prevalence from \n6.4% to 2.8%; 3) we increased the percentage of the total transmission that was blocked by the \nintervention from 75% to 88% (since there is an unknown, “true” value of the intervenable \nfraction, it may be more intuitive to think of this change as adding interventions until they target \npathways responsible for 88% of the transmission potential); 4) we increased the efficacy of the \nintervention at reducing transmission from 75% to 88%; or 5) we increased the community \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n9 \n \ncoverage from 11% to 22%. Disease could not be eliminated by increasing intervention \ncompliance from 75%, even to 100%.  \nThe intervention effectiveness outcome /g2013  in Scenario 2, given by the parameters in Table 1, \nwas also 50%, with a steady-state prevalence of 20.0% in the control arm and 10.0% in the \nintervention arm. Disease elimination would have been achieved in this hypothetical intervention \nif 1) we increased intervention compliance from 50% to 92%; 2) we reduced the disease \npotential transmission potential from /g1844 /g2868 =1.25 to /g1844 /g2868 =1.12, which is equivalent to reducing the \nbaseline disease prevalence from 20.0% to 10.7%; or 3) we increased the percentage of the \ntotal transmission that was blocked by the intervention from 35% to 65%. The disease could not \nbe eliminated with higher preexisting WASH conditions, higher efficacy, or higher community \ncoverage.  \nThe intervention effectiveness as a function of each pair of the six parameters is given in Figure \n2 for Scenario 1 and in Figure 3 for Scenario 2, with each baseline scenario indicated by the \nwhite points. For many pairs of parameters, there was little evidence of an interaction between \nthe factors (i.e., the contours of the heatmaps are approximately linear and parallel, except at \nextreme values). The primary exception to this pattern was coverage. In the inset in Figure 2, \nwe show, as an illustration, the interaction between coverage and compliance on the \nintervention effectiveness. When coverage is low and compliance is high (point A), it is easier to \nincrease intervention effectiveness by increasing coverage (gray arrow, moving along the x-\naxis), but when coverage is higher and compliance is low (point B), then it is easier to increase \nintervention effectiveness by increasing compliance (black arrow, moving along the y-axis). \n“Easier” here does not reflect cost or feasibility but only the result of a unit change for each \nindividual parameter. Cost-effectiveness is outside of the scope of this work but could be \nexplored in future analysis. Similarly, the coverage needed to achieve disease elimination \ndepended non-linearly on each of the other factors.  \nIncreasing the fraction of the population with preexisting WASH conditions improved \nintervention effectiveness in Scenario 1 (Figure 2) but decreased intervention effectiveness in \nScenario 2 (Figure 3). Increasing the fraction of the population with preexisting WASH \nconditions decreased prevalence in both the control and intervention arms, regardless of the \nspecific scenario, but the relative reduction depended on the other WASH factors. In Scenario 2, \nfor example, if the intervenable fraction were above 0.5 or if intervention compliance were above \n0.75, then increasing baseline WASH conditions would result in increased intervention \neffectiveness. \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n10 \n \nThe reader can explore the sensitivity of the model for other values of the WASH factors on the \nweb app available via https://umich-biostatistics.shinyapps.io/sise_rct/ or using the code \nincluded as supplementary material. \nDiscussion \nWe examined how the effectiveness of hypothetical single-intervention WASH RCTs depended \non both contextual factors (baseline disease prevalence and preexisting WASH conditions) and \nintervention factors (community coverage, compliance, efficacy, and the intervenable fraction of \ntransmission). Perhaps not surprisingly, the impact of changing one of some of these \nparameters was often highly dependent on the others. The effect of increasing community \ncoverage, in particular, had a strong interaction with the other factors. For example, increasing \nthe community coverage fraction could quickly lead to disease elimination if intervention \ncompliance and efficacy were high, but have little impact if either were low. Our work \ndemonstrates that it is important to understand the local, contextual conditions when developing \nrelative priorities for an intervention. Our mechanistic modeling approach could allow for a \ntailored approach to designing interventions and WASH programs based on local conditions. \nFor example, in some contexts with low baseline disease prevalence (like Scenario 1), \nsubstantial impacts might be achievable even with relatively low coverage.  In contrast, in some \ncontexts with high baseline disease prevalence (like Scenario 2), high coverage and compliance \nmay be necessary to achieve strong efficacy. \nOur findings offer a potential explanation for the high heterogeneity in the results of WASH \nintervention studies\n16 as well as the less-than-expected effectiveness of recent, large WASH \nintervention trials.9–15 An intervention that is effective in one location may be less effective in \nanother location because of differences in the preexisting WASH infrastructure (e.g., the new \nlocation has unimproved latrines rather than open defecation) or differences in the disease \npressure and baseline prevalence.  \nAdditionally, there may be substantial differences in the distribution of enteropathogens in \nlocations, as demonstrated by the MAL-ED and GEMS studies.19,21,22 These pathogens may use \ndifferent transmission pathways, and, as a result, the intervenable transmission fraction for the \nintervention may be different in different locations.\n4 For example, norovirus is one of the hardest \npathogens to control, as it can exploit multiple transmission pathways. Norovirus was \nparticularly important as a cause of diarrheal disease at the MAL-ED study site in Nepal but was \nnot detected at the site in India.\n19 Thus, an intervention blocking only one pathway might be less \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n11 \n \nlikely to reduce overall disease prevalence at the Nepal site, compared with India site. \nMoreover, the intervenable fraction may vary temporally within a site, as the dominant diarrheal \npathogens may vary seasonally in their incidence. Continuing with the norovirus example, \nsingle-intervention effectiveness might also vary throughout the year and be less pronounced \nduring cooler and wetter seasons, when norovirus is typically more prevalent.23 \nThe strength of this analysis lies in the mechanistic framework that allows us to connect \ndiarrheal disease outcomes in a WASH intervention context to the specific, measurable WASH \nfactors that characterize the location and the intervention. Because we were interested in \nproviding a basic understanding of the drivers of successful interventions, we decided to use \nhypothetical WASH factor values that were plausible but not specific to an existing trial. We also \nnote that our models assume a steady state value for compliance; in practice, however, \nintervention compliance may decline over time.\n24 We plan to expand this sensitivity analysis to a \nfull, multiple-intervention model and apply it to analyze real trials. \nIn the wake of the less-effective-than-expected large WASH intervention trial, a consensus \ngroup of WASH researchers called for a “pause for reflection” to re-evaluation the existing body \nof evidence.17 A recent meta-analysis has suggested that WASH is effective at reducing \ndiarrheal disease, though the outcomes are highly heterogeneous.16 Our mechanistic modeling \nframework is another approach that is well-suited to re-evaluating existing evidence and \ngenerating hypotheses for causal explanations of the results of these trials. Ultimately, our work \nwill help to provide evidence for developing locally specific policy recommendations and \nprogrammatic targets and for designing the next-generation WASH interventions.\n18,25,26 \n \nContributors \nJNSE, MCE, MCF, and AFB conceived of the study. JNSE and MCF secured funding for the \nstudy. AFB, MCE, and JNSE developed the model. AFB wrote and implemented the software \ncode, completed formal analysis and visualization, and curated the data and code. AFB wrote \nthe original draft with input from JNSE, MCF, and ANMK. All authors reviewed and edited the \nmanuscript. All authors had full access to all study data. \nAcknowledgements \nThis work was funded by the Bill & Melinda Gates Foundation (grant INV-005081) and the \nNational Science Foundation (grant DMS-1853032). Study sponsors had no role in the study \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n12 \n \ndesign, the analysis or interpretation of the results, the writing of the report, or in the decision to \nsubmit the paper for publication.  \nDeclaration of conflicts of interest: ANMK’s contributions were directly funded by the Bill and \nMelinda Gates Foundation and not as part of the foundation grant to the authors. ANMK is an \nemployee of the Bill and Melinda Gates Foundation; however, this study does not necessarily \nrepresent the views of the Bill and Melinda Gates Foundation. \nData availability statement \nNo data are associated with this article. The code is included as supplemental material. The \nSISE-RCT web app with the single-intervention model is available at https://umich-\nbiostatistics.shinyapps.io/sise_rct/. \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n13 \n \nReferences 1 \n1.  Troeger C, Blacker B, Khalil IA, et al. Estimates of the global, regional, and national 2 \nmorbidity, mortality, and aetiologies of lower respiratory infections in 195 countries, 1990–3 \n2016: a systematic analysis for the Global Burden of Disease Study 2016. Lancet Infect 4 \nDis. 2018;18(11):1191-1210. doi:10.1016/S1473-3099(18)30310-4 5 \n2.  Wolf J, Johnston RB, Ambelu A, et al. 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Effectiveness of Rotavirus 18 \nVaccination: A Systematic Review of the First Decade of Global Postlicensure Data, 19 \n2006–2016. Clin Infect Dis. 2017;65(5):840-850. doi:10.1093/cid/cix369 20 \n7.  Contreras JD, Eisenberg JNS. Does Basic Sanitation Prevent Diarrhea? Contextualizing 21 \nRecent Intervention Trials through a Historical Lens. Int J Environ Res Public Health. 22 \n2019;17(1):230. doi:10.3390/ijerph17010230 23 \n8.  Harris B, Helgertz J. Urban sanitation and the decline of mortality. Hist Fam. 24 \n2019;24(2):207-226. doi:10.1080/1081602X.2019.1605923 25 \n9.  Clasen T, Boisson S, Routray P, et al. Effectiveness of a rural sanitation programme on 26 \ndiarrhoea, soil-transmitted helminth infection, and child malnutrition in Odisha, India: A 27 \ncluster-randomised trial. Lancet Glob Heal. 2014;2(11):e645-e653. doi:10.1016/S2214-28 \n109X(14)70307-9 29 \n10.  Patil SR, Arnold BF, Salvatore AL, et al. The effect of India’s total sanitation campaign on 30 \n . 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Effects of water quality, sanitation, handwashing, 37 \nand nutritional interventions on diarrhoea and child growth in rural Bangladesh: A cluster 38 \nrandomised controlled trial. Lancet Glob Heal. 2018;6(3):e302-e315. doi:10.1016/S2214-39 \n109X(17)30490-4 40 \n13.  Null C, Stewart CP, Pickering AJ, et al. Effects of water quality, sanitation, handwashing, 41 \nand nutritional interventions on diarrhoea and child growth in rural Kenya: a cluster-42 \nrandomised controlled trial. Lancet Glob Heal. 2018;6(3):e316-e329. doi:10.1016/S2214-43 \n109X(18)30005-6 44 \n14.  Rogawski McQuade ET, Platts-Mills JA, Gratz J, et al. Impact of Water Quality, 45 \nSanitation, Handwashing, and Nutritional Interventions on Enteric Infections in Rural 46 \nZimbabwe: The Sanitation Hygiene Infant Nutrition Efficacy (SHINE) Trial. J Infect Dis. 47 \n2020;221(8):1379-1386. doi:10.1093/infdis/jiz179 48 \n15.  Knee J, Sumner T, Adriano Z, et al. Effects of an urban sanitation intervention on 49 \nchildhood enteric infection and diarrhea in Maputo, Mozambique: A controlled before-50 \nand-after trial. Elife. 2021;10. doi:10.7554/eLife.62278 51 \n16.  Wolf J, Hubbard S, Brauer M, et al. Effectiveness of interventions to improve drinking 52 \nwater, sanitation, and handwashing with soap on risk of diarrhoeal disease in children in 53 \nlow-income and middle-income settings: a systematic review and meta-analysis. Lancet. 54 \n2022;400(10345):48-59. doi:10.1016/S0140-6736(22)00937-0 55 \n17.  Cumming O, Arnold BF, Ban R, et al. The implications of three major new trials for the 56 \neffect of water, sanitation and hygiene on childhood diarrhea and stunting: A consensus 57 \nstatement. BMC Med. 2019;17(1):1-9. doi:10.1186/s12916-019-1410-x 58 \n18.  Pickering AJ, Null C, Winch PJ, et al. The WASH Benefits and SHINE trials: interpretation 59 \nof WASH intervention effects on linear growth and diarrhoea. Lancet Glob Heal. 60 \n2019;7(8):e1139-e1146. doi:10.1016/S2214-109X(19)30268-2 61 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n15 \n \n19.  Platts-Mills JA, Babji S, Bodhidatta L, et al. Pathogen-specific burdens of community 62 \ndiarrhoea in developing countries: A multisite birth cohort study (MAL-ED). Lancet Glob 63 \nHeal. 2015;3(9):e564-e575. doi:10.1016/S2214-109X(15)00151-5 64 \n20.  Brouwer AF, Eisenberg MC, Bakker KM, et al. Leveraging infectious disease models to 65 \ninterpret randomized controlled trials: Controlling enteric pathogen transmission through 66 \nwater, sanitation, and hygiene interventions. Lau EH, ed. PLOS Comput Biol. 67 \n2022;18(12):e1010748. doi:10.1371/journal.pcbi.1010748 68 \n21.  Kotloff KL, Nataro JP, Blackwelder WC, et al. Burden and aetiology of diarrhoeal disease 69 \nin infants and young children in developing countries (the Global Enteric Multicenter 70 \nStudy, GEMS): A prospective, case-control study. Lancet. 2013;382(9888):209-222. 71 \ndoi:10.1016/S0140-6736(13)60844-2 72 \n22.  Liu J, Platts-Mills JA, Juma J, et al. Use of quantitative molecular diagnostic methods to 73 \nidentify causes of diarrhoea in children: a reanalysis of the GEMS case-control study. 74 \nLancet. 2016;388(10051):1291-1301. doi:10.1016/S0140-6736(16)31529-X 75 \n23.  Ahmed SM, Lopman BA, Levy K. A Systematic Review and Meta-Analysis of the Global 76 \nSeasonality of Norovirus. Vespignani A, ed. PLoS One. 2013;8(10):e75922. 77 \ndoi:10.1371/journal.pone.0075922 78 \n24.  Humphrey JH. Reducing the user burden in WASH interventions for low-income 79 \ncountries. Lancet Glob Heal. 2019;7(9):e1158-e1159. doi:10.1016/S2214-80 \n109X(19)30340-7 81 \n25.  Levy K, Eisenberg JNS. Moving towards transformational WASH. Lancet Glob Heal. 82 \n2019;7(11):e1492. doi:10.1016/S2214-109X(19)30396-1 83 \n26.  Amebelu A, Ban R, Bhagwan J, et al. The Lancet Commission on water, sanitation and 84 \nhygiene, and health. Lancet. 2021;398(10310):1469-1470. doi:10.1016/S0140-85 \n6736(21)02005-5 86 \n  87 \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n16 \n \nTables \nTable 1: Parameters of the SISE-RCT model in two scenarios. The SISE-RCT model is a compartmental susceptible-infectious-susceptible \n(SIS) model with transmission through environmental (E) compartments and simulated to steady state to approximate an RCT. The intervention \neffectiveness in both scenarios in 50%, but the WASH parameters and baseline disease prevalence differ across scenarios. \n   Scenario 1 Scenario 2 \nParameter Definition Sensitivity \nrange \nBaseline \nvalue \nDisease \nelimination \nvalue \nBaseline \nvalue \nDisease \nelimination \nvalue \n/g2025 /g2868  Preexisting WASH conditions (fraction of \nindividuals in the community with \nintervention-level WASH infrastructure) \n0–1 0.25 0.31 0 — \n/g2025  Compliance (fraction of individuals in \nintervention arm using intervention) \n0–1 0.75 — 0.50 0.92 \n/g1844 /g2868 /g3404/g1844 /g2868,/g2869 /g3397/g1844 /g2868,/g2870  Transmission potential (basic \nreproduction number) \n1–2 1.25 1.20 1.25 1.12 \n/g2024 /g3030/g1499  Baseline disease prevalence † 6.4% 2.8% 20.0% 10.7% \n/g1844 /g2868,/g2869 //g4666/g1844 /g2868,/g2869 /g3397/g1844 /g2868,/g2870 /g4667  Intervenable fraction (fraction of \ntransmission that the intervention could \ntheoretically prevent \n0–1 0.75 0.88 0.35 0.65 \n1/g3398/g2030 /g2961  Intervention efficacy for reducing \nshedding  \n— 0 — 0 — \n1/g3398/g2030 /g2962  Intervention efficacy for reducing \ntransmission \n0–1 0.75 0.98 0.83 — \n/g2033  Community coverage fraction (fraction of \ncommunity included in the intervention \ntrial) \n0–1 0.11 0.22 0.75 — \n†: Baseline disease prevalence is a function of the transmission potential given the values of the other factors and was not varied independently of /g1844 /g2868 . \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n17 \n \nFigure captions \nFigure 1: Single-intervention SISE-RCT model diagram with an attenuated exposure population and a regular exposure population \ninteracting through shared environments. The SISE-RCT model is a compartmental susceptible-infectious-susceptible (SIS) model with \ntransmission through environmental (E) compartments and simulated to steady state to approximate an RCT. The black lines denote infection and \nrecovery, the blue lines denote shedding from infectious individuals into environmental compartments, the grey lines denote pick-up of pathogens \nfrom the environment by susceptible individuals, and the orange lines denote environmental pathogen decay. /g1845 /g2878 and /g1835 /g2878 denote susceptible and \ninfectious fraction of the attenuate exposure population, and /g1845 /g2879 and /g1835 /g2879 denote susceptible and infectious fraction of the regular exposure \npopulation. \nFigure 2: Intervention effectiveness as a function of WASH intervention factors in Scenario 1. The SISE-RCT model is a compartmental \nsusceptible-infectious-susceptible (SIS) model with transmission through environmental (E) compartments and simulated to steady state to \napproximate an RCT. A single-intervention implementation of the model was simulated at the Scenario 1 baseline values given in Table 1 \n(indicated by the white points), and the heatmaps denote how intervention effectiveness depends on each pair of WASH factors. The six WASH \nfactors are preexisting WASH conditions (fraction of individuals not enrolled in the intervention arm that are using preexisting infrastructure \ncomparable to the intervention), compliance (fraction of individuals enrolled in the intervention arm that are using the intervention), disease \ntransmission potential (summarize by the basic reproduction number /g1844 /g2868), intervenable fraction of transmission (how much of the transmission \ncould be prevented in a perfect intervention), intervention efficacy (fraction reduction in transmission or shedding when using the intervention), and \nthe community coverage fraction (fraction of the population enrolled in the trial). The inset enlarges the compliance vs coverage plot and overlays \ncontour lines to show the interaction between the two factors on intervention effectiveness. When coverage is low and compliance is high, it is \neasier to increase intervention effectiveness by increasing coverage, but when coverage is higher and compliance is low, then it is easier to \nincrease intervention effectiveness by increasing compliance. WASH = water, sanitation, & hygiene. \nFigure 3: Intervention effectiveness as a function of WASH intervention factors in Scenario 2. Analogously to Figure 2, a single-intervention \nimplementation of the model was simulated at the Scenario 2 baseline values given in Table 1 (and indicated by the white points), and the \nheatmaps denote how intervention effectiveness depends on each pair of WASH factors. \n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\nAttenuated exposure population\nRegular exposure population\nEnvironmental\npathways\nPathogen \nshedding\nPathogen\ndecay\nPathogen\npick-up\nRecovery\nTransmission𝑆𝑆+ 𝐼𝐼+\n𝑆𝑆− 𝐼𝐼−\n𝐸𝐸1 𝐸𝐸2\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n−50 −25 0 25 50\nChange in\nintervention\neffectiveness\n(percentage points)        \n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nEfficacy\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nIntervenable fraction\n 0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\nR0\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCompliance\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n1.00 1.25 1.50 1.75 2.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCoverage fraction\nBaseline conditions\n 0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nEfficacy\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nIntervenable fraction\n0.00\n0.25\n0.50\n0.75\n1.00\n1.00 1.25 1.50 1.75 2.00\nR0\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCompliance\nA\nB0.4\n0.6\n0.8\n1.0\n0.00 0.25 0.50 0.75 1.00\nCoverage\nCompliance\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint \n\n−50 −25 0 25 50\nChange in\nintervention\neffectiveness\n(percentage points)        \n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nEfficacy\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nIntervenable fraction\n 0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\nR0\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\n1.00\n1.25\n1.50\n1.75\n2.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCompliance\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\n0.00\n0.25\n0.50\n0.75\n1.00\n1.00 1.25 1.50 1.75 2.00\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCoverage fraction\nBaseline conditions\n 0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nEfficacy\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nIntervenable fraction\n0.00\n0.25\n0.50\n0.75\n1.00\n1.00 1.25 1.50 1.75 2.00\nR0\n0.00\n0.25\n0.50\n0.75\n1.00\n0.00 0.25 0.50 0.75 1.00\nCompliance\n . CC-BY 4.0 International licenseIt is made available under a \n is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)\nThe copyright holder for this preprint this version posted March 12, 2024. ; https://doi.org/10.1101/2024.03.09.24304020doi: medRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}