Participant eligibility criteria

In both countries, the trials enrol pregnant women identified in community-based surveys who expect to deliver in the 6 months following enrolment based on date of last menstruation. The study will enrol all children born in study clusters in the 6 months following the baseline survey (some target children will be born after 6 months due to inaccuracies in gestational age using reported date of last menstruation). Our target sample size of pregnant women at enrolment is 5760 in Bangladesh and 8000 in Kenya. The Kenya cohort will be larger because we expect to find more variation in child length for age than in Bangladesh (sample size details below). Within study compounds, the study enrols all children <36 months at baseline to measure diarrhoea outcomes over the study period; the study measures diarrhoea outcomes in a wider age group because older children are still at high risk for diarrhoeal disease.20

In both countries, compounds consist of multiple households (typically 3–10 in Bangladesh and 1–4 in Kenya), usually comprising blood relatives, who share a common courtyard. Compounds are eligible to participate if (1) they have a pregnant woman and (2) the woman plans to stay in the village for the next 12 months. The study excludes households who do not own their home to help mitigate attrition during follow-up. The Kenya trial excludes villages that have chlorine dispensers at water sources installed by programmes separate from the present study. In Bangladesh, the study excludes households who report high iron in their drinking water most of the year because pilot studies showed it was difficult to maintain the appropriate chlorine residual for continued disinfection in high-iron water. In cases in which the respondent is unsure about iron content, field staff check the water's chlorine demand using Aquatabs and a digital Hach Pocket Colorimeter II; if residual chlorine is below 0.2 mg/L after 30 min staff exclude the household. Within a study compound, the studies enrol pregnant women and children from the following age groups

1. Children in utero at enrolment (target children): all children born to enrolled mothers within approximately 6 months of the baseline survey.

2. Children 18–27  months old at enrolment (specimen collection): older children living in the compound and aged 18–27 months at enrolment will be eligible for stool and blood specimen collection. This age window reflects the age window of the target children at the final study measurement and serves as a baseline measure for the study population.

3. Children aged <36 months at enrolment (diarrhoea): All children aged <36 months living in the compound are eligible for caregiver-reported diarrhoea measurement.

4. Additional children born into study compounds after 6 months: We will enrol children born into study compounds who are too young to meet our enrolment criteria (group 1, above), deliver interventions to them according to randomised assignment and measure anthropometry and diarrhoea at follow-up surveys. These additional enrolees will not be included in the primary analysis because very young children may not be exposed to intervention for sufficient amount of time to expect to see impact on our primary outcomes (particularly length for age). However, the additional young children will provide information (in exploratory analyses) about the effect of established interventions on very young infants.

Field staff discuss the prospect for participation in the study with adults in each compound, including the mother/caregiver of the target infants. After providing time for discussion among the compound residents, a member of the field team seeks formal informed consent from pregnant women.

Bangladesh setting and enrolment

The Bangladesh trial is located in Gazipur, Mymensingh and Tangail districts. These three districts are located in the floodplain of central Bangladesh where the majority of the rural population is engaged in agriculture. The majority of the population uses shallow tubewells for drinking water, which are known to be frequently contaminated with faecal indicator bacteria.84 Enrolment commenced in June 2012. The study has enrolled compounds in communities that meet the following criteria.

• Located in a rural area.

• Drinking water with low levels of iron (<1 mg/L on average) and arsenic (<50µg/L on average) as documented in the collaborative assessments by the Government of Bangladesh and the British Geological Survey. Water chemistry eligibility criteria were used because pilot studies indicated that when iron or arsenic levels were high the chlorine demand for household water treatment was unpredictable.

• The Government of Bangladesh, international non-government organisations working in Bangladesh and local government authorities report that no major water, sanitation or focused nutrition programmes are currently operating or planned in the area in the next 2 years.

• Not located in haor areas (areas completely submerged during the monsoon season).

Each study cluster includes a group of compounds with eight eligible pregnant women. The compounds within a cluster are located sufficiently closely together so that a single promoter can reach each of the participating compounds by walking. If the compounds were too dispersed for a promoter to reach all of them on foot, they will then not be enrolled in the study. More than one cluster could be enrolled in a single village but clusters within the same village need to be separated from each other by a minimum of 15 min walking distance.

Kenya setting and enrolment

The Kenya trial is located in rural areas of 10 districts in Bungoma, Kakamega and Vihiga counties in the western part of the country. The region is populated mainly by subsistence farmers. Unimproved latrine coverage is high (at least 85%) and our pilot study in the region estimated that among children <27 months old, 11% had diarrhoea in the preceding 2 days. Very few (<5%) households have piped water and the majority of households report obtaining drinking water from sources, such as protected springs, where chlorination has previously been shown to be effective.85 Enrolment commenced in November 2012. The study region contains over 2000 villages, from which study villages were selected to form clusters using the following criteria:

• Located in a rural area (defined as villages with <25% residents living in rental houses, <2 gas/petrol stations and <10 shops);

• Not enrolled in ongoing WASH or nutrition programmes;

• Majority (>80%) of households do not have access to piped water into the home;

• At least six eligible pregnant women in the cluster at baseline.

Overview of the intervention approach and assumptions

The WASH Benefits study has focused on identifying and testing water, sanitation, handwashing and nutritional interventions that have strong potential to reduce infection and malnutrition during the first years of life. WASH Benefits is designed to measure intervention effects under conditions of high uptake in our target populations since our central hypotheses have not been tested rigorously in randomised studies. The enabling technologies and behavioural intervention packages were developed in the target populations over a 2-year period before the start of the trials. Details of the behaviour change theoretical frameworks and methods used in each country will be published in separate, forthcoming articles. Local promoters who are residents of the study villages deliver the interventions at the cluster level; each promoter completes at least 5 days of training and also attends refresher courses periodically throughout the study period. Promoters visit and counsel study compounds weekly in the early phase of intervention, with visits declining in frequency over time; we anticipate visits as infrequent as one per month after 1 year of intervention.

The environmental interventions in this study focus on modifying the compound environment to reduce infant exposure to enteric pathogens. The interventions focus on compound-level modifications because we assume that the dominant transmission pathways for the infants in our study will be within the compound. Since we expect on average 8–10 household-compounds with eligible children per study cluster, we expect to intervene in a small fraction of each community. While point-of-use water quality, hygiene and nutrition interventions operate at a household level, some sanitation interventions may require wider coverage in a neighbourhood, community or other larger environment in order to effectively mitigate personal exposure. However, cost and logistical limitations prevented us from extending implementation beyond the compound. Furthermore, a pilot study suggested that the compound was a relevant unit of intervention for modifying infant exposure to environmental conditions.63

Control

It is possible that the simple act of regular visits by intervention promoters could lead to improvements in the primary outcomes through unknown channels that are independent of WASH or nutrition interventions. The WASH Benefits team discussed this possibility extensively in the year preceding the trials and the teams agreed to pursue slightly different strategies in the two countries. The Bangladesh team concluded that their intervention behaviour change model is so tightly integrated into the enabling technology components that the effect of a visit is inseparable from the WASH and nutrition interventions themselves; moreover, it is fairly common for mothers in the study area to be visited by community promoters associated with other programmes. The control arm in Bangladesh will be a ‘passive’ control, meaning there is no promotion or intervention activity during the study.

The Kenya team was more concerned about the possibility of the promotion visits leading to changes in behaviours not related to WASH or nutrition that could nonetheless affect the primary outcomes since promoter visits are atypical in the Kenyan study area. For this reason, the Kenya team decided to include promoters in their control arm and to add a simple activity across all arms of the study: monthly measurement of mid-upper arm circumference (MUAC) or measuring the pregnant woman's belly circumference prior to the birth. The key assumption for the Kenya design is that whatever non-WASH-related or nutrition-related behaviour changes occur in the intervention arms will also occur in the control arm. The Kenya control arm promoters do not promote any WASH, or nutrition messages, and strictly engage in measuring child MUAC and mother belly circumference. In all arms, children >6 months old with MUAC <115 mm are classified as severely malnourished and are referred to treatment (details mentioned below in Referral guidelines).

Water quality

The Bangladesh study delivers a 10 L, insulated water storage vessel and a free supply of chlorine tablets (Aquatabs brand, sodium dichloroisocyanurate) to enrolled households to improve the microbiological quality of their drinking water.86 The Kenya study installs chlorine dispensers within the cluster boundary at public water sources used by study participants. All community members will be able to use the dispensers. After filling their water collection container (typically a 20 L plastic jerry can) at the source, users can place the container under the dispenser and turn a knob to release 3 mL of 1.25% sodium hypochlorite, an amount designed to yield 2 mL/L of free chlorine residual after 30 min for 20 L of water.87 The Kenya study also includes community level promotion of dispenser use and all households in the study compound receive bottles of sodium hypochlorite (6 months’ supply) to facilitate householders’ water treatment during periods when they rely on rainwater harvesting (common during the rainy season) or if they use a water source in which a dispenser has not been installed. In both countries, the behaviour change strategies target the consistent provision of treated water to all children living in the household.

Sanitation

Both the Bangladesh and Kenya studies include three enabling technologies in the compound-level sanitation intervention with the goals of reducing children's exposure to faeces in the household environment and increasing latrine use: (1) a locally developed sani-scoop dedicated to the removal of child and animal faeces from the compound,88 (2) plastic child potties for children aged 6 months and older until they use the latrine and (3) a new or upgraded latrine for each household in the compound. In Bangladesh, latrines are upgraded to a dual pit latrine with a water seal and super structure. In Kenya, plastic latrine slabs that include a tightly fitting hole-cover are installed to improve existing latrines that have a mud or wood floor. Simple pit latrines (unlined pits with an earthen superstructure and the plastic slab) are constructed in the compounds of study participants who do not have access to a latrine. The behaviour change strategies in both countries target the use of the latrine for defaecation and the safe disposal of faeces by all households in the compound to prevent contact by young children.

Handwashing

Both country studies install two handwashing stations for enrolled households: one near the latrine and one near the cooking area. In Bangladesh, handwashing stations include a locally made bucket with a tap fitting (40 L near the latrine and 16 L near the cooking area), a stool, a bowl and a bottle to dispense soapy water. In Kenya, handwashing stations are constructed from locally available materials and include a dual tippy-tap design with independent pedals attached to two 5 L jerry cans of clean water and soapy water.89 In both countries the studies provide soap to families free of charge to replenish the handwashing stations. The behaviour change strategies of the intervention target handwashing with soapy water messaging at two critical times for caregivers: after defaecation/cleaning the child's anus and before food preparation.90 Promoters frame the concept of handwashing as a nurturing behaviour facilitated by the ease and convenience of a nearby handwashing station.91

Combined water+sanitation+handwashing

In both countries, the combined water+sanitation+handwashing (WSH) intervention integrates all intervention components from the water quality, sanitation and handwashing arms. Intervention promoters sequence the interventions so that they are not introduced at the same time. In Bangladesh, the interventions are delivered sequentially in the following order: sanitation, handwashing and water treatment, with a minimum of 21 days between each start date. In Kenya, all intervention technologies aside from latrine construction are provided at the same time but the behaviour change counselling is rolled out in the following sequence approximately spaced around 2 weeks apart: handwashing and basic water treatment, sanitation, in-depth water treatment. The provision of latrines can range from one to several weeks after the start of work in a cluster in Kenya. The behaviour change strategy emphasises the interconnected aspect of WASH and the need to practice all behaviours in order to benefit from them.

Nutrition

In both countries, the nutrition intervention strategy targets age-appropriate behaviours (pregnancy to 24 months) including use of lipid-based nutrient supplements (LNSs; aged 6–24 months). The behaviour change counselling is modelled after the Guiding Principles for Complementary Feeding of the Breastfed Child,80 the UNICEF Program Guide for Infant and Young Child Feeding Practices81 and the Alive and Thrive initiative.79 Target behaviours include (1) practice exclusive breastfeeding from birth to 6 months of age and introduce complementary foods at 6 months of age while continuing to breastfeed; (2) continue breast feeding as you did before receiving study-provided nutritional supplements; (3) provide your child micronutrient-rich foods, such as meat, fish, eggs, and vitamin A rich fruits and vegetables (adapted to locally available food examples); and (4) feed your child complementary foods at least 2–3 times per day when 6–8 months old and 3–4 times per day when 9–24 months old.

When target children are between 6 and 24 months old, intervention promoters will deliver monthly supplies of LNS. The LNS used in the study is a next generation version of Nutributter.92 Online supplementary appendix 1 includes the specific LNS formulation. LNS is administered daily using 10 g sachets that can be mixed into pre-prepared meals (eg, porridge) or consumed directly from the sachet; a child eats two sachets per day. LNS is intended to supplement—and not replace—breastfeeding and locally available complementary foods, by providing 118 kcal/day and including a broad suite of essential fatty acids and micronutrients at dosages appropriate for children in this age group.92 It has an 18-month shelf life, does not spoil at high temperatures and costs as little as US$0.08/day. Reported adherence has been 88% of days in controlled trials,14 in part due to the ease of incorporating it into existing feeding routines. Breastfeeding is highly prevalent in both populations based on pilot studies and so we have focused on supplements that would not replace this essential source of nutrition.93 ,94 In Kenya, the trial will provide LNS to older, age-eligible siblings (6–24 months) living in study households to prevent potential sharing of LNS with older siblings. The Bangladesh trial will deliver LNS only to target children because older, age-eligible siblings are rare in the study population.

Nutrition+combined WSH

In both countries, the nutrition+combined WSH arm will include the interventions delivered in the nutrition and combined WSH arms. The nutrition intervention is delivered in parallel with the WSH interventions according to the stage of pregnancy and age of the target child.

Intervention monitoring

Given the importance of good uptake (also called take-up or compliance) for the success of the trial, it is essential for the team to have early and frequent feedback on intervention uptake. If an intervention has poor uptake, the team then needs to consider modifying or redoubling implementation efforts in that arm. To preserve external validity, each country team will document any adaptive changes used to modify the intervention. Investigators will be blinded to outcomes from the trial, so any adaptation to intervention will be based solely on information about intervention implementation and uptake.

Both country teams have in place a detailed implementation monitoring system. One of the outputs from the monitoring system is a summary of whether the implementation has achieved a limited set of critical benchmarks (see online supplementary appendix 2); benchmarks are intended to flag serious problems in implementation. If any of the uptake measures falls below its critical benchmark, then a qualitative team will review the monitoring and process documentation in the low-performing area, visit the site of the low uptake, meet with intervention promoters, supervisors and study participants and troubleshoot the cause of the low uptake. Because the interventions have each been piloted and the pilots achieved these benchmarks of uptake, we expect that uptake below the benchmark will indicate a problem where the intervention was not implemented as planned, and the investigation will identify what additional training or other support is required to achieve high intervention uptake.

Additional principles that we will follow with respect to adapting the interventions include:

1. If we identify easily fixable problems in an intervention that we expect will improve uptake, then we will make the change uniformly in the study population.

2. If we identify a problem in an intervention arm and devise a solution, the solution must be implemented in all clusters assigned to that intervention to ensure that we do not differentially modify the intervention on a subsample of the population.

3. Since WASH Benefits is an efficacy trial, we will replace broken hardware in our study population.

4. We will maintain a detailed record of the timing and scope of any changes to the interventions (if any).

Primary outcomes

Primary outcomes include length-for-age Z-scores (LAZ) measured 24 months after intervention initiation in target children and diarrhoea prevalence in compound children <36 months old at enrolment. Child age will be determined using birthdates verified when possible using vaccination cards. Following standard protocols for anthropometric outcomes measurement,95 ,96 pairs of trained anthropometrists will measure recumbent length (accurate to 0.1 cm) and weight without clothing (accurate to 0.1 kg) in triplicate. The median of the three measurements will be used in the analysis.97 We will measure diarrhoea at baseline among children <36 months old and again 12 and 24 months after intervention initiation using a definition of ≥3 loose or watery stools in 24 h or ≥1 stool with blood based on caregiver-reported symptoms98; we will use a 7-day recall period unless we find differential recall errors by the randomised group, in which case we will use a 2-day recall period.99 ,100

Secondary outcomes

Secondary outcomes include two additional measures of linear growth, child development measures and measures of EE. We will calculate differences between groups in LAZ at the 12-month measurement and stunting prevalence (LAZ<–2) at the 24-month measurement. At the 24-month visit, we will measure child development in communication, gross motor and personal/social domains using the Extended Ages and Stages Questionnaire11 ,101; the instrument has been adapted to each study population, relies on caregiver's report and has been used in many low-income countries.102 We will compare groups for each domain independently and overall by summing scores across domains. In a subsample of up to 1500 children across four arms of each trial, we will measure EE biomarkers at 3, 12 and 24 months following intervention initiation (figure 2); assays planned include: urinary lactulose-to-mannitol ratio,103 faecal myeloperoxidase,104 faecal α-1-antitrypsin,105 faecal neopterin106 and plasma total IgG.37

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Figure 2

Summary of EE subsample in both countries, including cluster and target child enrolment in each arm. The EE subsample includes an equal number of clusters and target children from four arms of the study. C, control; EE, environmental enteropathy; H, improved handwashing; N, improved nutrition; S, improved sanitation; W, improved water quality; WSH, combined improvements in water quality, sanitation and handwashing; WSH+N, combined improvements in water quality, sanitation, handwashing and nutrition.

Additional outcomes

The study will collect stool specimens from seven target children per cluster at the 24-month visit and from an older child living in the compound (figure 3), and will test specimens for soil-transmitted helminths (Ascaris lumbricoides, Trichuris trichiura, hookworm) using the Kato-Katz method107 and protozoans (Giardia lamblia, Cryptosporidium parvum, Entamoeba histolytica) using PCR methods (Bangladesh) and commercial ELISA kits (Kenya). Online supplementary appendix 3 includes a full list of tertiary outcomes. In a subsample of households in which the study measures EE biomarkers, we will also measure markers of environmental faecal contamination to help trace the causal path between the interventions and outcomes. Environmental contamination measures will include enumeration of faecal indicator bacteria (Escherichia coli) in household-stored drinking water, on child toy balls and child hand rinses. In addition, the study will collect quantitative measures of fly density at the latrine and the food preparation area.

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Figure 3

Summary of enteric parasite measurement in both countries, including cluster and target child enrolment in each arm. At enrolment stool specimens will be collected from an older sibling aged 18–27 months if present and will be tested for protozoan infections. At the final measurement, specimens will be collected from the same older siblings plus seven target children per cluster in each country, and analysed for protozoan infections and soil-transmitted helminth infections. C, control; EE, environmental enteropathy; H, improved handwashing; N, improved nutrition; S, improved sanitation; W, improved water quality; WSH, combined improvements in water quality, sanitation and handwashing; WSH+N, combined improvements in water quality, sanitation, handwashing and nutrition.

Soy or nut allergies related to LNS

In the LNS arms, intervention promoters will recommend that caregivers stop using LNS and notify one of the study staff immediately should their child have any adverse reactions shortly after ingesting the supplement (such as vomiting, stomach pain, rash and breathing problems with wheezing). In the event of an adverse reaction, study staff will assess the child's condition and, if necessary, provide transport to the closest medical facility for treatment.

Acute malnutrition

In the anthropometry and enteropathy assessment survey, children who are found to be acutely malnourished based on WHO/UNICEF criteria (severely wasted [weight for length Z-score <−3] and/or bipedal oedema) will be referred to the appropriate existing treatment programmes in each country. In Kenya, where promoters measure MUAC each month for all target children, children >6 months with MUAC <115 mm will be considered severely malnourished and will be referred to treatment.

Intestinal parasites

All children who provide a stool specimen in the 24-month survey will be offered deworming medication, which is consistent with national standards in both countries.

General analysis approach

Each study team will develop its own analysis plan, but both teams will include in their analyses unadjusted means and SDs by randomised groups, along with unadjusted comparisons between groups for the primary hypotheses.114 ,115 We will also re-estimate our parameters of interest in adjusted analyses (details below). We will produce public replication files for our primary analyses in both countries. We will analyse participants according to their randomised assignment (intention to treat).

Parameters of interest

This section discusses parameters of interest for the primary analyses. Let Y be an outcome of interest and let T index the randomised group assignment, where T∈ (C, W, S, H, WSH, N, NWSH). There are seven arms: C control; W water; S sanitation; H handwashing; WSH; N nutrition supplement; and NWSH nutrition plus combined WSH. Let Z be a set of indicators for matched blocks used in the randomisation. Finally, let ψ denote parameters of interest. In each comparison below, we define ψ as a difference between various randomised groups. For dichotomous outcomes like diarrhoea, this implies a risk difference. We will additionally report risk ratios for dichotomous outcomes as recommended by CONSORT.114

H1: water, sanitation, handwashing, nutrition and their combination reduce child diarrhoea and improve linear growth.

The mean outcomes in each active intervention arm will be compared to the mean outcomes in the control arm (6 comparisons per outcome). The null hypothesis is that there is no difference between intervention and control. The same control group (double sized) will be used in every comparison. The parameters of interest are the difference in means between the intervention groups and the control group. For t∈ (W, S, H, WSH, N, NWSH): H2: when delivered in combination, water, sanitation and handwashing interventions reduce child diarrhoea more than when delivered individually

The combined arm (WSH) treatment effect for diarrhoea will be compared to individual WASH treatment effects to determine whether the combined effect is larger than the individual effects. The parameters of interest are the difference in means between the combined group and the individual intervention groups. For t∈ (W, S, H): Note that this parameter and associated test differs from a test for interaction (departure from additive effects). We expect this study to have limited power to detect interactions between interventions, but describe tests in online supplementary appendix 5.

H3: combined nutrition and WASH interventions reduce diarrhoea and improve linear growth more than each component alone

We will compare the combined nutrition + WASH arm (NWSH) treatment effects for growth to the nutrition arm (N) and the combined WASH arm (WSH). The null hypothesis is that the treatment effect in the combined arm is equal to the single arms, and the parameter of interest is the difference in means between groups. For t∈ (WSH, N): As with H2, this hypothesis is not a hypothesis of interaction or synergy. Rather, it is a test to determine whether one intervention is better than another (additive interaction would test whether the combined arm is greater than the sum of the independent intervention arms). If the interaction were of equal magnitude to the overall treatment effect, a roughly fourfold increase in the sample size would be required,116 which would be logistically infeasible given the already large size of the trial.

Testing and estimation

One strength of a randomised trial is that it allows investigators to draw inference non-parametrically, relying only on randomisation.117 One approach to test for statistical significance is a permutation test based on randomly permuting randomised assignments in the data (following the original randomisation strategy, ie, permuting T within strata Z) and re-estimating a test statistic.117–121 We plan to use a rank-based test statistic, which has been shown to have good power against alternatives,122 and estimate it on unweighted cluster means.118 ,119 We will use one-sided tests because we would only expect the interventions to be beneficial.123 Owing to the relatively small number of tests involved, we do not plan to adjust the p values for multiple testing.124

The permutation test is a test for statistical independence with good power against alternatives but does not estimate a specific parameter of interest (and thus will not provide SEs and CIs for our parameters). Since the trials depart from an individually randomised design, we will bootstrap the dataset, resampling clusters in matched blocks with replacement and re-estimate our parameters of interest. Resampling matched blocks preserves the correlation structure in the data and retains any efficiency gains from the matched randomisation. Since we will have a large number of units to resample, the asymptotic assumptions will be reasonable, the bootstrap distribution will be smooth and percentile-based CIs will be accurate for all parameters of interest. We will examine the bootstrap estimate of the sampling distribution to confirm these assumptions. The SDs of the bootstrap distributions will provide estimates of SE.

We will complement our unadjusted analyses with a second set of estimates that are conditional on baseline covariates to potentially increase the efficiency of our analysis and reduce bias from any chance imbalances in prognostic covariates despite randomisation.125 It is straightforward to extend permutation tests to include covariate adjustment while still taking advantage of the exact distribution theory provided by randomised inference.118 ,120 For example, let Y_ijk be the outcome of interest for individual i in village j and randomisation stratum k; let T_jk be the randomised intervention indicator and X_ijk be a vector of adjustment covariates. Models are fit of the form: E[Y_ijk|X_ijk]=m(X_ijk), where m(.) is some function of the covariates X. For example, m(X_ijk)=α_k+β × X_ijk+ɛ_ijk for a linear regression, but it could be a more sophisticated prediction function. The residuals are then calculated using predicted values of Y_ijk from the model: and the permutation test is conducted on the residuals. The test has nominal size for the null hypothesis even if the model m(.) is mis-specified and if the covariates are measured with error.118 ,120 There is no stochastic model for m(.), just a reduced algorithmic fit; the approach increases statistical efficiency because the residuals are less variable than the original outcomes, assuming the covariates are strongly associated with the outcome or heterogeneous within the strata.118

Following CONSORT guidelines,114 ,115 we prespecify a repeatable, objective approach that we will use to identify adjustment covariates. We plan to consider the following covariates in adjusted models:

• Administrative union (Bangladesh) or location (Kenya);

• Field staff team member who recorded the measurement;

• Time between intervention delivery and measurement;

• Month of measurement, to account for seasonal variation;

• Household food insecurity;

• Child age;

• Child sex;

• Mother's age;

• Mother's height;

• Mother's education level and literacy;

• Number of children <15 years in the household;

• Number of individuals living in the compound;

• Distance (in minutes) to the primary water source;

• Housing materials (floor, walls and roof) and household assets.

We will use a repeatable data-adaptive algorithm to control for the covariates flexibly and semiparametrically that will be chosen before the analysis.126 We will calculate adjusted p values using the permutation test described above based on predicted residuals from the algorithm. We will estimate SEs and CIs for our parameters of interest using the bootstrap described in the unadjusted analysis section. Online supplementary appendix 5 includes the details of additional, prespecified analyses, including tests of interactions between interventions, subgroup analyses and tests for between-cluster spillover effects.

Differential attrition (loss to follow-up): detection and effect bounds calculation

The study will track enrolled participants carefully to help minimise attrition. We will compare attrition rates across randomised arms and also the characteristics of those lost to follow-up versus those that remain to determine whether attrition is random. If we find systematic attrition that is not balanced across arms, then we will conduct sensitivity analyses using ‘worst case’ imputation bounds for our effect estimates (proposed by Horowitz and Manski,127 and summarised by Duflo et al,108) and we will also calculate bounds proposed by Lee.128 If overall levels of attrition approach 20%, we will attempt to locate individuals who left the study area to measure outcomes at the 2-year measurement and include them in our analyses; if attrition is high we will also consider the use of semiparametric weighting using baseline characteristics.129

Interim analyses and stopping rules

Additional analyses

WASH Benefits is a large study with many collaborators and the research will be able to answer scientific questions beyond those posed in this protocol. Indeed, the study team expects to conduct and publish analyses that extend beyond those specified in this protocol. For example, objective 5 of the study is to explore the association among multiple enteric infection measures collected in the study. Yet, many promising multiplex antigen assays for parasitic infection are still in development and so the study plans to archive samples for future analyses.