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Background Supply driven programs that are not closely connected to community demand and demand-driven programs that fail to ensure supply both risk worsening inequity. Understanding patterns of uptake of behaviors among the poorest under ideal experimental conditions, such as those of an efficacy trial, can help identify strategies that could be strengthened in routine programmatic conditions for more equitable uptake. WASH Benefits Bangladesh was a randomized controlled efficacy trial that provided free-of cost WASH hardware along with behavior change promotion. The current paper aimed to determine the impact of the removal of supply and demand constraints on the uptake of handwashing and sanitation behaviors across wealth and education levels. Methods The current analysis selected 4 indicators from the WASH Benefits trial— presence of water and soap in household handwashing stations, observed mother’s hand cleanliness, observed visible feces on latrine slab or floor and reported last child defecation in potty or toilet. A baseline assessment was conducted immediately after enrolment and endline assessment was conducted approximately 2 years later. We compared change in uptake of these indicators including wealth quintiles (Q) between intervention and control groups from baseline to endline. Results For hand cleanliness, the poorest mothers improved more [Q1 difference in difference, DID: 16% (7, 25%)] than the wealthiest mothers [Q5 DID: 7% (− 4, 17%)]. The poorest households had largest improvements for observed presence of water and soap in handwashing station [Q1 DID: 82% (75, 90%)] compared to the wealthiest households [Q5 DID: 39% (30, 50%)]. Similarly, poorer household demonstrated greater reductions in visible feces on latrine slab or floor [Q1DID, − 25% (− 35, − 15) Q2: − 34% (− 44, − 23%)] than the wealthiest household [Q5 DID: − 1% (− 11, 8%). For reported last child defecation in potty or toilet, the poorest mothers showed greater improvement [Q1–4 DID: 50–54% (44, 60%)] than the wealthier mothers [Q5 DID: 39% (31, 46%). Conclusion By simultaneously addressing supply and demand-constraints among the poorest, we observed substantial overall improvements in equity. Within scaled-up programs, a separate targeted strategy that relaxes constraints for the poorest can improve the equity of a program. Trial registration WASH Benefits Bangladesh: ClinicalTrials.gov, identifier: NCT01590095. Date of registration: April 30, 2012 ‘Retrospectively registered’.

Additional file 2: Supplementary Table 2. Technological supplies and key behavioral messages for intervention households in the WASH Benefits trial, Bangladesh

Additional file 1: Supplementary Table 1. Participants enrolment and retention

Background: Supply driven programs that are not closely connected to community demand and demand-driven programs that fail to ensure supply both risk worsening inequity. Understanding patterns of uptake of behaviors among the poorest under ideal experimental conditions, such as those of an efficacy trial, can help identify strategies that could be strengthened in routine programmatic conditions for more equitable uptake. WASH Benefits Bangladesh was a randomized controlled efficacy trial that provided free-of cost WASH hardware along with behavior change promotion. The current paper aimed to determine the impact of the removal of supply and demand constraints on the uptake of handwashing and sanitation behaviors across wealth and education levels.Methods: The current analysis selected 4 indicators from the WASH Benefits trial— presence of water and soap in household handwashing stations, observed mother’s hand cleanliness, observed visible feces on latrine slab or floor and reported last child defecation in potty or toilet. A baseline assessment was conducted immediately after enrolment and endline assessment was conducted approximately 2 years later. We compared change in uptake of these indicators including wealth quintiles (Q) between intervention and control groups from baseline to endline.Results: For hand cleanliness, the poorest mothers improved more (Q1 difference in difference, DID: 16%) than the wealthiest mothers (Q5 DID: 7%). The poorest households had largest improvements for observed presence of water and soap in handwashing station (Q1 DID: 82%) compared to the wealthiest households (Q5 DID: 39%). Similarly, poorer household demonstrated greater reductions in visible feces on latrine slab or floor (Q1DID, -25% Q2: -34%) than the wealthiest household (Q5 DID: -1%). For reported last child defecation in potty or toilet, the poorest mothers showed greater improvement (Q1-4 DID: 50-54%) than the wealthier mothers (Q5 DID: 39%). Conclusion: By simultaneously addressing supply and demand-constraints among the poorest, we observed substantial overall improvements in equity. Within scaled-up programs, a separate targeted strategy that relaxes constraints for the poorest can improve the equity of a program. Trial registration: WASH Benefits Bangladesh: ClinicalTrials.gov, identifier: NCT01590095. Date of registration: April 30, 2012 ‘Retrospectively registered’URL: https://clinicaltrials.gov/ct2/show/NCT01590095

Managed aquifer recharge (MAR), a hydro-geological intervention designed to dilute groundwater salinity, pumps pond water treated through a slow sand filter into the underground aquifers. We evaluated the microbiological safety of the resulting MAR water at sites from three districts in southwest coastal Bangladesh. We collected monthly paired pond-MAR water samples from July 2016-June 2017 and enumerated fecal coliforms and E. coli using the IDEXX quanti-tray technique, by the most probable number (MPN) method. We used WHO risk categories for microbiological quality; no risk (10 MPN per 100 mL water). We estimated the difference in mean log10 MPN in pond and MAR water using linear mixed effect models with random intercepts and cluster adjusted robust standard error. Almost all pond water samples (292/299, 98%) had moderate- to high-risk level (>10 MPN) fecal coliforms and E. coli (283/299, 95%). In contrast, 81% (242/300) of MAR water samples had no or low risk level fecal coliforms (0-10 MPN), of which 60% (179/300) had no fecal coliforms. We detected no or low risk level E. coli in 94% (283/300) of MAR water samples of these 80% (240/300) had no E. coli. MAR samples had lower mean log10 MPN fecal coliforms (-2.37; 95% CI: -2.56, -2.19) and E. coli (-2.26; 95% CI: - 2.43, -2.09) than pond water; microbial reductions remained consistent during the wet (May-October) and dry seasons. MAR-systems provided water with reduced fecal indicator bacteria compared to infiltered pond water.

In clinical research, prediction models for binary data are frequently developed in logistic regression framework to predict the risk of patient’s health status such as death and illness. However, when the outcome is rare, the maximum likelihood (ML) based standard logistic regression has been reported to show poor predictive performance by providing overfitted model. To overcome this, penalized maximum likelihood (PML) based logistic models are being widely used in risk prediction, however, their predictive performance in validation settings is not well-documented. Several validation approaches, namely split-sample, crossvalidation, bootstrap validation and its two variants 0.632 and 0.632+, have been widely used to validate the performance of a prediction model, however, it is also unclear which one of these approaches best for estimating accurate predictive performance of a rare-outcome model. This paper focused on evaluating predictive performance of PML based logistic model in such validation settings in comparison with ML based standard model and identifying the effective validation method. An extensive simulation study was performed by creating several scenarios to reflect modeling in dataset with few events. The results revealed that PML based model showed better performance by reducing overfitting to some extent and increasing discriminatory ability over ML based model, irrespective of validation methods under study. Of the validation methods, regular bootstrap and its variants 0.632 and 0.632+, particularly 0.632+, performed well by providing nearly accurate and stable estimate of the true predictive performance. We also illustrated the methods applying them to cardiac data set with few events.

Generalized estimating equation (GEE) is a popular approach for analyzing correlated binary data. However, the problems of separation in GEE are still unknown. The separation created by a covariate often occurs in small correlated binary data and even in large data with rare outcome and/or high intra-cluster correlation and a number of influential covariates. This paper investigated the consequences of separation in GEE and addressed them by introducing a penalized GEE, termed as PGEE. The PGEE is obtained by adding Firth-type penalty term, which was originally proposed for generalized linear model score equation, to standard GEE and shown to achieve convergence and provide finite estimate of the regression coefficient in the presence of separation, which are not often possible in GEE. Further, a small-sample bias correction to the sandwich covariance estimator of the PGEE estimator is suggested. Simulations also showed that the GEE failed to achieve convergence and/or provided infinitely large estimate of the regression coefficient in the presence of complete or quasi-complete separation, whereas the PGEE showed significant improvement by achieving convergence and providing finite estimate. Even in the presence of near-to-separation, the PGEE also showed superior properties over the GEE. Furthermore, the bias-corrected sandwich estimator for the PGEE estimator showed substantial improvement over the standard sandwich estimator by reducing bias in estimating type I error rate. An illustration using real data also supported the findings of simulation. The PGEE with bias-corrected sandwich covariance estimator is recommended to use for small-to-moderate size sample (N ≤ 50) and even can be used for large sample if there is any evidence of separation or near-to-separation.