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. 2024 Feb 5;15:1069. doi: 10.1038/s41467-024-45152-y

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 5 — a Spatially heterogeneity in diarrhea prevalence in the control group in the WASH Benefits Bangladesh trial, visualized through universal outcome kriging with a Matérn spatial correlation structure. b Spatially smoothed average treatment effects (ATE) of matched-pair differences of diarrhea prevalence comparing nutrition and control clusters in the Bangladesh trial. c Posterior probability that the nutrition intervention reduced diarrhea in Bangladesh, derived from the geostatistical model used to smooth the ATE in panel b. d Spatial heterogeneity in Ascaris sp. infection prevalence in the Kenya trial. e Spatially smoothed ATE of matched-pair differences of Ascaris sp. prevalence comparing nutrition and control clusters in the WASH Benefits Kenya trial. f Posterior probability that the nutrition intervention reduced Ascaris sp. infection in Kenya, derived from the geostatistical model used to smooth the ATE in panel e. Smoothed surfaces at 1 km resolution were estimated using a geostatistical model with Matérn spatial covariance, trimmed by study subdistrict boundaries and a 10 km buffer around matched pair centroids. Insets of panels a, b, d and e show estimated parameters and Matérn correlation function with distance between matched pairs, illustrating no spatial correlation in the ATE for Ascaris sp. in Kenya. Points represent matched pair centroids and lines demark subdistricts in the study regions (zillas in Bangladesh, sub-counties in Kenya). In panels c and f, posterior probabilities were estimated from 1,000 simulation replicates at each location, drawn from the geostatistical model fits of the ATE (Methods) Created with notebook https://osf.io/j9r4k.