Table 3

Sample size and power calculation estimates for study aims

Aim	Exposure used for power calculation	Exposure prevalence	Outcome	Required sample size	Available sample size
1a	Household water access (as an example environmental exposure)	25%–50%*	Difference of 0.25† or more in class-level Chao1 species richness	1268–1800	1800
1b	Household water access (as an example environmental exposure)	5%–50%*	Excess risk of 12% or greater for any specific enteric infection‡	199–880	1080
2a	Any specific enteric infection	10%–50%‡	Excess risk of 8.2% of greater in symptomatic diarrhoea§	306–737	1080
2b	Number of enteric infections from 0 to 24 months	(1) 10%–25%¶ (2) 25%–50%¶	EED score** difference of (1) 0.7 or more; (2) 0.5 or more††	(1) 80–299 (2) 160–308	360
2c	Number of enteric infections from 0 to 24 months	10%–50%¶	Excess risk of 8.1% or greater in growth faltering‡‡ (eg, stunting)	306–737	1080
3a-b	Diarrheal status	50%§§	Difference of 0.40¶¶ or more in class-level Chao1 species richness	388	400^l
3a-b	(1) Enteric infection-specific prevalence of 25% or more‡ (2) Any enteric infection***	50%	(1) Difference of 0.80¶¶ or more in class-level Chao1 species richness (2) Difference of 0.45¶¶ or more in class-level Chao1 species richness	(1) 98 (2) 308	(1)~100††† (2)~308†††

*Prevalence of household piped water access is 47% across the 3 study sites.
†The mean differences in Chao1 species richness across the 3 study sites (most rural to most urban) is 1.1.
‡Prevalence of E.coli across the 3 study sites in the EcoZUR study was 24.5%.
§Based on symptomatic diarrhoea prevalence of 10% or more in the cohort—data from the “Ecologia, Desarrollo, Salud, y Sociedad” (EcoDeSS) study suggests diarrhoea prevalence of ~12%.41
¶"The Etiology, Risk Factors, and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project” (MAL-ED) prevalence of 29% of non-diarrheal stool samples containing 2 or more pathogens.79
**Based on the score developed by Kosek et al.49
††For comparison, George et al reported difference on the magnitude of 0.70–1.00 between children with and without specific environmental exposures.
‡‡Based on growth faltering prevalence of 10% or more in the cohort—previously characterised prevalence of stunting of 10%–14% in children<5 in “Ecologia, Desarrollo, Salud, y Sociedad” (EcoDeSS) study data.38
§§Case–control status selected based on diarrhoea status using banked samples.
¶¶For comparison, in the ”E. coli en Zonas Urbanas y Rurales” (EcoZUR) study data, differences between adults with vs without acute diarrhoea had Chao1 differences of approximately 0.5; ^l based on 1:1 case–control design (ie, 200 cases and 200 controls).
***"The Etiology, Risk Factors, and Interactions of Enteric Infections and Malnutrition and the Consequences for Child Health and Development Project” (MAL-ED) prevalence of ~77% of diarrheal stool samples containing one or more pathogens.79
†††Available sample size is dependent on specific pathogen prevalence in the 400 samples tested—we have based our estimate on (i) 24.5% prevalence of pathogenic E.coli=49 children infected, for a total sample size of 98 and (ii) 77% prevalence of any pathogen=154 children infected, for a total of 308.
‡‡‡
EED, environmental enteric dysfunction.