Comparing the Power of Low vs High-Precision Methods for Measuring <i>E. coli</i> in Drinking Water in Low-Resource Settings

Methods to measure <i>Escherichia coli</i> concentrations in water vary in precision, complexity, and cost. Low-precision methods are more affordable, faster, and simpler to implement in low-resource settings but may reduce statistical power. We compared the statistical power of low- and high-precision methods using data from UNICEF's Multiple Indicator Cluster Surveys across 11 low-income regions, and from a birth cohort study in Ecuador. Both data sets included continuous <i>E. coli</i> concentrations from high-precision methods, which we categorized to emulate low-precision methods outcomes. Using logistic regression, we modeled associations between water quality and two dichotomous outcomes: water treatment (treated/untreated) and water storage (stored/not stored). We compared the sample size needed to reach 80% power for detecting statistically significant differences between these groups. Power was calculated using a bootstrap-based algorithm. Compared to continuous measures, categorizing <i>E. coli</i> concentrations required 10-90% larger sample sizes in treatment models and about 10% in storage models, except in regions with good water quality, where similar or lower sample sizes were sufficient. Our findings indicate that low-precision methods can reliably infer associations between water practices and water quality but often require larger sample sizes, highlighting a trade-off between cost and statistical power in resource-limited settings.