Statistical analysis
REGRESSION
This analysis included deliveries reported in the 24-month and 36-month surveys only, because for many deliveries reported in the 12-month survey, some period of the pregnancy likely occurred in the preintervention period. We compared the characteristics of participants included in the analysis by trial arms. We reported the proportion of each outcome, by trial arms and years. Using the CHW application data, we also examined four or more and eight or more ANC contacts for pregnancies between February 2018 and February 2020, to align with the period of the survey data used.With individual deliveries as the unit, we performed intention-to-treat (ITT) analysis using multilevel logistic regression adjusting for the year of the trial. We used a random intercept to account for clustering of participants within a village cluster and quantified appropriate standard errors. Because the log-binomial models to generate risk ratio (RR) did not converge, we estimated OR from the logistic regression, which was converted to RR using the method proposed by Zhang and Yu.We examined heterogeneity of the intervention effects by strata of three prespecified factors: (A) distance to the nearest primary healthcare facility (5 km or less vs more than 5 km); (B) cluster population at baseline (less than 700 people vs 700 or more) and (C) household wealth (quintiles). Heterogeneity was measured using an interaction (product) term between intervention assignment and each of these prespecified factors.In addition to the ITT analysis, we conducted a per-protocol analysis, using the inverse probability weights adjustment method, proposed by Hernán and Robins.We also compared outcomes reported in the 24-month and 36-month surveys with that of the baseline. As in the ITT analysis, to allow adequate time for the intervention to have an effect we excluded deliveries reported in the 12-month survey.Finally, we performed sensitivity analyses by further adjusting the main models with additional covariates where some differences were observed by trial arms. In a second sensitivity analysis, we included deliveries reported in the 12-month survey to the main analytical cohort, to examine potential selection bias due to their exclusion. Separately, we compared the key characteristics of the participants who were excluded (reported delivery in the 12-month survey) with those who were included (reported delivery in the 24-month and 36-month surveys). We also observed that some control households reported having occasional CHW home visit(s) in non-adherence to the protocol. Thus, we conducted a third sensitivity analysis by excluding the control participants who reported CHW home visits in the month preceding the surveys. A post-hoc power calculation accounting for the design effect due to clustering is presented in 
