Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
The study is powered to the primary outcomes, which are: OFSP cultivation, frequency of OFSP consumption, and serum retinol to test for VAD status. For this analysis, we use the standard β=0.80 and α=0.05, indicating an 80% chance of correctly rejecting the null hypothesis of no change, with a .05 level of significance. Because the interventions are randomized to clusters (villages) rather than to individuals, we need to account for the design effect (DE = 1 + (m-1)ICC where m is the average number of subjects per cluster) under the assumption of between-subject homogeneity within clusters. This reduction in variability within clusters results in a loss of statistical power, and therefore requires an increase in sample size to compensate.
1) OFSP cultivation will be determined by a binary indicator indicating whether the household has planted OFSP in the most recent season. In order to detect a significant difference of 15% adoption between treatment arms (Cohen’s d = .3, a relatively small effect size), we will need to survey 176 households in each treatment arm, or 35 per cluster (village). For the design effect, we expect that agricultural patterns will be heterogeneous enough within villages to make ICC negligible. With 10% loss to follow up, we aim to survey 194 households per arm, or 39 households per village.
2) Frequency of consumption of orange sweet potato will be determined by a continuous variable indicating how many times OFSP was consumed during the most recent harvest season. This variable will be surveyed for both adults in the household and children under 5 in the household. In order to detect a significant difference of 1.5 days of consumption (a medium effect size of .42), we would need 90 households in each treatment arm (18 per village). Using an estimated ICC of 0.091 for vitamin A sources in diet within rural North Indian villages (Agarwal, Awasthi, & Walter, 2005), we have DE=2.547. With 10% loss to follow-up, we must recruit 253 households per arm, or 51 households per village.
3) Serum retinol will be measured in μmol/L, with measurement <.7 μmol/L indicating deficiency. A recent study of serum retinol in UP (Neufeld, 2017) found mean (SD) maternal serum retinol (n=1284) to be .73 μmol/L (.05) and for children 6-59 months (n=1238), .65 μmol/L (.05). Using the most conservative SD for serum retinol reported in the study (.07) and an ICC estimated from Agarwal et al. (2005), we estimate a required sample size of 100 mother/child pairs per treatment group, (20 per cluster) in order to detect a .05 μmol/L difference in serum retinol.
Based on these calculations, we will take the most conservative estimate to adequately power all primary outcomes. Therefore, our minimum sample size is 253 households per treatment arm. With 5 clusters in each treatment arm, we aim to recruit at least 51 households per cluster.