Table 3 Power for the three main outcomes for different combinations of effect sizes and assuming an ICC of 0.02, a CAC of 0.8, and a type I error rate of 0.05. Power for non-linear models calculated using a normal approximation. pp percentage point
Outcome | Assumed model | Assumed baseline | Effect size | Obs. per cluster period | Power | |
Primary outcomes | ||||||
 Water and food safety and hygiene behaviour | Binomial-logistic | 50% |  + 5 pp | 27 mother–child pairs 4 opportunities per pair | 69% | |
 + 10 pp |  > 99% | |||||
 + 20 pp |  > 99% | |||||
 Food and water contamination | Poisson | 10 cfu/g |  − 1 | 10 samples per cluster |  > 99% | |
 − 2 |  > 99% | |||||
 Diarrhoea | Binomial-logistic | 13% |  − 2 pp | 27 mother–child pairs | 33% | |
 − 3 pp | 64% | |||||
 − 5 pp | 97% | |||||
 − 7 pp |  > 99% | |||||
Outcome | Assumed model | Assumed baseline | Main effect | Interaction effect | Obs. per cluster period | Power |
Subgroup analyses | ||||||
 Water and food safety and hygiene behaviour | Binomial-logistic | 50% | 0 pp |  + 5 pp | 27 mother–child pairs 4 opportunities per pair | 67% |
0 pp |  + 10 pp |  > 99% | ||||
 + 5 pp |  + 5 pp | 69% | ||||
 + 5 pp |  + 10 pp |  > 99% | ||||
 Food and water contamination | Poisson | 10 cfu/g | 0 |  − 1 | 10 samples per cluster | 29% |
0 |  − 2 | 84% | ||||
 − 2 |  − 1 | 34% | ||||
 − 2 |  − 2 | 91% | ||||
 Diarrhoea | Binomial-logistic | 13% | 0 pp |  − 2 pp | 27 mother–child pairs | 11% |
0 pp |  − 5 pp | 54% | ||||
 − 2 pp |  − 2 pp | 13% | ||||
 − 2 pp |  − 5 pp | 65% | ||||
 − 5 pp |  − 2 pp | 18% | ||||