Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
It is hard to do properly evaluate the sample required for the evaluation. What we used is the variable "was not at the health centre in the year when he / she felt sick and had no means of being treated at home", which is an indicator closely related to our primary outcome and was present in data Cordaid collected in a household survey in 2012-2014. Back then the figure was, in the general population: 70% (standard deviation: 0.42, n = 4162) and 82% for the indigents (standard deviation: 0.38, n = 372). We therefore calculated our sample looking at the probability of detecting indigents falling back to the same level as the population (alpha 0.05, using the ICC found, which is 0.027) - comparing groups with each other and thus neglecting the benefits of factorial design, we found:
• With 20 health centres, 19 indigents per health centre: power = 0.86
• With 20 health centres, 26 indigents per health centre: power = 0.92
Taking into account attrition (expected at around 25%) and a willingness to get our power level at around 0.90, we decided to target 27 indigents per health centre.