1st objective assumptions:

• Infant mortality rate in Harmonia is 25 per 1,000 live births.Therefore, in the absence of recent census data, we will assume that the number of children in the target age-group 12-23 months of age is 650,000 x (1000-25)/1000 = 633,750. Hence, the percentage of individuals 12-23 months of age in the population is 633,750/22,000,000 = 2.9%.
• We will assume that the average household (HH) size is 6.We can expect on average to find a child 12-23 months of age in every 100/(6 x 2.9) = 5.7 (6, rounded) HH. We will assume that a survey team can visit 75 HH per day during their field work given the modest amount of data to be collected at each HH.Hence, we expect to find 75/6 = 12.5 (12, rounded) eligible children in each cluster.Assuming an intracluster correlation coefficient of 1/3, we will adopt a conservative survey design effect value of 4.
• We will assume that the real vaccination coverage for the primary vaccine dose (penta3) to be measured averages 85%.We will aim to measure coverage with a confidence interval of 5%.
• We will assume a non-compliance rate (no-one home or refusal) of 15%.

Therefore, for the first output, to generate a national coverage point estimate with confidence intervals of ±5% for each of the 5 vaccine doses among children 12-23 months of age, a sample size of 1 x 265 x 4 = 1,060 eligible children will be required[1]. To yield this number of eligible children, teams will have to visit 1,060 x 6 x 1.18 = 7,505 HH. These HH will be divided into 1,060/12 = 88 clusters, with 6 x 1.18 x 12 = 85 HH per cluster (this roughly confirms the estimate of 75 HH per cluster we assumed above).

[1] Calculations made in accordance with sample size guidance in WHO. Vaccination coverage cluster surveys. Geneva; 2015 (draft), Annex B.