Sample size
The trial consisted of two co-primary outcomes, so we used a two sided α of 0.025 to take account of this. Both sample size calculations used a comparison of two proportions and assumed 90% power, an intra-cluster correlation coefficient of 0.03, a coefficient of variation of 0.65, and an estimated 750 children (registered 0-9 year olds) per practice. We estimated that 33 items would be dispensed and one hospital admission would occur per 100 children. To detect a 10% reduction, to 29 items, in dispensing data (superiority) and no more than an absolute 1% increase, to two, in hospital admissions (non-inferiority), we needed 155 practices per arm. We could conclude non-inferiority if the rate ratio, comparing the intervention arm with the control, had an upper confidence interval ≤1.01.