Optimal two-stage sampling for mean estimation in multilevel populations when cluster size is informative.

To estimate the mean of a quantitative variable in a hierarchical population, it is logistically convenient to sample in two stages (two-stage sampling), i.e. selecting first clusters, and then individuals from the sampled clusters.

Relative efficiency of unequal cluster sizes for variance component estimation in cluster randomized and multicentre trials.

Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance patients within clinics or pupils within schools. Although equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible. This paper addresses the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in cluster randomized trials and in multicentre trials with person randomization within centres, assuming a quantitative outcome.