  This paper devises a fully Bayesian sample size determination method for
hierarchical model-based small area estimation with a decision risk approach. A
new loss function specified around a desired maximum posterior variance target
implements conventional official statistics criteria of estimator reliability
(coefficient of variation of up to 20 per cent). This approach comes with an
efficient binary search algorithm identifying the minimum effective sample size
needed to produce small area estimates under this threshold constraint.
Traditional survey sampling design tools can then be used to plan appropriate
data collection using the resulting effective sample size target. This approach
is illustrated in a case study on small area prevalence of life limiting health
problems for 6 age groups across 1,956 small areas in Northern England, using
the recently developed Integrated Nested Laplace Approximation method for
spatial generalised linear mixed hierarchical models.
