Distribution estimators and confidence intervals for stereological volumes

Assessing the precision of volume estimates from systematic samples is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. The approach taken in this paper is more ambitious than earlier methodologies, the goal of which was estimation of the variance of a volume estimator v̂, rather than estimation of the distribution of v̂. We shall show that bootstrap methods yield consistent estimators of the distribution of v̂, and also suggest a variety of confidence intervals for the true volume. Our new methodology covers cases where serial sections are exactly periodic, as well as instances where the physical slicing procedure introduces errors in the placement of the sampling points. Measurement errors within sections are also taken into account. The performance of the method is illustrated by a simulation study with synthetic data, and also applied to real datasets. Copyright 2011, Oxford University Press.