Sample size for estimating the quantiles of endothelial cell-area distribution

The estimation of corneal endothelium mean cell area (and, hence, mean cell density) is an important problem in clinical ophthalmology. Mitotic division of these cells is not known to occur, and cell deaths are followed by the enlargement of adjacent cells. As a consequence, cell-area distributions change drastically as functions of age and disease. Changes in cell-area distributions, in particular multimodality and skewness due to aging, are observed, and give rise to some difficult sampling problems. In this paper, sample quantiles are investigated as an alternative to the use of the sample mean. Asymptotic approximations are provided for the sample sizes required to estimate population quantiles with a desired precision. Asymptotic sample sizes are then compared with those obtained from tolerance limits. Empirical sample quantiles that can be used as benchmarks to compare corneas of normal individuals against corneas with unknown cell-area distributions are also presented. Aspects that merit further investigation are noted.