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

Area of Science:

• Ophthalmology
• Biostatistics

Background:

• Corneal endothelium cell area estimation is vital in clinical ophthalmology.
• These cells do not divide mitotically; cell death leads to adjacent cell enlargement.
• Cell-area distributions change significantly with age and disease, complicating analysis.

Purpose of the Study:

• To investigate sample quantiles as an alternative to the sample mean for corneal endothelium cell-area distribution analysis.
• To provide asymptotic approximations for sample sizes needed to estimate population quantiles accurately.
• To present empirical sample quantiles for comparing corneal health.

Main Methods:

• Utilized sample quantiles to analyze corneal endothelium cell-area distributions.
• Derived asymptotic approximations for sample size calculations.
• Compared asymptotic sample sizes with those from tolerance limits.
• Developed empirical sample quantiles for benchmarking.

Main Results:

• Sample quantiles offer a viable alternative to the sample mean for analyzing complex cell-area distributions.
• Asymptotic approximations provide a method for determining required sample sizes for quantile estimation.
• Empirical quantiles serve as benchmarks for assessing corneal health.

Conclusions:

• Sample quantiles are effective for analyzing age and disease-related changes in corneal endothelium cell-area distributions.
• The study provides tools for sample size determination and corneal health benchmarking.
• Further research into these methods is warranted.