Confidence limits for lognormal percentiles and for lognormal mean based on samples with multiple detection limits

Area of Science:

• Occupational Health
• Environmental Statistics
• Biostatistics

Background:

• Assessing occupational exposure often involves analyzing data that follows a lognormal distribution.
• Existing methods for estimating exposure levels, especially the mean or upper percentiles, can be challenging with censored data (multiple detection limits).

Purpose of the Study:

• To develop and validate inferential statistical methods for constructing confidence limits for lognormal distribution parameters (mean and upper percentiles).
• To extend these methods for analyzing data from gamma distributions.
• To provide practical tools for occupational exposure assessment with censored data.

Main Methods:

• The study proposes methods based on maximum likelihood estimates (MLEs).
• It focuses on constructing upper confidence limits for percentiles and confidence intervals for the mean.
• The methods are designed to handle samples with multiple detection limits.

Main Results:

• The proposed methods demonstrate good performance in terms of coverage probabilities and statistical power.
• They are effective even with small sample sizes.
• The approaches are also applicable to gamma distribution percentiles.

Conclusions:

• The developed inferential methods offer a robust solution for occupational exposure assessment with censored lognormal and gamma-distributed data.
• Ease of computation and implementation is a key advantage.
• The methods are validated with real and simulated datasets.