Observations below multiple lower limits of quantification: How to estimate the mean and variance

Area of Science:

• Analytical Chemistry
• Biostatistics
• Environmental Science

Background:

• Multiple lower limits of quantification (MLOQs) arise from inter-laboratory analysis of concentration data where some values are unquantifiable.
• Existing methods like Helsel's multiple regression are limited for normally distributed data under MLOQs.

Purpose of the Study:

• To propose and evaluate new statistical methods for estimating mean and variance in datasets with MLOQs.
• To compare the performance of proposed methods against Helsel's method using simulation studies.

Main Methods:

• Developed a simple imputation method and two maximum likelihood estimation methods: multiple truncated sample and multiple censored sample.
• Conducted a simulation study comparing proposed methods with Helsel's method using root mean squared error (RMSE) and bias.
• Investigated performance under varying numbers of lower limits of quantification (LLOQs), rates of unquantifiable observations, sample sizes, and model misspecification.

Main Results:

• All methods showed decreased accuracy with higher rates of unquantified observations; larger sample sizes reduced bias.
• The multiple censored sample method yielded superior RMSE and bias estimates for smaller variances.
• Helsel's method showed better bias performance for larger variances, but was inferior under model misspecification.

Conclusions:

• For large sample sizes and normally distributed data with MLOQs, Helsel's method is recommended.
• Otherwise, the multiple censored sample method is advised for accurate estimation of mean and variance in data with MLOQs.