Confidence interval comparison: Precision of maximum likelihood estimates in LLOQ affected data.

Area of Science:

• Biostatistics
• Statistical Modeling
• Analytical Chemistry

Background:

• Data below the lower limit of quantification (LLOQ) presents challenges in parameter estimation and precision assessment.
• Accurate handling of unquantifiable observations is crucial for reliable statistical inference.
• Existing methods for dealing with LLOQ data require careful evaluation for different distributional assumptions.

Purpose of the Study:

• To assess the precision of censored sample maximum likelihood estimates of the mean for normal, exponential, and Poisson distributions affected by LLOQs.
• To compare the performance of asymptotic and bias-corrected accelerated bootstrap confidence intervals (CI) using coverage proportion and interval width.
• To evaluate the impact of varying proportions of unquantifiable observations on CI performance.

Main Methods:

• A simulation study was conducted to compare asymptotic and bootstrap CIs for the mean.
• Analytical expressions for maximum likelihood estimates were derived for exponential and Poisson distributions.
• Censored sample and simple imputation methods were used to account for LLOQs, with varying proportions of censored data.

Main Results:

• Bootstrap CIs based on censored sample estimates showed higher coverage proportion and narrower interval width than asymptotic CIs.
• The performance varied by distribution; normality assumption data was most affected by high proportions of unquantifiable observations.
• Censored sample estimates are preferable over simple imputation due to lower bias, which improves CI coverage.

Conclusions:

• Bootstrap CIs provide a more precise and reliable method for estimating the mean of LLOQ-affected data across various distributions.
• The censored sample method is recommended for deriving point estimates for confidence intervals.
• This study offers a widely usable tool for handling LLOQ-affected data effectively.