Evaluation of statistical methods for left-censored environmental data with nonuniform detection limits

Area of Science:

• Environmental statistics
• Statistical modeling
• Data analysis

Background:

• Estimating constituent concentrations from left-censored environmental data presents statistical challenges.
• Nonuniform detection limits further complicate the accurate estimation of upper confidence limits.

Purpose of the Study:

• To evaluate statistical methods for estimating 95% upper confidence limits of mean constituent concentrations for left-censored data.
• To compare method efficacy using Monte Carlo simulations under varying percentages of nondetected samples.

Main Methods:

• Monte Carlo simulations were employed to generate left-censored data sets with random sample sizes and percentages of nondetected samples.
• Evaluated methods included trimmed mean, Winsorization, Aitchison's, log-probit regression, and a bounding method.
• Efficacy was assessed by comparing confidence limits and determining percent coverage of the true mean (μ).

Main Results:

• For 15-50% nondetected samples, log-probit regression demonstrated superior performance with 99-100% coverage and high correlation (r²=0.99).
• For 51-80% nondetected samples, a bounding method proved effective (95-98% coverage, r²=0.96-0.99), except for low coefficients of variation.
• Chebyshev theorem was recommended for estimating 95% upper confidence limits in both scenarios.

Conclusions:

• Log-probit regression is the recommended method for datasets with 15-50% nondetected values.
• A bounding method is effective for datasets with 51-80% nondetected values, with caveats for low variability.
• Accurate estimation of upper confidence limits for censored environmental data is crucial for risk assessment.