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

Monte Carlo simulations were used to evaluate statistical methods for estimating 95% upper confidence limits of mean constituent concentrations for left‐censored data with nonuniform detection limits. Two primary scenarios were evaluated: data sets with 15 to 50% nondetected samples and data sets with 51 to 80% nondetected samples. Sample size and the percentage of nondetected samples were allowed to vary randomly to generate a variety of left‐censored data sets. All statistical methods were evaluated for efficacy by comparing the 95% upper confidence limits for the left‐censored data with the 95% upper confidence limits for the noncensored data and by determining percent coverage of the true mean (μ). For data sets with 15 to 50% nondetected samples, the trimmed mean, Winsorization, Aitchison's, and log‐probit regression methods were evaluated. The log‐probit regression was the only method that yielded sufficient coverage (99–100%) of μ, as well as a high correlation coefficient ( r 2 = 0.99) and small average percent residuals (− 0.1%) between upper confidence limits for censored versus noncensored data sets. For data sets with 51 to 80% nondetected samples, a bounding method was effective ( r 2 = 0.96–0.99, average residual = −5% to −7%, 95‐98% coverage of μ), except when applied to distributions with low coefficients of variation (standard deviation/μ < 0.5). Thus, the following recommendations are supported by this research: data sets with 15 to 50% nondetected samples—log‐probit regression method and use of Chebyshev theorem to estimate 95% upper confidence limits; data sets with 51 to 80% nondetected samples— bounding method and use of Chebyshev theorem to estimate 95% upper confidence limits.