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 (micro). 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 micro, as well as a high correlation coefficient (r2 = 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 (r2 = 0.96 - 0.99, average residual = -5% to -7%, 95-98% coverage of micro), except when applied to distributions with low coefficients of variation (standard deviation/micro < 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.