Introduction: Data below a limit of detection (LOD) can be analyzed using methods of survival analysis for left-censored data. The reverse Kaplan-Meier (KM) estimator provides an effective method of estimating population percentiles for such data. Materials and methods: The reverse KM estimator is illustrated using serum dioxin data from both the University of Michigan Dioxin Exposure Study (UMDES) and the National Health and Nutrition Examination Survey (NHANES). The reverse KM can be calculated using commonly available software for the KM estimator. SAS, JMP, R and Minitab will calculate the reverse KM directly using their Turnbull estimator routines. (The Turnbull estimator, developed for the more general interval censoring case, is equivalent to the reverse KM for left-censored data.) Results and Discussion: In this setting, the reverse KM estimator is the recommended method in the statistical literature. For estimation of the distribution function and population percentiles, the reverse KM estimator is recommended in preference to commonly used methods such as substituting LOD/2 or LOD/√2 for values below the LOD, assuming a known parametric distribution, or using single or multiple imputation to replace the left-censored values.
Gillespie B W Reichert H Chen Q Franzblau A Lepkowski J Adriaens P Demond A Luksemburg W Garabrant D
Department of Biostatistics,School of Public Health,University of Michigan,Ann Arbor,MI 48109-2029 C Center for Statistical Consultation and Research,University of Michigan,Ann Arbor,MI 48109-1070 Department of Biostatistics,School of Public Health,University of Michigan,Ann Arbor,MI 48109-2029 Department of Environmental Health Sciences,University of Michigan,Ann Arbor,MI 48109-2029 Institute for Social Research,University of Michigan,Ann Arbor,Michigan 48109-1248 USA Department of Civil and Environmental Engineering,University of Michigan College of Engineering,Ann Vista Analytical Laboratory,El Dorado Hills,California 95762 USA