USING THE REVERSE KAPLAN-MEIER TO ESTIMATE POPULATION DISTRIBUTIONS WITH DATA BELOW A LIMIT OF DETECTION

摘要

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.