Censored Data and Statistics: How to Estimate Percentiles

The statistical analysis of data, which includes observations below a laboratory's reporting limit, is challenging. We present an overview of the statistical literature to estimate percentiles for censored data. Furthermore, we compare different methods in a simulation study and show applications of these methods in an example from occupational epidemiology. In the simulation study, we constructed complete datasets of 50, 100, and 250 observations drawn from a log-normal distribution 10,000 times each. Then the proportion of censored observations was set to 10%, 25%, and 50%. The 25th, 50th, 75th, 90th, and 95th percentiles were estimated using three different naive methods (simple substitution by one-half times the reporting limit, simple substitution by two-thirds times the reporting limit, and simple substitution by one over the square root of two times the reporting limit), best-case and worst-case scenarios, Kaplan-Meier estimation, maximum likelihood estimation, and multiple imputation. The methods were compared according to their relative bias and root mean square error. The simulation study showed that naive methods lead to biased estimates and are inferior to other statistical methods. The maximum likelihood estimates were generally the most accurate and precise. With an example from occupational epidemiology, we show that statistical methods for censored data can be readily applied on real datasets.