Nonparametric methods for measurements below detection limit

Analytical data are often subject to left-censoring when the actual values to be quantified fall below the limit of detection. The primary interest of this paper is statistical inference for the two-sample problem. Most of the current publications are centered around naive approaches or the parametric Tobit model approach. These methods may not be suitable for data with high censoring rates and relatively small sample sizes. In this paper, we establish the theoretical equivalence of three nonparametric methods: the Wilcoxon rank sum, the Gehan, and the Peto-Peto tests, under fixed left-censoring and other mild conditions. We then develop a nonparametric point and interval estimation procedure for the location shift model. A large set of simulations compares 14 methods including naive, parametric, and nonparametric methods. The results clearly favor the nonparametric methods for a range of sample sizes and censoring rates. Simulations also demonstrate satisfactory point and interval estimation results. Finally, a real data example is given followed by discussion.