Nonparametric methods for measurements below detection limit.

Area of Science:

• Statistics
• Biostatistics

Background:

• Analytical data frequently exhibit left-censoring when values fall below detection limits.
• Existing statistical inference methods for left-censored data, such as naive approaches and the parametric Tobit model, may be inadequate for high censoring rates and small sample sizes.

Purpose of the Study:

• To establish the theoretical equivalence of three nonparametric methods (Wilcoxon rank sum, Gehan, and Peto-Peto tests) under fixed left-censoring.
• To develop a nonparametric point and interval estimation procedure for the location shift model.
• To compare the performance of various statistical methods for left-censored data.

Main Methods:

• Theoretical equivalence established for Wilcoxon rank sum, Gehan, and Peto-Peto nonparametric tests.
• Development of a nonparametric point and interval estimation procedure for location shift models.
• Extensive simulations comparing 14 methods (naive, parametric, nonparametric) across different sample sizes and censoring rates.

Main Results:

• Nonparametric methods demonstrated superior performance compared to naive and parametric approaches across various sample sizes and censoring rates.
• Simulations confirmed satisfactory point and interval estimation accuracy using the developed nonparametric procedures.
• The study provides a robust framework for statistical inference with left-censored analytical data.

Conclusions:

• Nonparametric statistical methods are highly recommended for analyzing left-censored data, particularly in scenarios with high censoring rates and limited sample sizes.
• The established theoretical equivalence and validated estimation procedures offer reliable tools for statistical inference.
• The findings support the broader application of these nonparametric techniques in scientific research involving censored data.