Statistical methods for handling nondetected results in food chemical monitoring data to improve food risk assessments

Abstract

Chemical risk assessment is important for risk management, and estimates of chemical exposure must be as accurate as possible. Chemical concentrations in food below the limit of detection are known as nondetects and result in left‐censored data. During statistical analysis, the method used for handling values below the limit of detection is important. Many risk assessors employ widely used substitution methods to treat left‐censored data, as recommended by international organizations. The National Institute of Food and Drug Safety Evaluation of South Korea also recommends these methods, which are currently used for chemical exposure assessments. However, these methods have statistical limitations, and international organizations recommend more advanced alternative statistical approaches. In this study, we assessed the validity of currently used statistical methods for handling nondetects. To identify the most suitable statistical method for handling nondetection, we created virtual data and conducted simulation studies. Based on both simulation and case studies, the Maximum Likelihood Estimation (MLE) and Robust Regression on Order Statistics (ROS) methods were found to be the best options. The statistical values obtained from these methods were similar to those obtained from the commonly used 1/2 Limit of Detection (LOD) substitution method for nondetection treatment. In three case studies, we compared the various methods based on the root mean squared error. The data for all case studies were from the same source, to avoid heterogeneity. Across various sample sizes and nondetection rates, the mean and 95th percentile values for all treatment methods were similar. However, “lognormal maximum likelihood estimation” method was not suitable for estimating the mean. Risk assessors should consider statistical processing of monitoring data to reduce uncertainty. Currently used substitution methods are effective and easy to apply to large datasets with nondetection rates <80%. However, advanced statistical methods are required in some circumstances, and national guidelines are needed regarding their use in risk assessments.

Evaluation of Statistical Treatment of Left-Censored Contamination Data: Example Involving Deoxynivalenol Occurrence in Pasta and Pasta Substitute Products

“…In other words, whether a sample contains 1% or 90% detected values does not drive the way the non-detected values are treated. This applies even in cases where the two types of samples have different features [ 11 ], with the most critical situation being that with the highest number of non-detected values and the presence of multiple LOQ values [ 11 , 12 ].…”

“…However, when left-censored data are at hand, more complex methods are needed. ML estimation in the context of data left-censored by an LOQ [ 11 , 12 ] should consider the fraction of values above the LOQ and, therefore, the fraction of data below the LOQ, as well as the distribution for measured VALs. To summarise, let denote an indicator that is equal to 1 when the observation is noted and 0 when it is not.…”

“…Such drawbacks have been an object of study, and more recently the international interest has moved towards the application of stochastic approaches to impute (multiple) non-detected values in food contamination data. The literature includes several efforts to deal with the issue of non-detected values, especially via maximum likelihood (ML) estimation applied to parametric models with censored data [ 11 , 12 ]. For this purpose, several attempts have been made using marginal and pseudo-likelihood-based methods [ 13 ] by fitting truncated parametric (e.g., lognormal) distributions to observed data [ 14 ]; log-probit regression (LPR) [ 15 ]; or non-parametric methods, such as the non-parametric estimator of the survival function [ 12 , 16 , 17 , 18 ].…”