Optimal definition of the limit of detection (LOD) in detecting genetically modified grains from heterogeneous grain lots

Abstract

A limit of detection (LOD) of analytical instruments is usually arbitrarily defined, for example, as the level of contamination at which the probability of detection (POD) is 50 or 95%. However, these definitions are ignoring the sampling uncertainty that emerges in the process of preparing test portions. Consequently, the actual POD becomes considerably smaller than the nominal POD. In this paper, we propose a procedure for determining LOD appropriately to control the actual POD in detecting the contamination by genetically modified grains (GM grains) from heterogeneous grain lots. We consider an actual procedure used in the sampling inspection. (1) The sample grains are drawn as increments from a lot. (2) The collected grains are combined to yield a composite to transport to the laboratory. (3) The test portions are created by sub-sampling from the composite in the laboratory. We first show that we can construct an optimal sampling plan for controlling POD under a given value of LOD: optimal number of sampled increments, optimal number of grains in the laboratory sample, and optimal number of test portions. Then, we show that we can determine the optimal value of LOD that minimizes the total cost of inspection.

Keywords:

• Composite sampling
• increment sampling
• probability of detection
• sub-sampling

Acknowledgments

We thank two anonymous referees for their comments that helped us in greatly improving the manuscript. This work was supported in part by the grants from the Agriculture, Forestry and Fisheries Research Council of Japan (‘Research project for Genomics for Agricultural Innovation’, GAM-206).