Inferring the distribution of norovirus in individual oysters below the limit of quantification by pooled sampling

Norovirus (NoV) in oysters is a food safety risk of much concern. In order to assess the risk of the exposure, the distribution of the number of NoV copies contained in each oyster should be acquired first for comprehensively quantifying the associated risks. However, the part of the distribution below the limit of quantification cannot be obtained directly by laboratory detecting methods, which hampers accurate assessment. To tackle this challenging problem, a systematic method (Distribution Inference Method by Pooled Sampling) is proposed to infer the unobservable part of distribution based upon all measurements of the pooled samples with n = 2. Using convolutional integrals and real-coded genetic algorithm for inferring, this method has neither requirements for the type or properties of the original distribution, nor requirements for historical data, even nor requirements for the relationship between observable and unobservable parts of the distribution. A series of experiments were conducted on simulated datasets of a variety of types, including normal distribution, uniform distribution, gamma distribution, lognormal distribution, zero-inflated Poisson distribution, their combinations, and even their splicing, covering common distribution types in oyster NoV scenario and more general scenarios. The results show that almost all inferred simulation data and their original counterparts passed Kolmogorov-Smirnov tests, which implies that they are essential of the same distribution. Based on this method, a ready-to-use web system was developed for researchers to infer their original distribution with pooled-sampling measurements from the detection of NoV or even other substances.