Common practice of either ignoring non-detects (NDs) or replacing them with ‘simple substitution’ values, e.g., half the reporting limit (RL), has led to calls for greater statistical sophistication via left-censored data models. Less clear is if the assumptions underlying a censored model are always satisfied , or whether such a model leads to more accurate results.
Simple substitution of half the reporting limit (RL) can be viewed as replacing each non-detect with its expected value under a mixture model that draws non-detects from a uniform distribution on the interval (0, DL). We propose an extension to this model whereby non-detects are drawn with Monte Carlo sampling from one of a class of bounded distributions on (0, DL), e.g., uniform, beta, triangle. We also propose repeated draws from the mixture model to generate a series of data realizations, from which the statistical properties of any desired estimator can be computed.
The benefits of this combined mixture model and computational strategy are explored, including algorithmic and computational feasibility, and better visualization and assessment of ND-associated uncertainty.