The role of parameterization in comparing source attribution models based on microbial subtyping for salmonellosis

Source attribution methods attribute human cases of a zoonotic disease to a certain source putatively responsible for this disease. Identifying and quantifying the contribution of different sources to human infections is important for taking appropriate actions for reducing the exposure of the consumer to zoonotic pathogens. One widely used method is the microbial subtyping approach, whose principle is to compare the frequency of pathogen subtypes from different sources (e.g. animals or food) with the frequency of these subtypes in human cases. This paper studies the relationship between a Bayesian microbial subtyping approach described by Hald and coworkers subsequently modified by David and coworkers, here called the Hald model, and a frequentist approach known as the "Dutch model." The comparison between the Bayesian and frequentist model is done for two data sets on salmonellosis in Germany from different time periods (year 2004-2007 and 2010-2011). The results of both approaches are in good agreement with each other for the used data. It is shown here mathematically that a certain parameterization can be used to transform the probabilistic Hald model into a deterministic form, which is equivalent to the Dutch model. That certain parameterization secures independence of the model outcomes from the choice of so-called unique subtypes (which are unique in the sense that they are found exclusively in one of the sources). It is shown that deviating from that certain parameterization leads variations in the model outcome dependent on which unique subtypes are chosen in the process of modelling.