Modeling and correction of sensitivity thresholds determined by best EstimateThreshold (BET)

The r-Alternative Forced Choice (r-AFC) test is a test of discrimination in which the subject is presented with three samples, one of which is a test sample containing a nominated stimulus (test sample), the other being references. The subject is instructed to indicate the test sample. Taste and odor sensitivity thresholds are frequently determined using successive r-AFC tests with stimuli in increasing concentrations. The Best Estimate Threshold (BET) method consists in using successive 3-AFC with increasing concentrations to estimate sensitivity threshold. Then, the threshold is estimated using the geometrical mean of the highest concentration that caused an error and the concentration directly below it. However, a subject who feels no difference between the samples may give a correct answer by chance. It leads to consequent potential bias in the determination of the sensitivity thresholds. This paper aims to formalize and model the thresholds obtained in successive r-AFC in order to quantify the errors inherent in such protocols. It establishes that, when you assumed that the distribution of the true sensitivity threshold is known in the population, the threshold obtained by r-AFC can be modelled with a variable following a specific probability law. This paper presents the theory of this model, then illustrate it with simulations and application on a real dataset. An R package dedicated to these analyses, AFCR, was also created and is available on github ( https://github.com/ChemoSens/AFCR ). Therefore, sensory scientists could use the package as a help to set up their sensory protocol or-to analyze their own data. • A ‘guessing by chance’ bias is inherent in BET and can be corrected. • A probabilistic model can be used to model BET as random variable. • BET corrections are available in AFCR R package.