A perspective of randomness in a clinical test of olfactory performance

Abstract Background Random walks describe stochastic processes that result from a sequence of indeterminate changes in a random variable that are not correlated with past changes. This report describes a random walk component of a clinical sensory test of olfactory performance. The formal description of the stochastic process during the clinical test allows precise cutoffs to be set for the diagnosis of olfactory loss. Methods While odor discrimination (D) and odor identification (I) are tested in the Sniffin`Sticks olfactory test battery with four- and three-alternative forced-choice designs, respectively, the odor threshold (T) test embeds a three-alternative forced-choice paradigm in a seven-alternative staircase paradigm. This was investigated in computer simulation scenarios and then formally described. Results Odor threshold assessment test consists of two sequential parts, the first of which determines the starting point for the next. Both parts can be described as a biased random walk with highly unequal probabilities of moving toward higher (11%) or lower scores (89%). The odor concentration from which the first test part begins, and the length of the random walk in the subsequent second part were critical factors in the probability of accidentally achieving high test scores. Conclusions By changing the odor concentration from where the starting point determination for the second test part begins, the current cut-off of a composite test score at T + D + I < 16 indicating anosmia was raised from representing the 87th quantile of random test scores to representing the 97th quantile. The results likely apply to other sensory tests using the staircase paradigm that can also be described as random walks.