The ordinal engine’s first design tab allows the user to define prior exponents for Dirichlet distributions. If the user has selected independent Dirichlets on the Study Info tab for ordinal outcome modeling, each experimental arm gets its own set of exponents. If the user has selected cumulative logistic modeling, only the control arm gets a set of exponents, and the prior distributions for other experimental arms are derived from this one set of exponents and the prior distributions for the dose-response model parameters.
Prior exponents for Dirichlet distributions are often interpreted as counts of subjects observed in an earlier experiment, but positive non-integer values are allowed.
The prior mean for the probability of a given ordinal outcome under the Dirichlet distribution is the exponent corresponding to that outcome, divided by the sum of the exponents. For example, if there are four ordinal outcomes and the prior exponents are 10, 20, 30, and 40, the prior probabilities of the four outcomes are 0.1, 0.2, 0.3, and 0.4.
If a relatively non-informative prior distribution is desired, one suggestion is to use equal exponents that add up to approximately 0.8, i.e. \(0.8/K\) where \(K\) is the number of ordinal outcomes (Berger, Bernardo, and Sun, Bayesian Analysis 2015).