  This paper presents three objective Bayesian methods for analyzing bilateral
data under Dallal's model and the saturated model. Three parameters are of
interest, namely, the risk difference, the risk ratio, and the odds ratio. We
derive Jeffreys' prior and Bernardo's reference prior associated with the three
parameters that characterize Dallal's model. We derive the functional forms of
the posterior distributions of the risk difference and the risk ratio and
discuss how to sample from their posterior distributions. We demonstrate the
use of the proposed methodology with two real data examples. We also
investigate small, moderate, and large sample properties of the proposed
methodology and the frequentist counterpart via simulations.
