to determine which one provides a better fit to the data. @PeiTangWongGuo2010 present asymptotic confidence intervals under the equal correlation model and evaluate their performance. @PeiTangGuo2008 present a test for the equality of $\lambda_0$ and $\lambda_1$ when unilateral and bilateral data are combined under the equal correlation model.

Among these five models, the independence model is rarely used in practice in the context of bilateral data. The objective priors for the saturated model have already been investigated in the literature. The challenge with Rosner’s model is that it is difficult to justify this model from a biological point of view. Only the equal correlation model and the equal conditional probability model (Dallal’s model) have sound statistical foundations and biological interpretation. Indeed, one can always characterize a bivariate discrete distribution for two binary random variables by making assumptions about (i) their marginal distributions and the correlation they share or (ii) their marginal distributions and the two conditional distributions they share. For Rosner’s model and the equal correlation model, Jeffreys’ prior and Bernardo’s reference prior are too complex to be of much practical use. Dallal’s model is the only model for which we could derive useful closed-form expressions for various objective priors. 