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abstract: '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.'
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title: Objective Bayesian Inference for Bilateral Data
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Introduction {#sec1}
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Bilateral data arise in medicine when a group of randomly chosen patients with a condition receive a new treatment, for example, surgery, on paired body parts within the same individual (eyes, ears, breasts, arms, hands, knees, legs, or feet), while another group of patients with this condition receive a control treatment, for example, the currently accepted medical treatment. The investigator records paired Bernoulli outcomes about a particular characteristic, for example, absence of the condition, that 