Retrospective-prospective symmetry in the likelihood and Bayesian analysis of case-control studies

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Retrospective-prospective symmetry in the likelihood and Bayesian analysis of case-control studies

Byrne, SPJ; Dawid, AP; (2014) Retrospective-prospective symmetry in the likelihood and Bayesian analysis of case-control studies. Biometrika (2014) 101 (1), pages 189-204 , 101 (1) pp. 189-204. 10.1093/biomet/ast050. Green open access

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Abstract

Prentice & Pyke (1979) established that the maximum likelihood estimate of an odds-ratio in a case-control study is the same as would be found by running a logistic regression: in other words, for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model. Similar results have been obtained for other models, and conditions have also been identified under which the corresponding Bayesian property holds, namely that the posterior distribution of the odds-ratio be the same, whether computed using the prospective or the retrospective likelihood. Here we demonstrate how these results follow directly from certain parameter independence properties of the models and priors, and identify prior laws that support such reverse analysis, for both standard and stratified designs.

Type:	Article
Title:	Retrospective-prospective symmetry in the likelihood and Bayesian analysis of case-control studies
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1093/biomet/ast050
Publisher version:	http://dx.doi.org/10.1093/biomet/ast050
Additional information:	C � 2013 Biometrika Trust. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. 16 pages, to appear in Biometrika
UCL classification:	UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
URI:	https://discovery.ucl.ac.uk/id/eprint/1348504