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On the equivalence of posterior inference based on retrospective and prospective likelihoods: application to a case‐control study of colorectal cancer
Author(s) -
Ghosh M.,
Song J.,
Forster J.J.,
Mitra R.,
Mukherjee B.
Publication year - 2012
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5358
Subject(s) - categorical variable , inference , bayesian probability , prior probability , computer science , odds ratio , statistics , equivalence (formal languages) , bayesian inference , posterior probability , colorectal cancer , mathematics , econometrics , medicine , artificial intelligence , cancer , discrete mathematics
The paper develops a class of priors that leads to equivalent posterior inference for odds ratio parameters based on prospective and retrospective models for categorical response data. The results are applicable to both unmatched and matched case‐control studies. The results hold for a general class of link functions for categorical response. The proposed method can accommodate multiple and possibly ordered disease states. The results are applied to the analysis of discrete subtypes in an ongoing case‐control study of colorectal cancer. A simulation study illustrates the need for carefully considering prior choices in Bayesian analysis of data collected under retrospective design. Copyright © 2012 John Wiley & Sons, Ltd.