On the equivalence of posterior inference based on retrospective and prospective likelihoods: application to a case-control study of colorectal cancer

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.

Exact tests of goodness of fit of log-linear models for rates

We propose Metropolis-Hastings sampling methods for estimating the exact conditional p-value for tests of goodness of fit of log-linear models for mortality rates and standardized mortality ratios. We focus on two-way tables, where the required conditional distribution is a multivariate noncentral hypergeometric distribution with known noncentrality parameter. Two examples are presented: a 2 x 3 table, where the exact results, obtained by enumeration, are available for comparison, and a 9 x 7 table, where Monte Carlo methods provide the only feasible approach for exact inference.

Monte Carlo exact methods used for analysing interethnic unions in Great Britain

The value of using exact rather than asymptotic tests to measure intermarriage in the United Kingdom is examined. "We develop Markov chain Monte Carlo methods for estimating the exact conditional p-value and the exact distribution of the residuals, for quasi-independence and quasi-symmetry. These methods are used to analyse a sparse 10 x 10 symmetric table of interethnic unions, extracted from the 1% household sample of anonymized records from the 1991 U.K. census. With the exception of Pakistani/White and Other Asian/White unions, there is no evidence against quasi-symmetry. We conclude that, with these exceptions, there are no gender differences in the affinities between ethnic groups."