HIERARCHICAL BAYESIAN ANALYSIS OF BINARY MATCHED PAIRS DATA

The paper introduces a hierarchical Bayesian analysis of binary matched pairs data with noninformative prior distributions. Certain properties of the poste- rior distributions, including their propriety, are established. The Bayesian methods are implemented via Markov chain Monte Carlo integration techniques, and nu- merical illustrations are provided. For the logit link, the conditional and marginal maximum likelihood estimators of a treatment effect depend only on the off-main- diagonal elements of a 2 × 2 contingency table, and the same is true of McNemar's test. By contrast, the hierarchical Bayes estimators and subsequent analyses de- pend also on the main-diagonal elements in a natural way.

[1]  P. M. E. Altham,et al.  The analysis of matched proportions , 1971 .

[2]  D. Cox.  Two further applications of a model for binary regression , 1958 .

[3]  O. Barndorff-Nielsen.  On a formula for the distribution of the maximum likelihood estimator , 1983 .

[4]  E. B. Andersen,et al.  Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[5]  D. Krewski,et al.  Statistical Methods in Cancer Research: Volume III: The Design and Analysis of Long-Term Animal Experiments , 1987 .

[6]  N. Breslow,et al.  Statistical methods in cancer research. Vol. 1. The analysis of case-control studies. , 1981 .

[7]  W. G. Cochran.  The comparison of percentages in matched samples. , 1950, Biometrika.

[8]  John D. Kalbfleisch,et al.  Application of Likelihood Methods to Models Involving Large Numbers of Parameters , 1970 .

[9]  Robert Tibshirani,et al.  A Simple Method for the Adjustment of Profile Likelihoods , 1990 .

[10]  N. Breslow,et al.  Statistical methods in cancer research: volume 1- The analysis of case-control studies , 1980 .

[11]  P. Simpson,et al.  Statistical methods in cancer research , 2001, Journal of surgical oncology.

[12]  E. B. Andersen,et al.  CONDITIONAL INFERENCE FOR MULTIPLE‐CHOICE QUESTIONNAIRES , 1973 .

[13]  J. D. Kalbfleisch,et al.  Conditions for consistent estimation in mixed-effects models for binary matched-pairs data† , 1994 .

[14]  G. Rasch.  On General Laws and the Meaning of Measurement in Psychology , 1961 .

[15]  D. Cox,et al.  Parameter Orthogonality and Approximate Conditional Inference , 1987 .