| The 2 x 2 contingency table arises often in biostatistics to describe the association between two binary variables. A variety of parameters have been proposed to describe the difference in risk between the two populations. Risk difference (RD), relative risk (RR) and odds ratio (OR) are three measures of association extensively used in medical literature.; The main goals of this dissertation are to develop new methods to analyze 2 x 2 contingency tables with small sample sizes, and possibly missing data. This dissertation is divided into four distinct, but interconnected chapters related to the analysis of 2 x 2 tables and possibly missing data: (1) Chapter 3. Exact bootstrap confidence intervals for the risk difference of two probabilities using data from independent binomial samples with small sample sizes; (2) Chapter 4. Bayesian estimates of the odds ratios for 2 x 2 tables with incompletely classified data; (3) Chapter 5. Bayesian Extension of Fisher's Exact Test in the Presence of Missing Data; (4) Chapter 6. Bayesian Analysis of correlated proportions (Matched-pair data) in 2 x 2 Tables with Incompletely Classified Data: Bayesian Extension of McNemar's test to missing data.; In the rest of this dissertation, we specifically focus on the situation that some of observations are only partially cross-classified, either by row classification or column classification. In particular, each subject is classified at least by one binary variable and ignorable missing mechanism is assumed to be either missing completely at random (MCAR) or missing at random (MAR).; In these four studies, we develop methods to analyze 2 x2 contingency tables of small sample sizes and possibly with missing data. (Abstract shortened by UMI.)... |
