Goodness-of-fit tests for correlated paired binary data.

We review a few popular statistical models for correlated binary outcomes, present maximum likelihood estimates for the model parameters, and discuss model selection issues using a variety of goodness-of-fit test statistics. We apply bootstrap strategies that are computationally efficient to evaluate the performance of goodness-of-fit statistics and observe that generally the power and the type I error rate of the goodness-of-fit statistics depend on the model under investigation. Our simulation results show that careful choice of goodness-of-fit statistics is an important issue especially when we have a small sample and the outcomes are highly correlated. Two biomedical applications are included.

Asymptotic confidence interval construction for proportion difference in medical studies with bilateral data.

Bilateral dichotomous data are very common in modern medical comparative studies (e.g. comparison of two treatments in ophthalmologic, orthopaedic and otolaryngologic studies) in which information involving paired organs (e.g. eyes, ears and hips) is available from each subject. In this article, we study various confidence interval estimators for proportion difference based on Wald-type statistics, Fieller theorem, likelihood ratio statistic, score statistics and bootstrap resampling method under the dependence or/and independence models for bilateral binary data. Performance is evaluated with respect to the coverage probability and expected width via simulation studies. Our empirical results show that (1) ignoring the dependence feature of bilateral data could lead to severely incorrect coverage probabilities; and (2) Wald-type, score-type and bootstrap confidence intervals based on the dependence model perform satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the pre-specified nominal confidence level and are hence recommended. A real data from an otolaryngologic study is used to illustrate the proposed methods.

Sample size for testing difference between two proportions for the bilateral-sample design.

In this article, we consider approximate sample size formulas for testing difference between two proportions for bilateral studies with binary outcomes. Sample size formulas are derived to achieve a prespecified power of a statistical test at a prechosen significance level. Four statistical tests are considered. Simulation studies are conducted to investigate the accuracy of various formulas. In general, the sample size formula for Rosner's statistic based on the dependence assumption is highly recommended in the sense that its actual power is satisfactorily close to the desired power level. An example from an otolaryngological study is used to demonstrate the proposed methodologies.