Notes on Interval Estimation of Odds Ratio in Matched Pairs under Stratified Sampling

We develop four asymptotic interval estimators and one exact interval estimator for the odds ratio (OR) under stratified random sampling with matched pairs. We apply Monte Carlo simulation to evaluate the performance of these five interval estimators. We note that the conditional score test-based interval estimator with a monotonic transformation and the interval estimator based on the Mantel–Haenszel (MH) type point estimator with the logarithmic transformation are generally preferable to the others considered here. We also note that the conditional exact confidence interval can be of use when the total number of matched pairs with discordant responses is small.     

Hypothesis Tests for Neyman's Bias in Case–Control Studies

Survival bias is a long recognized problem in case–control studies, and many varieties of bias can come under this umbrella term. We focus on one of them, termed Neyman's bias or ‘prevalence–incidence bias’. It occurs in case–control studies when exposure affects both disease and disease-induced mortality, and we give a formula for the observed, biased odds ratio under such conditions. We compare our result with previous investigations into this phenomenon and consider models under which this bias may or may not be important. Finally, we propose three hypothesis tests to identify when Neyman's bias may be present in case–control studies. We apply these tests to three data sets, one of stroke mortality, another of brain tumors, and the last of atrial fibrillation, and find some evidence of Neyman's bias in the former two cases, but not the last case.     

A pattern-mixture odds ratio model for incomplete categorical data

Most models for incomplete data are formulated within the selection model framework. Pattern-mixture models are increasingly seen as a viable alternative, both from an interpretational as well as from a computational point of view (Little 1993, Hogan and Laird 1997, Ekholm and Skinner 1998). Whereas most applications are either for continuous normally distributed data or for simplified categorical settings such as contingency tables, we show how a multivariate odds ratio model (Molenberghs and Lesaffre 1994, 1998) can be used to fit pattern-mixture models to repeated binary outcomes with continuous covariates. Apart from point estimation, useful methods for interval estimation are presented and data from a clinical study are analyzed to illustrate the methods.     

Analysis of longitudinal multiple-source binary data using generalized estimating equations

Summary.  We present a multivariate logistic regression model for the joint analysis of longitudinal multiple-source binary data. Longitudinal multiple-source binary data arise when repeated binary measurements are obtained from two or more sources, with each source providing a measure of the same underlying variable. Since the number of responses on each subject is relatively large, the empirical variance estimator performs poorly and cannot be relied on in this setting. Two methods for obtaining a parsimonious within-subject association structure are considered. An additional complication arises with estimation, since maximum likelihood estimation may not be feasible without making unrealistically strong assumptions about third- and higher order moments. To circumvent this, we propose the use of a generalized estimating equations approach. Finally, we present an analysis of multiple-informant data obtained longitudinally from a psychiatric interventional trial that motivated the model developed in the paper.     

Transformed Logit Confidence Intervals for Small Populations in Single Capture–Recapture Estimation

The good performance of logit confidence intervals for the odds ratio with small samples is well known. This is true unless the actual odds ratio is very large. In single capture–recapture estimation the odds ratio is equal to 1 because of the assumption of independence of the samples. Consequently, a transformation of the logit confidence intervals for the odds ratio is proposed in order to estimate the size of a closed population under single capture–recapture estimation. It is found that the transformed logit interval, after adding .5 to each observed count before computation, has actual coverage probabilities near to the nominal level even for small populations and even for capture probabilities near to 0 or 1, which is not guaranteed for the other capture–recapture confidence intervals proposed in statistical literature. Thus, given that the .5 transformed logit interval is very simple to compute and has a good performance, it is appropriate to be implemented by most users of the single capture–recapture method.     

Notes on Test Homogeneity of the Odds Ratio in Matched Pairs Under Stratified Sampling: A Monte Carlo Evaluation

Using Monte Carlo simulation, we compare the performance of five asymptotic test procedures and a randomized permutation test procedure for testing the homogeneity of odds ratio under the stratified matched-pair design. We note that the weighted-least-square test procedure is liberal, while Pearson's goodness-of-fit (PGF) test procedure with the continuity correction is conservative. We note that PGF without the continuity correction, the conditional likelihood ratio test procedure, and the randomized permutation test procedure can generally perform well with respect to Type I error. We use the data taken from a case–control study regarding the endometrial cancer incidence published elsewhere to illustrate the use of these test procedures.     

Statistical Inference of Adaptive Designs with Binary Responses

Adaptive designs of clinical trials are ethical alternatives when the traditional randomization becomes ethically infeasible in desperate medical situations. However, such a design creates a dependency among trial data and its statistical analysis becomes more complex than the analysis for traditional randomized clinical trials. In this article, we examine adaptive designs with dichotomous responses from two treatments and extend some commonly used statistical methods for independent data. Under a regularity condition, the estimated odds ratio and its logarithm are shown to follow asymptotically normal distributions. Moreover, the ordinary goodness-of-fit test statistic for two-by-two contingency tables with dependent data is shown to be asymptotically chi-square distributed. We also discuss the consistency of maximum likelihood estimators of the unknown parameters for a wide class of adaptive designs.     

Ranges of Measures of Association for Familial Binary Variables

Familial binary data occur in a wide range of scientific investigations. Numerous measures of association have been proposed in the literature for the study of intra-family dependence of the binary variables. These measures include correlations, odd ratios, kappa statistics, and relative risks. We study the permissible ranges of these measures of association such that a joint distribution exists for the familial binary variables. Our results are useful for developing efficient estimation methods for the measures of association.     

A simulation study of estimators of a common odds ratio in several 2 × 2 tables

For the situation of several 2 × 2 tables two approaches are presented to jackknife the well-known estimators of a common odds ratio proposed by Woolf (1955) and by Mantel and Haenszel (1959). These estimators are compared w.r.t. their bias and mean squared error by means of a Monte Carlo study for a wide range of parameters.