Interval estimation of relative risks for combined unilateral and bilateral correlated data.

Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

Fast QLB algorithm and hypothesis tests in logistic model for ophthalmologic bilateral correlated data.

In ophthalmologic or otolaryngologic studies, bilateral correlated data often arise when observations involving paired organs (e.g., eyes, ears) are measured from each subject. Based on Donner's model , in this paper, we focus on investigating the relationship between the disease probability and covariates (such as ages, weights, gender, and so on) via the logistic regression for the analysis of bilateral correlated data. We first propose a new minorization-maximization (MM) algorithm and a fast quadratic lower bound (QLB) algorithm to calculate the maximum likelihood estimates of the vector of regression coefficients, and then develop three large-sample tests (i.e., the likelihood ratio test, Wald test, and score test) to test if covariates have a significant impact on the disease probability. Simulation studies are conducted to evaluate the performance of the proposed fast QLB algorithm and three testing methods. A real ophthalmologic data set in Iran is used to illustrate the proposed methods.

Common risk difference test and interval estimation of risk difference for stratified bilateral correlated data.

Bilateral correlated data are often encountered in medical researches such as ophthalmologic (or otolaryngologic) studies, in which each unit contributes information from paired organs to the data analysis, and the measurements from such paired organs are generally highly correlated. Various statistical methods have been developed to tackle intra-class correlation on bilateral correlated data analysis. In practice, it is very important to adjust the effect of confounder on statistical inferences, since either ignoring the intra-class correlation or confounding effect may lead to biased results. In this article, we propose three approaches for testing common risk difference for stratified bilateral correlated data under the assumption of equal correlation. Five confidence intervals of common difference of two proportions are derived. The performance of the proposed test methods and confidence interval estimations is evaluated by Monte Carlo simulations. The simulation results show that the score test statistic outperforms other statistics in the sense that the former has robust type I error rates with high powers. The score confidence interval induced from the score test statistic performs satisfactorily in terms of coverage probabilities with reasonable interval widths. A real data set from an otolaryngologic study is used to illustrate the proposed methodologies.