Interval Estimation of Relative Risks for Combined Unilateral and Bilateral Correlated Data

TL;DR

This paper develops and evaluates three confidence intervals for estimating relative risks from combined unilateral and bilateral correlated data, with a focus on ophthalmology and medical studies, using maximum likelihood estimates and simulation studies.

Contribution

It introduces three new confidence intervals for relative risk in combined correlated data, based on maximum likelihood and Fisher scoring, with comprehensive performance evaluation.

Findings

Score confidence interval controls coverage probability well.

Proposed methods outperform existing approaches in simulations.

Recommended score interval for practical applications.

Abstract

Measurements are generally collected as unilateral or bilateral data in clinical trials 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.