Testing the Equality of Proportions for Combined Unilateral and Bilateral Data

TL;DR

This paper extends existing methods for testing the equality of proportions to datasets that include both unilateral and bilateral data, proposing a score test that performs well in simulations and real clinical trial data.

Contribution

It introduces a new testing procedure based on likelihood estimates for combined unilateral and bilateral data, improving upon previous methods.

Findings

Score test maintains proper type I error rates.

Score test exhibits high power in simulations.

Application demonstrated in a clinical trial.

Abstract

Measurements are generally collected as unilateral or bilateral data in clinical trials or observational studies. For example, in ophthalmologic studies, statistical tests are often based on one or two eyes of an individual. For bilateral data, recent literatures have shown some testing procedures that take into account the intra-class correlation between two eyes of the same person. Ma et al. (2015) investigated three testing procedures under Rosner's model. In this paper, we extend Ma's work for bilateral data to combined bilateral and unilateral data. The proposed procedures are based on the likelihood estimate algorithm derived from the root of 4th order polynomial equations and fisher scoring iterations. Simulation studies are performed to compare the testing procedures under different parameter configurations. The result shows that score test has satisfactory type I error rates and powers. Therefore, we recommend score test for testing the equality of proportions. We illustrate the application of the proposed methods with a double-blind randomized clinical trial.