Testing Risk Difference of Two Proportions for Combined Unilateral and Bilateral Data

TL;DR

This paper develops and compares likelihood-based tests for assessing risk difference in paired unilateral and bilateral binary data, demonstrating their effectiveness through simulations and real data applications.

Contribution

It introduces three likelihood-based tests under Donner's model for combined unilateral and bilateral data, recommending the score test for practical use.

Findings

All tests control type I error well.

The tests have comparable power, with the score test being slightly more stable.

Applications show the methods' usefulness in real clinical data.

Abstract

In clinical studies with paired organs, binary outcomes often exhibit intra-subject correlation and may include a mixture of unilateral and bilateral observations. Under Donner's constant correlation model, we develop three likelihood-based test statistics (the likelihood ratio, Wald-type, and score tests) for assessing the risk difference between two proportions. Simulation studies demonstrate good control of type I error and comparable power among the three tests, with the score test showing slightly better stability. Applications to otolaryngologic and ophthalmologic data illustrate the methods. An online calculator is also provided for power analysis and risk difference testing. The score test is recommended for practical use and future studies with combined unilateral and bilateral binary data.