Logistic Mixed‐Effects Model Analysis With Pseudo‐Observations for Estimating Risk Ratios in Clustered Binary Data Analysis

ABSTRACT Logistic mixed‐effects model has been a standard multivariate analysis method for analyzing clustered binary outcome data, for example, longitudinal studies, clustered randomized trials, and multicenter/regional studies. However, the resultant odds ratio estimator cannot be directly interpreted as an effect measure, and it is only interpreted as an approximation of the risk ratio estimator when the frequency of events is small. In this article, we propose a new statistical analysis method that enables providing a risk ratio estimator in the multilevel statistical model framework. The valid risk ratio estimation is realized via augmenting pseudo‐observations to the original dataset and then analyzing the modified dataset by the logistic mixed‐effects model. The resultant estimators of fixed effect coefficients are theoretically shown to be consistent estimators of the risk ratios. Also, the standard errors and confidence intervals of the risk ratios can be calculated by the bootstrap method. All of the computations are simply implementable by using the R package “glmmrr.” We illustrate the effectiveness of the proposed method via applications to a cluster‐randomized trial of the maternal and child health handbook and a longitudinal study of respiratory disease. Also, we provide simulation‐based evidence for the accuracy and precision of estimation of risk ratios by the proposed method.