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Using ranked set sampling with binary outcomes in cluster randomized designs

We study the use of ranked set sampling (RSS) with binary outcomes in cluster‐randomized designs (CRDs), where a generalized linear mixed model (GLMM) is used to model the hierarchical data structure involved. Under the GLMM‐based framework, we propose three different approaches to estimate the treatment effect, including the nonparametric (NP), maximum likelihood (ML) and pseudo likelihood (PL) estimators. We investigate their asymptotic properties and examine their finite‐sample performance via simulation. Based on these three RSS estimators, we further develop procedures for testing the existence of the treatment effect. We examine the power and size of our proposed RSS tests and compare them with existing tests based on simple random sampling (SRS). All the proposed RSS estimation and test methods are illustrated with two data examples, one for rare events and the other for non‐extreme events. Throughout our investigations, we also consider the possible effect of imperfect ranking. Among the proposed methods, we provide recommendations on whether to use RSS rather than SRS with binary outcomes in CRDs and, if yes, when to use which RSS method. The Canadian Journal of Statistics 48: 342–365; 2020 © 2019 Statistical Society of Canada