Using ranked set sampling with binary outcomes in cluster randomized designs

Abstract

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

Empirical likelihood inference for area under the receiver operating characteristic curve using ranked set samples

“…Various topics have been studied on RSS such as distribution functions, 11 nonparametric two-sample tests, 12,13 and rank regression. 14 In the past decade, RSS has been applied to diverse areas including agriculture, 15,16,17,18,19 education, 20 engineering, 21 environment, 22,23 public health, 24,25,26,27,28 and medicine. 29,27 The main theme of this paper is the inference on the AUC based on EL when data are obtained from RSS.…”

Statistical Inference from Partially Nominated Sets: An Application to Estimating the Prevalence of Osteoporosis

“…These include, among others, the estimation of the population mean (Takahasi and Wakitomo, 1968;Ozturk, 2011;Frey, 2012;Frey and Feeman, 2016), the CDF (Stokes and Sager, 1988;Samawi and Al-Sagheer, 2001;Duembgen and Zamanzade, 2020), the population proportion (Chen et al, 2005;Zamanzade and Mahdizadeh, 2017;Omidvar et al, 2018;Frey andZhang, 2019, 2021), perfect ranking tests (Frey et al, 2007;Frey and Zhang, 2017;Frey andWang, 2013, 2014), odds ratio (Samawi and Al-Saleh, 2013), logistic regression (Samawi and Al-Saleh, 2013;Samawi et al, , 2018? ), the Youden index , parameter estimation (Chen et al, 2018(Chen et al, , 2019He et al, 2020He et al, , 2021Qian et al, 2021), randomized cluster design (Ahn et al, 2017;Wang et al, 2016Wang et al, , 2017Wang et al, , 2020 and statistical control quality charts (Al-Omari and Haq, 2011;Haq et al, 2013;.…”

Empirical Likelihood Inference for Area under the ROC Curve using Ranked Set Samples

“…Various topics have been studied on ranked set samples such as distribution functions (Stokes and Sager, 1988), nonparametric two-sample tests Wolfe, 1992, 1994), and rank regression (Ozturk, 2002). In the past decade, research effort remains abundant in RSS, e.g., Ozturk (2012); Hatefi et al (2015); Wang et al (2016); Frey and Zhang (2017); Ghosh et al (2017); Omidvar et al (2018); Ozturk (2018); Frey (2019); Frey and Zhang (2019); Li et al (2019); Ozturk (2019); Dümbgen and Zamanzade (2020); Hatefi et al (2020); Wang et al (2020); Zamanzade and Mahdizadeh (2020). For detailed reviews of RSS, see Chen et al (2004), Wolfe (2012), and references therein.…”