Testing homogeneity for multiple nonnegative distributions with excess zero observations

Wang, Chunlin; Marriott, Paul; Li, Pengfei

doi:10.1016/j.csda.2017.04.011

Cited by 19 publications

(32 citation statements)

References 31 publications

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“…The DRM has been investigated extensively because of its flexibility and efficiency. For example, it has been applied to multiple-sample hypothesis-testing problems (Fokianos et al, 2001;Cai et al, 2017;Wang et al, 2017Wang et al, , 2018 and quantile and quantile-function estimation (Zhang, 2000;. These inference problems can be viewed as special cases, without auxiliary information, of the first goal to be achieved in this paper.…”

Section: Literature Reviewmentioning

confidence: 99%

Semiparametric empirical likelihood inference with estimating equations under density ratio models

Yuan¹,

Li²,

Wu³

2021

Preprint

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The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or additional auxiliary information expressed as estimating equations. We examine the asymptotic properties of the maximum empirical likelihood estimators (MELEs) of the unknown parameters in the DRMs and/or defined through estimating equations, and establish the chi-square limiting distributions for the empirical likelihood ratio (ELR) statistics. We show that the asymptotic variance of the MELEs of the unknown parameters does not decrease if one estimating equation is dropped. Similar properties are obtained for inferences on the cumulative distribution function and quantiles of each of the populations involved. We also propose an ELR test for the validity and usefulness of the auxiliary information. Simulation studies show that correctly specified estimating equations for the auxiliary information result in more efficient estimators and shorter confidence intervals. Two real-data examples are used for illustrations.

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Section: Literature Reviewmentioning

confidence: 99%

Semiparametric empirical likelihood inference with estimating equations under density ratio models

Yuan¹,

Li²,

Wu³

2021

Preprint

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“…The DRM is also closely connected with several classical statistical models, such as parametric exponential family, logistic regression and biased sampling . The DRM has been found successful in various multisample inference problems . In the next section, we apply the empirical likelihood method to develop a semiparametric test for H 0 under the above models and .…”

Section: The Bootstrap Semiparametric Homogeneity Testmentioning

confidence: 99%

A bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data, with applications to analysis of quality of life outcomes in clinical trials

Wang

2020

Statistics in Medicine

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This article is concerned about the test for the difference in the distributions of multigroup proportional data, which is motivated by the problem of comparing the distributions of quality of life (QoL) outcomes among different treatment groups in clinical trials. The proportional data, such as QoL outcomes assessed by answers to questions on a questionnaire, are bounded in a closed interval such as [0, 1] with continuous observations in (0, 1) and, in addition, excess observations taking the boundary values 0 and/or 1. Common statistical procedures used in practice, such as t-and rank-based tests, may not be very powerful since they ignore the specific feature of the proportional data. In this article, we propose a three-component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in (0, 1). A semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi-squared random variable under null hypothesis. A nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test. Simulation studies are performed to evaluate the empirical type I error and power of the proposed test procedure and compare it with likelihood ratio tests (LRTs) under parametric distribution assumptions, rank-based Kruskal-Wallis test, and Wald-type test.The proposed test procedure is also applied to the analysis of QoL outcomes from a clinical trial on colorectal cancer that motivated our study. K E Y W O R D S bootstrap, Box-Cox transformation, density ratio model, proportional data, semiparametric empirical likelihood, zero-and/or-one-inflation Statistics in Medicine. 2020;39:1715-1731.wileyonlinelibrary.com/journal/sim

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“…Later on, Wan & Zhang (2008) and Zhang & Zhang (2014) considered the inference problems for the difference of AUCs for two correlated ROC curves under a DRM. Other applications of DRMs include multiple‐sample hypothesis‐testing problems (Cai, Chen, & Zidek, 2017; Wang, Marriott, & Li, 2017a, 2018), quantile and quantile function estimation (Chen & Liu 2013), and dominance index estimation (Zhuang, Hu, & Chen, 2019). More detailed reviews can be found in Wang (2017).…”

Section: Introductionmentioning

confidence: 99%

Semiparametric inference of the Youden index and the optimal cut‐off point under density ratio models

Yuan

2021

Can J Statistics

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The Youden index is a popular summary statistic for receiver operating characteristic curves. It gives the optimal cut‐off point of a biomarker to distinguish the diseased and healthy individuals. In this article, we model the distributions of a biomarker for individuals in the healthy and diseased groups via a semiparametric density ratio model. Based on this model, we propose using the maximum empirical likelihood method to estimate the Youden index and the optimal cut‐off point. We further establish the asymptotic normality of the proposed estimators and construct valid confidence intervals for the Youden index and the corresponding optimal cut‐off point. The proposed method automatically covers both cases when there is no lower limit of detection (LLOD) and when there is a fixed and finite LLOD for the biomarker. Extensive simulation studies and a real data example are used to illustrate the effectiveness of the proposed method and its advantages over the existing methods.

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Testing homogeneity for multiple nonnegative distributions with excess zero observations

Cited by 19 publications

References 31 publications

Semiparametric empirical likelihood inference with estimating equations under density ratio models

Semiparametric empirical likelihood inference with estimating equations under density ratio models

A bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data, with applications to analysis of quality of life outcomes in clinical trials

Semiparametric inference of the Youden index and the optimal cut‐off point under density ratio models

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