Statistical inference for P(X&lt;Y)

a b s t r a c tIn this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve. By applying the standard empirical likelihood method for a mean to the jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure is easy to implement. Wilks' theorem for the empirical likelihood ratio statistic is proved and a simulation study is conducted to compare the performance of the proposed method with other methods.

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“…For some inference problems related to the ROC curve see, e.g., [10,11]. Using the fact that √ m + n{R m,n (t) − R(t)} d → N(0, σ 2 (t)),…”

Section: Introductionmentioning

confidence: 99%

Smoothed jackknife empirical likelihood method for ROC curve

Gong

Peng

2010

Journal of Multivariate Analysis

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“…4, No. 3 DOI: 10.1080/19466315.2011 and Hanson 1964;Downton 1973;Reiser and Guttman 1986;McGraw and Wong 1992;Senn 1997;Acion, Peterson, Temple, and Arndt 2006;Newcombe 2006;Zhou 2008;Jing, Yuan, and Zhou 2009) for a distributional comparison of two groups. In addition to probabilistic indices, a category of analytic methods for comparing groups beyond traditional contrast analysis is the use of certain parameters or statistics to capture the ratio of mean and variability of values in groups, which includes various effect sizes similar to standardized mean differences (Cohen 1962;Glass 1976;Hedges 1981;Rosenthal, Rosnow, and Rubin 2000;Huberty 2002;Timm 2004;Zhang 2007a,b).…”

Section: Introductionmentioning

confidence: 99%

Contrast Variable for Group Comparisons in Biopharmaceutical Research

Zhang

Heyse

2012

Statistics in Biopharmaceutical Research

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Group comparisons can be conducted at three levels: (1) group means, (2) both group means and variabilities, and (3) group distributions. A traditional contrast is defined as a linear combination of group means; thus, traditional contrast analysis may only effectively address group comparisons in the first level. The concept of a contrast variable has recently been proposed. A contrast variable is defined as a linear combination of random variables (each variable representing random values in a group) instead of group means. Based on a contrast variable, we can use the mean of a contrast to address questions on group comparisons at the first level as in traditional contrast analysis. Meanwhile, we can use the ratio of mean to standard deviation of a contrast variable, that is, standardized mean of a contrast variable (SMCV), to effectively address questions at the second level. We can further use the probability that a contrast variable obtains a positive value, that is, c + -probability, to effectively address questions at the third level. In this article, we explore the use of contrast variable, SMCV, and c + -probability for comparing multiple groups in biopharmaceutical studies. Contrast variable, c + -probability, and SMCV are applicable in a comparison context with or without independence and with or without homoscedasticity.

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“…Recently, Hauck et al (2000) introduced the use of P X > Y in clinical trials as an alternative way of describing treatment effects, namely, the generalized treatment effect, and considered a method for confidence interval estimation of P X > Y with normally distributed outcomes. Zhou (2007) makes inference about P X > Y through the Edgeworth expansions and the bootstrap approximations of Studentized Wilcoxon-Mann-Whitney statistics. Tian (2008) compared a large sample approach, a generalized variable approach and a bootstrap approach for confidences interval estimation of generalized treatment effects in linear models.…”

Section: Introductionmentioning

confidence: 99%

Testing Equality of Generalized Treatment Effects

Tian

Yan

2012

Journal of Biopharmaceutical Statistics

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Recently, the concept of generalized treatment effect, defined as P(X > Y) where X and Y denote continuous outcome variables for treatment arm and control arm, respectively, has been proposed as an appropriate measure of treatment effect in clinical trials with parallel design. Compared to the mean difference, the generalized treatment effect has many advantages; for example, it is a scaleless measure and it does not change under monotonic transformations. This article investigates the problem of testing equality of generalized treatment effects among several clinical trials. The proposed approach follows the same vein as the generalized variable method for testing equality of several log-normal means proposed by Li (2009). Numerical study demonstrates that the proposed test has excellent type I error control for clinical trials with small to medium sample sizes. Robustness study shows that the proposed method performs reasonably for categorical data.

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Statistical inference for P(X<Y)

Abstract: Let X and Y be two independent continuous random variables. We make statistical inference about theta=P(X

Cited by 56 publications

References 39 publications

Smoothed jackknife empirical likelihood method for ROC curve

Smoothed jackknife empirical likelihood method for ROC curve

Contrast Variable for Group Comparisons in Biopharmaceutical Research

Testing Equality of Generalized Treatment Effects

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