Extension of the Wilcoxon-Mann-Whitney Test to Samples Censored at the Same Fixed Point

Halperin, Max

doi:10.1080/01621459.1960.10482053

Cited by 66 publications

(28 citation statements)

References 6 publications

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“…Here, P is simply the ranking of the n1 + n2 observations. If there are no ties and all censored observations occur after the (n1 + n2-rl-r2)th failure, i.e.ml =... = Ms = 1, 11 = S.. = l1 = 0, Is = rl+r2,ands = n1+n2-rr-r2wehave (n, + n2) (n-+ n2-1) {(n1 + n2) (r1 + r2) + 1[(n1 + n--)2 -which is that expected from the relation between W and the U, of Halperin (1960). Hemelrijk (1952) has given a formula for the variance of the Mann-Whitney statistic, U', allowing for ties.…”

Section: The Conditional Mean and Variance Of Wmentioning

confidence: 81%

“…Halperin (1960), for his case, has stated that when n1 = n2 = 8 the asymptotic normal theory is adequate for all practical purposes up to about 75 % censoring (no tying) at both the 5 and 1 % significance levels. Lehman (1961) considered the exact and approximate distributions of the Wilcoxon statistic when n1 = n2 = 5 for five cases of varying degrees of tying.…”

Section: Loss Rate Different In the Two Groupsmentioning

confidence: 97%

“…The last is also true when ties are present. When all censored observations have the value T, Halperin's (1960) statistic U, is defined by…”

Section: The W Statistic and Relation To Other Statisticsmentioning

confidence: 99%

“…The test is conditional on the given pattern of failures and censored observations. Halperin (1960) and Rao, Savage & Sobel (1960) have considered two-sample tests with censoring, though all assume that times to censoring are the same in both samples. Recently, Alling (1963) has proposed a modified Wilcoxon test to be calculated sequentially so that an early decision may possibly be reached.…”

Section: Introductionmentioning

confidence: 98%

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A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples

Gehan¹

1965

Biometrika

660

663

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Section: The Conditional Mean and Variance Of Wmentioning

confidence: 81%

Section: Loss Rate Different In the Two Groupsmentioning

confidence: 97%

“…The last is also true when ties are present. When all censored observations have the value T, Halperin's (1960) statistic U, is defined by…”

Section: The W Statistic and Relation To Other Statisticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples

Gehan¹

1965

Biometrika

660

663

View full text Add to dashboard Cite

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“…The statistical model and approach of this article constitute a fairly straightforward generalization of work by Halperin (1960), in which he assumed that one had independent samples of size N , ( i = 1, 2) where the sample of size N , consistcd of iid random variables distributed according to O l x < t ,…”

Section: Background and Outline Of Derivation Of Parameter-free Distrmentioning

confidence: 99%

Conditional Distribution-Free Tests for the Two-Sample Problem in the Presence of Right Censoring

Halperin

Ware

1980

Journal of the American Statistical Association

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Two-sample rank tests for survival data in the presence of arbitrary right censoring are considered. We distinguish between administrative censoring, arising because survival study participants do not enter as a cohort, and censoring due to "loss to follow-up." We show how conditionally distribution-free tests can be constructed in certain situations. Conditional versions of the generalized Wilcoxon and Mantel statistics are shown to be asymptotically normal in the conditional reference set, but with modified means and variances. Efficiency of these tests relative to asymptotically distribution-free competitors is unity, providing the censoring distributions are discrete, the same for both samples, and providing loss-to-follow-up (LFU) distributions are the same for the two samples. When these assumptions do not hold, efficiency can deteriorate considerably, being poorest, other things being equal, when the censoring distribution is continuous.

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Clinical Trials, Early Cancer and Heart Disease

Schneiderman¹,

Gehan

2005

Encyclopedia of Biostatistics

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Early developments in controlled clinical trials at the National Institutes of Health (NIH) took place mainly at the National Cancer Institute (NCI) and what was then the National Heart Institute (NHI) (subsequently the National Heart, Lung, and Blood Institute (NHLBI))beginning in the 1950s. This article reviews the developments from the early 1950s to the late 1960s at both institutes, summarizing the early efforts in clinical trials, the organizations set up to conduct and monitor the clinical trials, and the developments in statistical methodology that have formed the basis for conducting many of the present day randomized controlled trials. The early history of clinical trials at these institutes has been reviewed in more detail at NCI by Gehan & Schneiderman and at NHLBI by Halperin et al.

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Extension of the Wilcoxon-Mann-Whitney Test to Samples Censored at the Same Fixed Point

Cited by 66 publications

References 6 publications

A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples

A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples

Conditional Distribution-Free Tests for the Two-Sample Problem in the Presence of Right Censoring

Clinical Trials, Early Cancer and Heart Disease

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