Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.     

塔克尔莫乎尔沙漠银沙槐群落主要植物的种间关系

根据野外调查的样地数据资料,运用2×2列联表的Fisher精确检验、Pearson相关系数和Spearman秩相关系数检验,并结合DCA排序,分析塔克尔莫乎尔沙漠银沙槐群落主要植物种群之间的种间关系。结果表明:Fisher精确检验有3个种对呈显著正关联,3个种对呈显著负关联;Pearson相关系数检验有1个种对呈显著正相关,12个种对呈显著负相关;Spearman秩相关系数检验,有14个种对存在显著相关,其中负相关13对,占所有种对数的14.29%,正相关1对,占所有种对数的1.1%。银沙槐群落种间关系相对松散,反映出植物群落随着环境变化其物种组成也发生相应变化,正向着相对稳定独立的无关联方向发展。     

Nonparametric All‐Pairs Multiple Comparisons

Nonparametric all‐pairs multiple comparisons based on pairwise rankings can be performed in the one‐way design with the Steel‐Dwass procedure. To apply this test, Wilcoxon's rank sum statistic is calculated for all pairs of groups; the maximum of the rank sums is the test statistic. We provide exact calculations of the asymptotic critical values (and P‐values, respectively) even for unbalanced designs. We recommend this asymptotic method whenever large sample sizes are present. For small sample sizes we recommend the use of the new statistic according to Baumgartner , Weiss , and Schindler (1998, Biometrics 54 , 1129–1135) instead of Wilcoxon's rank sum for the multiple comparisons. We show that the resultant procedure can be less conservative and, according to simulation results, more powerful than the original Steel‐Dwass procedure. We illustrate the methods with a practical data set.     

Properties of Statistical Tests of Neutrality for DNA Polymorphism Data

A class of statistical tests based on molecular polymorphism data is studied to determine size and power properties. The class includes TAJIMA''s D statistic as well as the D* and F* tests proposed by FU and LI. A new method of constructing critical values for these tests is described. Simulations indicate that TAJIMA''s test is generally most powerful against the alternative hypotheses of selective sweep, population bottleneck, and population subdivision, among tests within this class. However, even TAJIMA''s test can detect a selective sweep or bottleneck only if it has occurred within a specific interval of time in the recent past or population subdivision only when it has persisted for a very long time. For greatest power against the particular alternatives studied here, it is better to sequence more alleles than more sites.     

Extension of Peto's Test by Attribution of Tumor Lethality in the Absence of Cause‐of‐Death Information

A new statistical testing approach is developed for rodent tumorigenicity assays that have a single terminal sacrifice or occasionally interim sacrifices but not cause‐of‐death data. For experiments that lack cause‐of‐death data, statistically imputed numbers of fatal tumors and incidental tumors are used to modify Peto's cause‐of‐death test which is usually implemented using pathologist‐assigned cause‐of‐death information. The numbers of fatal tumors are estimated using a constrained nonparametric maximum likelihood estimation method. A new Newton‐based approach under inequality constraints is proposed for finding the global maximum likelihood estimates. In this study, the proposed method is concentrated on data with a single sacrifice experiment without implementing further assumptions. The new testing approach may be more reliable than Peto's test because of the potential for a misclassification of cause‐of‐death by pathologists. A Monte Carlo simulation study for the proposed test is conducted to assess size and power of the test. Asymptotic normality for the statistic of the proposed test is also investigated. The proposed testing approach is illustrated using a real data set.     

A Modified Exact Test for 2 × 2 Contingency Tables

A modified exact test is proposed for 2×2 contingency tables. This test, which is based on a less conservative definition of the concept of significance (STONE, 1969) is compared with a modified form of Pearson's X² test and with Tocher's randomized exact (UMPU) test. The sizes of the new test lie near the nominal 0.05 levels while those of the X² test usually exceed the nominal level, sometimes by a factor of 2 or more. The power of the modified test is usually close to that of the UMPU test.     

Exact,Distribution Free Confidence Intervals for Late Effects in Censored Matched Pairs

When comparing censored survival times for matched treated and control subjects, a late effect on survival is one that does not begin to appear until some time has passed. In a study of provider specialty in the treatment of ovarian cancer, a late divergence in the Kaplan–Meier survival curves hinted at superior survival among patients of gynecological oncologists, who employ chemotherapy less intensively, when compared to patients of medical oncologists, who employ chemotherapy more intensively; we ask whether this late divergence should be taken seriously. Specifically, we develop exact, permutation tests, and exact confidence intervals formed by inverting the tests, for late effects in matched pairs subject to random but heterogeneous censoring. Unlike other exact confidence intervals with censored data, the proposed intervals do not require knowledge of censoring times for patients who die. Exact distributions are consequences of two results about signs, signed ranks, and their conditional independence properties. One test, the late effects sign test, has the binomial distribution; the other, the late effects signed rank test, uses nonstandard ranks but nonetheless has the same exact distribution as Wilcoxon's signed rank test. A simulation shows that the late effects signed rank test has substantially more power to detect late effects than do conventional tests. The confidence statement provides information about both the timing and magnitude of late effects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Multistage Procedure for Analyzing Unreplicated Factorial Experiments

A multistage procedure, which is based on the likelihood principle, is proposed to identify active effects in unreplicated factorial designs and their fractions. The proposed procedure controls the experimental error rate (EER) at any prespecified level in industrial and biomedical experiments. Extensive comparison with Lenth 's (1989) test is discussed.     

Verifying zero-infestation in pest control: A simple sequential test based on the succession of zero-samples

A simple sequential test based on the succession of ‘zero's or uninfested sampling units is proposed for use in verifying zero-infestation in pest control surveys. The method is applicable efficiently to both finite and infinite populations. Problems concerning its efficiency on application are discussed.     

Statistical Basis for Predicting Technological Progress

Forecasting technological progress is of great interest to engineers, policy makers, and private investors. Several models have been proposed for predicting technological improvement, but how well do these models perform? An early hypothesis made by Theodore Wright in 1936 is that cost decreases as a power law of cumulative production. An alternative hypothesis is Moore''s law, which can be generalized to say that technologies improve exponentially with time. Other alternatives were proposed by Goddard, Sinclair et al., and Nordhaus. These hypotheses have not previously been rigorously tested. Using a new database on the cost and production of 62 different technologies, which is the most expansive of its kind, we test the ability of six different postulated laws to predict future costs. Our approach involves hindcasting and developing a statistical model to rank the performance of the postulated laws. Wright''s law produces the best forecasts, but Moore''s law is not far behind. We discover a previously unobserved regularity that production tends to increase exponentially. A combination of an exponential decrease in cost and an exponential increase in production would make Moore''s law and Wright''s law indistinguishable, as originally pointed out by Sahal. We show for the first time that these regularities are observed in data to such a degree that the performance of these two laws is nearly the same. Our results show that technological progress is forecastable, with the square root of the logarithmic error growing linearly with the forecasting horizon at a typical rate of 2.5% per year. These results have implications for theories of technological change, and assessments of candidate technologies and policies for climate change mitigation.     

The Determination of Sample Sizes in the Comparison of Two Multinomial Proportions from Ordered Categories

We consider sample size determination for ordered categorical data when the alternative assumption is the proportional odds model. In this paper the sample size formula proposed by Whitehead (Statistics in Medicine, 12 , 2257–2271, 1993) is compared with the methods based on exact and asymptotic linear rank tests with Wilcoxon and trend scores. We show that Whitehead's formula, which is based on a normal approximation, works well when the sample size is moderate to large but recommend the exact method with Wilcoxon scores for small sample sizes. The consequences of misspecification in models are also investigated.     

Some Simple Statistics to Test Against Ordered Alternatives in Complete Block Designs

Consider testing the hypothesis of no treatment effects against a postulated ranking of the m treatments, given data from n Complete Blocks. A suitable test statistic is the weighted average rank correlation w = σb_QiC_i where C_i is the correlation between the postulated ranking and the ranking observed within the ith block, Q_i is the rank of the ith block with respect to credibility, and the b_i's are weights such that 0 ≦ b¹ ≦ … ≦ bn. In this paper we introduce some simple statistics: the first extends the signed-rank statistic to m ≦ 3, the second uses a simple measure of correlation based on the antirank, and the third a statistic based on Spearman's footrule. Tables for critical values are provided and the normal approximation is investigated.     

Tests for Trend in Binary Response

Tests for trend are important in analyzing data where the binary response in ordered categories is of interest. An example is in toxicology where the response in various dose groups is observed. For testing an association between the dose and the response the approach from Cochran and Armitage is widely used. However the result of this test is highly dependent on the scores assigned to the dose groups. Various dose assignments can lead to different outcomes. As an alternative the isotonic regression, a nonparametric method, is proposed. The outcome of this approach is independent of the quantification of the dose. Both methods (Cochran‐Armitage test and isotonic regression) are compared within a simulation study to an isotonic version of the Pearson's Chi‐squared test and the Wilcoxon rank sum test.     

Tests for Homogeneity of Variances Using Robust Weighted Likelihood Estimates

The classical normal-theory tests for testing the null hypothesis of common variance and the classical estimates of scale have long been known to be quite nonrobust to even mild deviations from normality assumptions for moderate sample sizes. Levene (1960) suggested a one-way ANOVA type statistic as a robust test. Brown and Forsythe (1974) considered a modified version of Levene's test by replacing the sample means with sample medians as estimates of population locations, and their test is computationally the simplest among the three tests recommended by Conover , Johnson , and Johnson (1981) in terms of robustness and power. In this paper a new robust and powerful test for homogeneity of variances is proposed based on a modification of Levene's test using the weighted likelihood estimates (Markatou , Basu , and Lindsay , 1996) of the population means. For two and three populations the proposed test using the Hellinger distance based weighted likelihood estimates is observed to achieve better empirical level and power than Brown-Forsythe's test in symmetric distributions having a thicker tail than the normal, and higher empirical power in skew distributions under the use of F distribution critical values.     

Comparison of adjustment methods for stratified two‐sample tests in the context of ROC analysis

We compare several nonparametric and parametric weighting methods for the adjustment of the effect of strata. In particular, we focus on the adjustment methods in the context of receiver‐operating characteristic (ROC) analysis. Nonparametrically, rank‐based van Elteren's test and inverse‐variance (IV) weighting using the area under the ROC curve (AUC) are examined. Parametrically, the stratified t‐test and IV AUC weighted method are applied based on a binormal monotone transformation model. Stratum‐specific, pooled, and adjusted estimates are obtained. The pooled and adjusted AUCs are estimated. We illustrate and compare these weighting methods on a multi‐center diagnostic trial and through extensive Monte‐Carlo simulations.     

A Comparison between the LEHMACHER & WALL Rank Tests and Pyhel's Permutation Test for the Analysis of r Independent Samples of Response Curves

LEHMACHER & WALL'S (1978) example of the application of a rank test for the comparison of two independent samples of response curves is reanalyzed by PYHEL'S (1980) permutation test for the hypothesis of parallelism of response curves. This permutation test is part of a complete evaluation of effects for a split-plot design using the permutation test based procedure by WILLMES & PYHEL (1981). Differences in test decisions are discussed.     

An Extended Class of Ranking Models

A further enlargement of the class of generalized Mallow's ranking models considered by Fligner and Verducci is proposed. Included in this enlarged class are rank probability distributions other than the uniform that lead to symmetric distributions for many of the common measures used to assess distances between rankings. A particular application to the standard Kendall distance is illustrated in more detail.     

An enhanced quantile approach for assessing differential gene expressions

Summary .   Due to the small number of replicates in typical gene microarray experiments, the performance of statistical inference is often unsatisfactory without some form of information-sharing across genes. In this article, we propose an enhanced quantile rank score test (EQRS) for detecting differential expression in GeneChip studies by analyzing the quantiles of gene intensity distributions through probe-level measurements. A measure of sign correlation, δ, plays an important role in the rank score tests. By sharing information across genes, we develop a calibrated estimate of δ, which reduces the variability at small sample sizes. We compare the EQRS test with four other approaches for determining differential expression: the gene-specific quantile rank score test, the quantile rank score test assuming a common δ, a modified t -test using summarized probe-set-level intensities, and the Mack–Skillings rank test on probe-level data. The proposed EQRS is shown to be favorable for preserving false discovery rates and for being robust against outlying arrays. In addition, we demonstrate the merits of the proposed approach using a GeneChip study comparing gene expression in the livers of mice exposed to chronic intermittent hypoxia and of those exposed to intermittent room air.     

A Robust Test for Multi-Sample Location Problems with Unequal Group Variances and Nonnormality

A robust test (to be referred to as M^* test) is proposed for testing equality of several group means without assuming normality and equality of variances. This test statistic is obtained by combining Tiku's MML robust procedure with the James statistic. Monte Carlo simulation studies indicate that the M^* test is more powerful than the Welch test, the James test, and the tests based on Huber's M-estimators over a wide range of nonnormal universes. It is also more powerful than the Brown and Forsythe test under most of nonnormal distributions and has substantially the same power as the Brown and Forsythe test under normal distribution. Comparing with Tan-Tabatabai test, M^* is almost as powerful as Tan-Tabatabai test.     

Raynaud's phenomenon and thermal entrainment: an objective test.

A new objective test for diagnosing Raynaud''s phenomenon was assessed in practice. The test is based on entrainment of the thermal vasomotor control system and entails non-invasive measurement of blood-flow responses in one hand while alternating thermal stimuli are applied to the contralateral hand. A significant (p less than 0.001) abnormality of vasomotor control was found in patients with Raynaud''s phenomenon compared with normal subjects. When applied clinically this test is diagnostic and indicates the severity of the disease and the effect of treatment.