Comparing Survival Curves Using Rank Tests

Survival times of patients can be compared using rank tests in various experimental setups, including the two-sample case and the case of paired data. Attention is focussed on two frequently occurring complications in medical applications: censoring and tail alternatives. A review is given of the author's recent work on a new and simple class of censored rank tests. Various models for tail alternatives are discussed and the relation to censoring is demonstrated.     

A Test of Equality of Survival Distributions for Two Sample Censored Grouped Survival Data

A common testing problem for a life table or survival data is to test the equality of two survival distributions when the data is both grouped and censored. Several tests have been proposed in the literature which require various assumptions about the censoring distributions. It is shown that if these conditions are relaxed then the tests may no longer have the stated properties. The maximum likelihood test of equality when no assumptions are made about the censoring marginal distributions is derived. The properties of the test are found and it is compared to the existing tests. The fact that no assumptions are required about the censoring distributions make the test a useful initial testing procedure.     

Formulas for the Computation of the WILCOXON Test and other Rank Statistics

A simple program for the computation of the WILCOXON test is introduced, which is suitable for implementation on a programmable desk computer. The allocation of ranks R_i is not necessary (see BERCHTOLD, 1979). In an analogous manner any ranks respectively rank sums also can be calculated, so that any test criterion or statistical estimate called rank statistic, may be completely constituted by computer programs without explicitely ranging of values.     

Permutation‐based inference for the AUC: A unified approach for continuous and discontinuous data

We investigate rank‐based studentized permutation methods for the nonparametric Behrens–Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner‐Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation‐based range‐preserving confidence intervals. Extensive simulation studies show that the permutation‐based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application.     

Orthogonal Components of the Kruskal-Wallis and Related K-sample Linear Rank Statistics

It is shown that the KRUSKAL -WALLIS statistic may be decomposed into components designed to detect trends in the underlying distributions. Extensions to other K sample linear rank statistics and to nonparametric regression statistics are noted.     

Using Weighted Kaplan-Meier Statistics in Nonparametric Comparisons of Paired Censored Survival Outcomes

This research introduces methods for nonparametric testing of weighted integrated survival differences in the context of paired censored survival designs. The current work extends work done by Pepe and Fleming (1989, Biometrics 45, 497-507), which considered similar test statistics directed toward independent treatment group comparisons. An asymptotic closed-form distribution of the proposed family of tests is presented, along with variance estimates constructed under null and alternative hypotheses using nonparametric maximum likelihood estimates of the closed-form quantities. The described method allows for additional information from individuals with no corresponding matched pair member to be incorporated into the test statistic in sampling scenarios where singletons are not prone to selection bias. Simulations presented over a range of potential dependence in the paired censored survival data demonstrate substantial power gains associated with taking into account the dependence structure. Consequences of ignoring the paired nature of the data include overly conservative tests in terms of power and size. In fact, simulation results using tests for independent samples in the presence of positive correlation consistently undershot both size and power targets that would have been attained in the absence of correlation. This additional worrisome effect on operating characteristics highlights the need for accounting for dependence in this popular family of tests.     

Maximally Selected Rank Statistics for Dose‐Response Problems

We consider the bivariate situation of some quantitative, ordinal, binary or censored response variable and some quantitative or ordinal exposure variable (dose) with a hypothetical effect on the response. Data can either be the outcome of a planned dose‐response experiment with only few dose levels or of an observational study where, for example, both exposure and response variable are observed within each individual. We are interested in testing the null hypothesis of no effect of the dose variable vs. a dose‐response function depending on an unknown ‘threshold’ parameter. The variety of dose‐response functions considered ranges from no observed effect level (NOEL) models to umbrella alternatives. Here we discuss generalizations of the method of Lausen & Schumacher (Biometrics, 1992, 48, 73–85)which are based on combinations of two‐sample rank statistics and rank statistics for trend. Our approach may be seen as a generalization of a proposal for change‐point problems. Using the approach of Davies (Biometrika, 1987, 74, 33–43)we derive and approximate the asymptotic null distribution for a large number of thresholds considered. We use an improved Bonferroni inequality as approximation for a small number of thresholds considered. Moreover, we analyse the small sample behaviour by means of a Monte‐Carlo study. Our paper is illustrated by examples from clinical research and epidemiology.     

西南区玉米品种的产量性能及稳定性评价的秩次分析法

用秩次分析法分别对参加2003-2005年中国西南区玉米区域试验1组和2组的各品种进行产量性能和稳产性评价.结果表明,1组25个品种中中单808、渝单8号和遵玉8号表现高产且稳定性强,辽127和YA04273表现高产但稳定性中等.2组29个品种中DH3831、GM4095和鑫丰1号表现高产且稳定性强,承玉15、东4243、X1152A、DH3838、DH3632和奥试3202表现高产但稳定性中等.其中,中单808、渝单8号、遵玉8号、辽127、DH3831、东4243、X1152A、DH3838、DH3632和奥试3202这些品种分别在2004年和2005年通过国家审定,在实践上证明秩次分析法能客观、公正地对品种的产量性能和稳定性进行评价.建议用加权法计算品种秩次平均数和秩次方差的平均数、标准差和50%置信度的置信下限和置信上限.     

Parameters Estimation in a Simple Linear Regression Using Rank Set Sampling

Ranked set sampling (RSS) as suggested by MCINTYRE (1952) and TAKAHASI and WAKIMOTO (1968) may be used to estimate the parameters of the simple regression line. The objective is to use the RSS method to increase the efficiency of the estimators relative to the simple random sampling (SRS) method. Estimators of the slope and intercept are considered. Computer simulated results are given, and an example using real data presented to illustrate the computations.     

Estimating errors and confidence intervals for branch lengths in phylogenetic trees by a bootstrap approach

A method, based on the bootstrap procedure, is proposed for the estimation of branch-length errors and confidence intervals in a phylogenetic tree for which equal rates of substitution among lineages do not necessarily hold. The method can be used to test whether an estimated internodal distance is significantly greater than zero. In the application of the method, any estimator of genetic distances, as well as any tree reconstruction procedure (based on distance matrices), can be used. Also the method is not limited by the number of species involved in the phylogenetic tree. An example of the application of the method in the reconstruction of the phylogenetic tree for the four hominoid species—human, chimpanzee, gorilla, and orangutan—is shown. Correspondence to: J. Dopazo     

The Highest Confidence Density Region and Its Usage for Joint Inferences about Constrained Parameters

Summary Suppose that we are interested in making joint inferences about a set of constrained parameters. Confidence regions for these parameters are often constructed via a normal approximation of the distribution of a consistent estimator for a transformation of the parameters. In this article, we utilize the confidence distribution, a frequentist counterpart to the posterior distribution in Bayesian statistics, to obtain optimal confidence regions for the parameters. Members of such a region can be generated efficiently via a standard Markov chain Monte Carlo algorithm. We then apply this technique to draw inferences about the temporal profile of the survival function with censored observations. We illustrate the new proposal with the survival data from the well‐known Mayo primary biliary cirrhosis study and show that the volume of the new 0.95 confidence region is only one thirty‐fourth of that of the conventional confidence band.     

利用次序统计量估计种群的平均寿命

本文讨论威布尔分布Ｗ（α,λ）中次序统计量的分布;建立了用次序统计量对威布尔分布进行参数估计,进而估计种群平均寿命和方差的方法,该方法可广泛用于可靠性统计产品平均寿命和方差的估计。     

Fine Mapping Causal Variants with an Approximate Bayesian Method Using Marginal Test Statistics

Two recently developed fine-mapping methods, CAVIAR and PAINTOR, demonstrate better performance over other fine-mapping methods. They also have the advantage of using only the marginal test statistics and the correlation among SNPs. Both methods leverage the fact that the marginal test statistics asymptotically follow a multivariate normal distribution and are likelihood based. However, their relationship with Bayesian fine mapping, such as BIMBAM, is not clear. In this study, we first show that CAVIAR and BIMBAM are actually approximately equivalent to each other. This leads to a fine-mapping method using marginal test statistics in the Bayesian framework, which we call CAVIAR Bayes factor (CAVIARBF). Another advantage of the Bayesian framework is that it can answer both association and fine-mapping questions. We also used simulations to compare CAVIARBF with other methods under different numbers of causal variants. The results showed that both CAVIARBF and BIMBAM have better performance than PAINTOR and other methods. Compared to BIMBAM, CAVIARBF has the advantage of using only marginal test statistics and takes about one-quarter to one-fifth of the running time. We applied different methods on two independent cohorts of the same phenotype. Results showed that CAVIARBF, BIMBAM, and PAINTOR selected the same top 3 SNPs; however, CAVIARBF and BIMBAM had better consistency in selecting the top 10 ranked SNPs between the two cohorts. Software is available at https://bitbucket.org/Wenan/caviarbf.     

Estimating the Population Mean Using Extreme Ranked Set Sampling

Precision of the estimate of the population mean using ranked set sample (RSS) relative to using simple random sample (SRS), with the same number of quantified units, depends upon the population and success in ranking. In practice, even ranking a sample of moderate size and observing the ith ranked unit (other than the extremes) is a difficult task. Therefore, in this paper we introduce a variety of extreme ranked set sample (ERSSs) to estimate the population mean. ERSSs is more practical than the ordinary ranked set sampling, since in case of even sample size we need to identify successfully only the first and/or the last ordered unit or in case of odd sample size the median unit. We show that ERSSs gives an unbiased estimate of the population mean in case of symmetric populations and it is more efficient than SRS, using the same number of quantified units. Example using real data is given. Also, parametric examples are given.     

FLAGS: A Flexible and Adaptive Association Test for Gene Sets Using Summary Statistics

Genome-wide association studies (GWAS) have been widely used for identifying common variants associated with complex diseases. Despite remarkable success in uncovering many risk variants and providing novel insights into disease biology, genetic variants identified to date fail to explain the vast majority of the heritability for most complex diseases. One explanation is that there are still a large number of common variants that remain to be discovered, but their effect sizes are generally too small to be detected individually. Accordingly, gene set analysis of GWAS, which examines a group of functionally related genes, has been proposed as a complementary approach to single-marker analysis. Here, we propose a flexible and adaptive test for gene sets (FLAGS), using summary statistics. Extensive simulations showed that this method has an appropriate type I error rate and outperforms existing methods with increased power. As a proof of principle, through real data analyses of Crohn’s disease GWAS data and bipolar disorder GWAS meta-analysis results, we demonstrated the superior performance of FLAGS over several state-of-the-art association tests for gene sets. Our method allows for the more powerful application of gene set analysis to complex diseases, which will have broad use given that GWAS summary results are increasingly publicly available.     

Using Standard Statistics to Consider Uncertainty in Industry-Based Life Cycle Inventory Databases (7 pp)

Goal, Scope and Background Decision-makers demand information about the range of possible outcomes of their actions. Therefore, for developing Life Cycle Assessment (LCA) as a decision-making tool, Life Cycle Inventory (LCI) databases should provide uncertainty information. Approaches for incorporating uncertainty should be selected properly contingent upon the characteristics of the LCI database. For example, in industry-based LCI databases where large amounts of up-to-date process data are collected, statistical methods might be useful for quantifying the uncertainties. However, in practice, there is still a lack of knowledge as to what statistical methods are most effective for obtaining the required parameters. Another concern from the industry's perspective is the confidentiality of the process data. The aim of this paper is to propose a procedure for incorporating uncertainty information with statistical methods in industry-based LCI databases, which at the same time preserves the confidentiality of individual data. Methods The proposed procedure for taking uncertainty in industry-based databases into account has two components: continuous probability distributions fitted to scattering unit process data, and rank order correlation coefficients between inventory flows. The type of probability distribution is selected using statistical methods such as goodness-of-fit statistics or experience based approaches. Parameters of probability distributions are estimated using maximum likelihood estimation. Rank order correlation coefficients are calculated for inventory items in order to preserve data interdependencies. Such probability distributions and rank order correlation coefficients may be used in Monte Carlo simulations in order to quantify uncertainties in LCA results as probability distribution. Results and Discussion A case study is performed on the technology selection of polyethylene terephthalate (PET) chemical recycling systems. Three processes are evaluated based on CO2 reduction compared to the conventional incineration technology. To illustrate the application of the proposed procedure, assumptions were made about the uncertainty of LCI flows. The application of the probability distributions and the rank order correlation coefficient is shown, and a sensitivity analysis is performed. A potential use of the results of the hypothetical case study is discussed. Conclusion and Outlook The case study illustrates how the uncertainty information in LCI databases may be used in LCA. Since the actual scattering unit process data were not available for the case study, the uncertainty distribution of the LCA result is hypothetical. However, the merit of adopting the proposed procedure has been illustrated: more informed decision-making becomes possible, basing the decisions on the significance of the LCA results. With this illustration, the authors hope to encourage both database developers and data suppliers to incorporate uncertainty information in LCI databases.