A Note on Non-Parametric Tests for the Change-Point Problem

Two general classes of non-parametric tests for the change-point problem are introduced. In-variance principles lead to accessible asymptotic distribution theory.     

Non-parametric statistics for nucleic acid sequence study

The use of non-parametric statistics for nucleic acid sequence studies is illustrated by some examples. This method is highly flexible and allows design of specific tests for detecting sequence structure. Tests devoted to local repetitivity, codon nearest neighbors, and dinucleotide avoidance are discussed in detail. An appendix indicates all computations required to use these tests.     

SEARCHING FOR EVOLUTIONARY PATTERNS IN THE SHAPE OF A PHYLOGENETIC TREE

If all species in a clade are equally likely to speciate or become extinct, then highly symmetric and highly asymmetric phylogenetic trees are unlikely to result. Variation between species in speciation and extinction rates can cause excessive asymmetry. We developed six non-parametric statistical tests that test for nonrandom patterns of branching in any bifurcating tree. The tests are demonstrated by applying them to two published phylogenies for genera of beetles. Comparison of the power of the six statistics under a simple model of biased speciation suggests which of them may be most useful for detecting nonrandom tree shapes.     

A Note Concerning “Some Nonparametric Tests of Predicted Order”

SARRIS and WILKENING (1977) have recently proposed some non-parametric trend tests, which they view as extensions of MOSTELLER 'S test of predicted order. The present paper notes some errors in SARRIS and WILKENING 's determination of significance levels for these tests, and describes how these errors may be corrected.     

Semi-parametric ROC regression analysis with placement values

Advances in technology provide new diagnostic tests for early detection of disease. Frequently, these tests have continuous outcomes. One popular method to summarize the accuracy of such a test is the Receiver Operating Characteristic (ROC) curve. Methods for estimating ROC curves have long been available. To examine covariate effects, Pepe (1997, 2000) and Alonzo and Pepe (2002) proposed distribution-free approaches based on a parametric regression model for the ROC curve. Cai and Pepe (2002) extended the parametric ROC regression model by allowing an arbitrary non-parametric baseline function. In this paper, while we follow the same semi-parametric setting as in that paper, we highlight a new estimator that offers several improvements over the earlier work: superior efficiency, the ability to estimate the covariate effects without estimating the non-parametric baseline function and easy implementation with standard software. The methodology is applied to a case control dataset where we evaluate the accuracy of the prostate-specific antigen as a biomarker for early detection of prostate cancer. Simulation studies suggest that the new estimator under the semi-parametric model, while always being more robust, has efficiency that is comparable to or better than the Alonzo and Pepe (2002) estimator from the parametric model.     

Exploring interactions by second-stage community analyses

Many biological data sets, from field observations and manipulative experiments, involve crossed factor designs, analysed in a univariate context by higher-way analyses of variance which partition out ‘main’ and ‘interaction’ effects. Indeed, tests for significance of interactions among factors, such as differing Before-After responses at Control and Impact sites, are the basis of the widely used BACI strategy for detecting impacts in the environment. There are difficulties, however, in generalising simple univariate definitions of interaction, from classic linear models, to the robust, non-parametric multivariate methods that are commonly required in handling assemblage data. The size of an interaction term, and even its existence at all, depends crucially on the measurement scale, so it is fundamentally a parametric construct. Despite this, certain forms of interaction can be examined using non-parametric methods, namely those evidenced by changing assemblage patterns over many time periods, for replicate sites from different experimental conditions (types of ‘Beyond BACI’ design) - or changing multivariate structure over space, at many observed times. Second-stage MDS, which can be thought of as an MDS plot of the pairwise similarities between MDS plots (e.g. of assemblage time trajectories), can be used to illustrate such interactions, and they can be formally tested by second-stage ANOSIM permutation tests. Similarities between (first-stage) multivariate patterns are assessed by rank-based matrix correlations, preserving the fully non-parametric approach common in marine community studies. The method is exemplified using time-series data on corals from Thailand, macrobenthos from Tees Bay, UK, and macroalgae from a complex recolonisation experiment carried out in the Ligurian Sea, Italy. The latter data set is also used to demonstrate how the analysis copes straightforwardly with certain repeated-measures designs.     

Non-parametric interval mapping in half-sib designs: use of midranks to account for ties

In QTL analysis of non-normally distributed phenotypes, non-parametric approaches have been proposed as an alternative to the use of parametric tests on mathematically transformed data. The non-parametric interval mapping test uses random ranking to deal with ties. Another approach is to assign to each tied individual the average of the tied ranks (midranks). This approach is implemented and compared to the random ranking approach in terms of statistical power and accuracy of the QTL position. Non-normal phenotypes such as bacteria counts showing high numbers of zeros are simulated (0-80% zeros). We show that, for low proportions of zeros, the power estimates are similar but, for high proportions of zeros, the midrank approach is superior to the random ranking approach. For example, with a QTL accounting for 8% of the total phenotypic variance, a gain from 8% to 11% of power can be obtained. Furthermore, the accuracy of the estimated QTL location is increased when using midranks. Therefore, if non-parametric interval mapping is chosen, the midrank approach should be preferred. This test might be especially relevant for the analysis of disease resistance phenotypes such as those observed when mapping QTLs for resistance to infectious diseases.     

A statistical approach to bioclimatic trend detection in the airborne pollen records of Catalonia (NE Spain)

Airborne pollen records are a suitable indicator for the study of climate change. The present work focuses on the role of annual pollen indices for the detection of bioclimatic trends through the analysis of the aerobiological spectra of 11 taxa of great biogeographical relevance in Catalonia over an 18-year period (1994–2011), by means of different parametric and non-parametric statistical methods. Among others, two non-parametric rank-based statistical tests were performed for detecting monotonic trends in time series data of the selected airborne pollen types and we have observed that they have similar power in detecting trends. Except for those cases in which the pollen data can be well-modeled by a normal distribution, it is better to apply non-parametric statistical methods to aerobiological studies. Our results provide a reliable representation of the pollen trends in the region and suggest that greater pollen quantities are being liberated to the atmosphere in the last years, specially by Mediterranean taxa such as Pinus, Total Quercus and Evergreen Quercus, although the trends may differ geographically. Longer aerobiological monitoring periods are required to corroborate these results and survey the increasing levels of certain pollen types that could exert an impact in terms of public health.     

Testing quantitative traits for association and linkage in the presence or absence of parental data

Zhu and Elston developed a transmission disequilibrium test for quantitative traits by defining a linear transformation to condition out founder information. The method tests the null hypothesis of no linkage or association and can be applied to general pedigree structures. However, this method requires both genotype and phenotype parental information, which may be difficult to obtain. In this paper, we describe parametric and non-parametric methods to relax this requirement when only nuclear families are sampled. We show that neither method is affected by population stratification in the absence of linkage. The statistical power and validity of the tests are investigated by simulation. A simple simulation method to calculate the power of the nonparametric method is also discussed. In practice, the data may have some families with parental phenotype and genotype information available and some without. We briefly discuss how all the data may be analyzed jointly.     

A Matched Pairs Selection method for the analysis of abundance data with many zero values

Abstract. A simple method is described to analyze plant species abundance data with many zero values. To investigate the impact of an environmental factor on rare species, two subsets of sampling plots are selected pair-wise from the original data set. They differ in the value of the particular factor under consideration but are similar with respect to all other factors. Subsequently, the botanical composition of these subsets, including rare species, is compared using non-parametric tests. An example is given from a study on ditch bank vegetation. Some limitations, and a method for taking into account the dependence of the statistical tests, are discussed.     

Diffprot - software for non-parametric statistical analysis of differential proteomics data

Mass spectrometry-based global proteomics experiments generate large sets of data that can be converted into useful information only with an appropriate statistical approach. We present Diffprot - a software tool for statistical analysis of MS-derived quantitative data. With implemented resampling-based statistical test and local variance estimate, Diffprot allows to draw significant results from small scale experiments and effectively eliminates false positive results. To demonstrate the advantages of this software, we performed two spike-in tests with complex biological matrices, one label-free and one based on iTRAQ quantification; in addition, we performed an iTRAQ experiment on bacterial samples. In the spike-in tests, protein ratios were estimated and were in good agreement with theoretical values; statistical significance was assigned to spiked proteins and single or no false positive results were obtained with Diffprot. We compared the performance of Diffprot with other statistical tests - widely used t-test and non-parametric Wilcoxon test. In contrast to Diffprot, both generated many false positive hits in the spike-in experiment. This proved the superiority of the resampling-based method in terms of specificity, making Diffprot a rational choice for small scale high-throughput experiments, when the need to control the false positive rate is particularly pressing.     

A class of goodness of fit tests for a copula based on bivariate right-censored data

The copula of a bivariate distribution, constructed by making marginal transformations of each component, captures all the information in the bivariate distribution about the dependence between two variables. For frailty models for bivariate data the choice of a family of distributions for the random frailty corresponds to the choice of a parametric family for the copula. A class of tests of the hypothesis that the copula is in a given parametric family, with unspecified association parameter, based on bivariate right censored data is proposed. These tests are based on first making marginal Kaplan-Meier transformations of the data and then comparing a non-parametric estimate of the copula to an estimate based on the assumed family of models. A number of options are available for choosing the scale and the distance measure for this comparison. Significance levels of the test are found by a modified bootstrap procedure. The procedure is used to check the appropriateness of a gamma or a positive stable frailty model in a set of survival data on Danish twins.     

Lipopolysaccharide-Induced CXCL10 mRNA Level and Six Stimulant-mRNA Combinations in Whole Blood: Novel Biomarkers for Bortezomib Responses Obtained from a Prospective Multicenter Trial for Patients with Multiple Myeloma

To identify predictive biomarkers for clinical responses to bortezomib treatment, 0.06 mL of each whole blood without any cell separation procedures was stimulated ex vivo using five agents, and eight mRNAs were quantified. In six centers, heparinized peripheral blood was prospectively obtained from 80 previously treated or untreated, symptomatic multiple myeloma (MM) patients with measurable levels of M-proteins. The blood sample was procured prior to treatment as well as 2-3 days and 1-3 weeks after the first dose of bortezomib, which was intravenously administered biweekly or weekly, during the first cycle. Six stimulant-mRNA combinations; that is, lipopolysaccharide (LPS)-granulocyte-macrophage colony-stimulating factor (GM-CSF), LPS-CXCL chemokine 10 (CXCL10), LPS-CCL chemokine 4 (CCL4), phytohemagglutinin-CCL4, zymosan A (ZA)-GMCSF and ZA-CCL4 showed significantly higher induction in the complete and very good partial response group than in the stable and progressive disease group, as determined by both parametric (t-test) and non-parametric (unpaired Mann-Whitney test) tests. Moreover, LPS-induced CXCL10 mRNA expression was significantly suppressed 2-3 days after the first dose of bortezomib in all patients, as determined by both parametric (t-test) and non-parametric (paired Wilcoxon test) tests, whereas the complete and very good partial response group showed sustained suppression 1-3 weeks after the first dose. Thus, pretreatment LPS-CXCL10 mRNA and/or the six combinations may serve as potential biomarkers for the response to bortezomib treatment in MM patients.     

REPLI: A program in BASIC for determination of approximate sample size

REPLI, a program written in elementary BASIC, calculates the approximate sample size, which is required to detect a desired difference between any two group means in an experiment with n groups for a given probability and at three significance levels of the means difference. A prior knowledge of the variability of data in the groups is expected in order to base the estimate on a rational footing. If this knowledge does not exist, an educated guess and/or several trials with different assumptions on the most likely variability can be used. The a priori estimate prevents that sample sizes are completely out of a reasonable range. Since the program is applicable for experimental settings where several groups need be investigated, it is particularly interesting to users of ANOVA and/or comparable non-parametric tests.     

Non-parametric optimal design in dose finding studies

We describe a non-parametric optimal design as a theoretical gold standard for dose finding studies. Its purpose is analogous to the Cramer-Rao bound for unbiased estimators, i.e. it provides a bound beyond which improvements are not generally possible. The bound applies to the class of non-parametric designs where the data are not assumed to be generated by any known parametric model. Whenever parametric assumptions really hold it may be possible to do better than the optimal non-parametric design. The goal is to be able to compare any potential dose finding scheme with the optimal non-parametric benchmark. This paper makes precise what is meant by optimal in this context and also why the procedure is described as non-parametric.     

Improving data interpretation of fragmentary data-sets on invertebrate dispersal with permutation tests

Biological data often tend to have heterogeneous, discontinuous non-normal distributions. Statistical non-parametric tests, like the Mann–Whitney U-test or the extension for more than two samples, the Kruskal–Wallis test, are often used in these cases, although they assume certain preconditions which are often ignored. We developed a permutation test procedure that uses the ratio of the interquartile distances and the median differences of the original non-classified data to assess the properties of the real distribution more appropriately than the classical methods. We used this test on a heterogeneous, skewed biological data set on invertebrate dispersal and showed how different the reactions of the Kruskal–Wallis test and the permutation approach are. We then evaluated the new testing procedure with reproducible data that were generated from the normal distribution. Here, we tested the influence of four different experimental trials on the new testing procedure in comparison to the Kruskal–Wallis test. These trials showed the impact of data that were varying in terms of (a) negative correlation between variances and means of the samples, (b) changing variances that were not correlated with the means of the samples, (c) constant variances and means, but different sample sizes and in trials (d) we evaluated the testing power of the new procedure. Due to the different test statistics, the permutation test reacted more sensibly to the data presented in trials (a) and c) and non-uniformly in trial (b). In the evaluation of the testing power, no significant differences between the Kruskal–Wallis test and the new permutation testing procedure could be detected. We consider this test to be an alternative for working on heterogeneous data where the preconditions of the classical non-parametric tests are not met.     

Addressing the complexity in non-linear evolution of vegetation phenological change with time-series of remote sensing images

Earth observation based monitoring of change in vegetation phenology and productivity is an important and widely used approach to quantify degradation of ecosystems due to climatic or human influences. Most satellite based studies apply linear or polynomial regression methods for trend detections. In this paper it is argued that natural systems hardly react to human or natural influences in a linear or a polynomial manner. At shorter time-scales of few decades natural systems fluctuate to a certain extent in a non-systematic manner without necessarily changing equilibrium. Finding a systematic model that describes this behavior on large spatial scales is certainly a difficult challenge. Furthermore, the manner vegetation phenology reacts to climate and to socio-economic changes is also dependent on the land cover type and on the bioclimatic region. In addition to this, traditional parametric methods require the fulfillment of several statistical criteria. In case these criteria are violated confidence intervals and significance tests of the models may be biased, even misleading. This paper proposes an alternative approach termed the Steadiness to traditional trend analysis methods. Steadiness combines the direction or tendency of the change and the net change of the time-series over a selected time period. It is a non-parametric approach which can be used without violation of statistical criteria, it can be applied on short time-series as well and results are not dependent on the significance test or on thresholds. To demonstrate differences, a time-series of satellite derived Season Length images for 24 years is analyzed for the entire European continent using linear regression and the Steadiness approach. Spatial and temporal change patterns and sensitivity to pre-processing algorithms are compared between the two methods. We show that linear regression limits the possibilities of assessing fluctuating ecosystem changes whereas the non-parametric Steadiness index more consistently confirms the fluctuating phenological change patterns.     

Axiomatic methods, dopamine and reward prediction error

The phasic firing rate of midbrain dopamine neurons has been shown to respond both to the receipt of rewarding stimuli, and the degree to which such stimuli are anticipated by the recipient. This has led to the hypothesis that these neurons encode reward prediction error (RPE)-the difference between how rewarding an event is, and how rewarding it was expected to be. However, the RPE model is one of a number of competing explanations for dopamine activity that have proved hard to disentangle, mainly because they are couched in terms of latent, or unobservable, variables. This article describes techniques for dealing with latent variables common in economics and decision theory, and reviews work that uses these techniques to provide simple, non-parametric tests of the RPE hypothesis, allowing clear differentiation between competing explanations.