Modified Kolmogorov-Smirnov Test Research Articles

Treatment Efficacy Score—continuous residual cancer burden-based metric to compare neoadjuvant chemotherapy efficacy between randomized trial arms in breast cancer trials

Difference in pathologic complete response (pCR) rate after neoadjuvant chemotherapy does not capture the impact of treatment on downstaging of residual cancer in the experimental arm. We developed a method to compare the entire distribution of residual cancer burden (RCB) values between clinical trial arms to better quantify the differences in cytotoxic efficacy of treatments. The Treatment Efficacy Score (TES) reflects the area between the weighted cumulative distribution functions of RCB values from two trial arms. TES is based on a modified Kolmogorov-Smirnov test with added weight function to capture the importance of high RCB values and uses the area under the difference between two distribution functions as a statistical metric. The higher the TES the greater the shift to lower RCB values in the experimental arm. We developed TES from the durvalumab+ olaparib arm (n= 72) and corresponding controls (n= 282) of the I-SPY2 trial. The 11 other experimental arms and control cohorts (n= 947) were used as validation sets to assess the performance of TES. We compared TES to Kolmogorov-Smirnov, Mann-Whitney, and Fisher's exact tests to identify trial arms with higher cytotoxic efficacy and assessed associations with trial arm level survival differences. Significance was assessed with a permutation test. In the validation set, TES identified arms with a higher pCR rate but was more accurate to identify regimens as less effective if treatment did not reduce the frequency of high RCB values, even if the pCR rate improved. The correlation between TES and survival was higher than the correlation between the pCR rate difference and survival. TES quantifies the difference between the entire distribution of pathologic responses observed in trial arms and could serve as a better early surrogate to predict trial arm level survival differences than pCR rate difference alone.

Identification of Nifurtimox and Chrysin as Anti-Influenza Virus Agents by Clinical Transcriptome Signature Reversion.

The rapid development in the field of transcriptomics provides remarkable biomedical insights for drug discovery. In this study, a transcriptome signature reversal approach was conducted to identify the agents against influenza A virus (IAV) infection through dissecting gene expression changes in response to disease or compounds’ perturbations. Two compounds, nifurtimox and chrysin, were identified by a modified Kolmogorov–Smirnov test statistic based on the transcriptional signatures from 81 IAV-infected patients and the gene expression profiles of 1309 compounds. Their activities were verified in vitro with half maximal effective concentrations (EC50s) from 9.1 to 19.1 μM against H1N1 or H3N2. It also suggested that the two compounds interfered with multiple sessions in IAV infection by reversing the expression of 28 IAV informative genes. Through network-based analysis of the 28 reversed IAV informative genes, a strong synergistic effect of the two compounds was revealed, which was confirmed in vitro. By using the transcriptome signature reversion (TSR) on clinical datasets, this study provides an efficient scheme for the discovery of drugs targeting multiple host factors regarding clinical signs and symptoms, which may also confer an opportunity for decelerating drug-resistant variant emergence.

Left-turn conflict identification at signal intersections based on vehicle trajectory reconstruction under real-time communication conditions

Connected vehicle (CV)technologies offer promising solutions to several problems in transportation systems. The trajectory data generated from CV technology can be used to identify real-time conflicts in intersections. To perform such identification, accurate vehicle localisation should be obtained to clearly recognise the conflicts between left-turning vehicles and straight-through vehicles in the opposite direction at the signal control intersection. This study presents a CV framework that uses the two-way time of arrival to locate the vehicles on the basis of the Intelligent Vehicle Infrastructure Cooperative Environment. Kalman Filter (KF) is used to improve the accuracy of the vehicle location, and the corresponding algorithm is used to estimate the vehicle trajectory to obtain the vehicle kinematics information via the on-board system. The traffic conflict areas of the left-turning vehicles and straight-through vehicles in the opposite direction are determined through vehicle trajectory extrapolation, and the left-turn collision at the signal intersection is identified using the post-encroachment time algorithm and vehicle movement information. In addition, Anderson–Darling and modified Kolmogorov–Smirnov tests are performed to verify the goodness of fit of the data. Results show that the vehicle speed and localisation errors of the proposed method decreased by 66.67 % and 83.33 % compared with the results before filtering, respectively. Moreover, the results of the conflict recognition method based on CV trajectory reconstruction is consistent for both goodness of fit tests under real-time communication conditions. This study can provide driving decision for drivers of left-turning vehicles under the Intelligent Vehicle Infrastructure Cooperative Environment and provide technical support for the research and development of left-turn anti-collision systems.

Tangential streaming potential, transmembrane flux, and chemical cleaning of ultrafiltration membranes

Transmembrane flux measurements are the only practical tools used to evaluate the degree of organic fouling and the efficiency of chemical cleaning of ultrafiltration membranes in situ. Tangential pH-streaming potential profiles may become a comprehensive in situ method to analyse cleaning efficiency versus potential membrane damage. A parallel implementation of the two methods was used to assist in tuning an efficient cleaning protocol for 300 kDa polyethersulfone membranes. The membranes were fouled with a mixture of organics and cleaned with nitric acid, acetic acid, caustic soda or liquid bleach, each at concentrations of 1, 5, or 10 mg/L. A modified Kolmogorov-Smirnov test for divergence in datasets clearly indicated cleaning with 5 mg/L NaOH or NaOCl. These findings were confirmed by atomic force microscopy surface contouring and infrared spectra recording.Tangential pH-streaming potential profiling is easy in terms of operation and maintenance, inexpensive, and may be conducted in situ. Implementation of two independent tests is instrumental in the validation of the cleaning agent efficiency, optimisation of the cleaning dose and pH, and assessment of membrane fouling potential by complex organic mixtures. A combination of transmembrane flux and tangential streaming potential tests may reduce the cost of chemical cleaning and suspend membrane ageing.

How Accurately Do Structural Asymmetric First-Price Auction Estimates Represent True Valuations?

Abstract Structural asymmetric first-price auction estimation methods have provided numerous empirical studies. However, due to the latent nature of underlying valuations, the accuracy of estimates is not feasibly testable with field data, a fact that could inhibit empirical auction market designs and applications based on structural estimates. To assess their accuracy, we provide an analysis of estimates derived from experimental asymmetric auction data, in which researchers observe valuations. We test the null of statistical equivalence between the estimated and true value distributions against the alternative of non-equivalence. When advanced models are used, the Modified Kolmogorov-Smirnov test fails to reject the distributional equivalence, supporting structural asymmetric auction estimations for auction market studies. In addition, recovered efficiencies have plus-minus 2.5 percent precision, compared to the true efficiencies.

Temporally Distinct Developmental Waves of Erythropoiesis from Human Pluripotent Stem Cells

Mammalian erythropoiesis during embryogenesis occurs in several distinct stages or "waves" that vary according to timing, site of production, gene expression and physiology. The ontogeny of mammalian erythropoiesis is most thoroughly studied in mice where the earliest circulating erythroblasts released from the yolk sac are termed primitive. Later, the first definitive erythroid lineage is established by erythro-myeloid progenitors (EMPs) that originate in the yolk sac and migrate to the fetal liver for terminal differentiation. A second wave of definitive erythropoiesis is established from hematopoietic stem/progenitor cells that originate in the dorsal aorta and migrate to later stage fetal liver for terminal differentiation. Finally around birth, definitive erythropoiesis shifts to the bone marrow. The ontogeny of erythropoiesis overlaps in mice and humans, although less is known about the latter, as hematopoietic tissues from precisely staged early human embryos are difficult to obtain. We hypothesized that the initial steps of human erythroid ontogeny could be recapitulated by induced pluripotent stem cells (iPSCs) induced to undergo hematopoietic differentiation. We used a serum- and feeder-free protocol to differentiate iPSCs into embryoid bodies (EBs) that produced two sequential waves of distinctly different erythroid precursors. At day 8 of differentiation, EBs began to release hematopoietic precursors. Thereafter, erythroid precursors were released from the EBs in the presence of stem cell factor (SCF), erythropoietin (EPO) and insulin-like growth factor 1 (IGF-1). Erythroid precursors produced during wave 1 (days 12-23 of differentiation) were relatively large and expressed embryonic-type globins (zeta and epsilon), resembling those produced during primitive erythropoiesis. In contrast, wave 2 erythroblasts (day 27 and later) were smaller and expressed mainly gamma and alpha globins with some beta globin, suggestive of fetal-type definitive erythropoiesis. To investigate further the similarity of wave 1 and wave 2 erythroblasts to cells at the primitive and definitive stages of ontogeny, respectively, we used Affymetrix Genechips to analyze the global transcriptomes of stage-matched (CD235+ CD71high) cells. As primary human primitive erythroblasts were not available for comparison, we compared the transcriptomes from the iPSC-derived erythroblasts with those of primary murine definitive and primitive erythroblasts that were flow cytometry-purified from embryonic day 15.5 (E15.5) fetal liver and E10.5 bloodstream, respectively. The comparisons showed that wave 1 erythroblasts from human pluripotent cells resembled more closely the erythroid primitive lineage from mice, while wave 2 erythroblasts from the human cells resembled the erythroid definitive lineage of mice (P-value < 0.05 by a modified Kolmogorov-Smirnov test). For example, SOX6 and BCL11A, preferentially expressed during definitive erythropoiesis, were expressed at relatively high levels in wave 2 erythroblasts. In addition, gene set enrichment analysis (GSEA) demonstrated that wave 2 human iPSC-derived erythroblasts and primary murine definitive erythroblasts expressed numerous genes related to immune/inflammatory pathways that were shown previously to be important for the formation of definitive hematopoietic stem and progenitor cells in zebrafish and mouse embryos. Our findings demonstrate that human iPSC-derived embryoid bodies recapitulate early stages of erythroid ontogeny with respect to the timing of emerging lineages and their gene expression. Additionally, gene expression studies of human iPSC-derived primitive and definitive erythroblasts indicate inflammatory signaling as a potential regulator of the later stage of erythroid development. DisclosuresNo relevant conflicts of interest to declare.

Global DNA promoter methylation in frontal cortex of alcoholics and controls

To determine if ethanol consumption and alcoholism cause global DNA methylation disturbances, we examined alcoholics and controls using methylation specific microarrays to detect all annotated gene and non-coding microRNA promoters and their CpG islands. DNA was isolated and immunoprecipitated from the frontal cortex of 10 alcoholics and 10 age and gender-matched controls then labeled prior to co-hybridization. A modified Kolmogorov–Smirnov test was used to predict differentially enriched regions (peaks) from log-ratio estimates of amplified vs input DNA. More than 180,000 targets were identified for each subject which correlated with >30,000 distinct, integrated peaks or high probability methylation loci. Peaks were mapped to regions near 17,810 separate annotated genes per subject representing hypothetical methylation targets. No global methylation differences were observed between the two subject groups with 80% genetic overlap, but extreme methylation was observed in both groups at specific loci corresponding with known methylated genes (e.g., H19) and potentially other genes of unknown methylation status. Methylation density patterns targeting CpG islands visually correlated with recognized chromosome banding. Our study provides insight into global epigenetic regulation in the human brain in relationship to controls and potentially novel targets for hypothesis generation and follow-up studies of alcoholism.

Logcondens: Computations Related to Univariate Log-Concave Density Estimation

Maximum likelihood estimation of a log-concave density has attracted considerable attention over the last few years. Several algorithms have been proposed to estimate such a density. Two of those algorithms, an iterative convex minorant and an active set algorithm, are implemented in the <b>R</b> package <b>logcondens</b>. While these algorithms are discussed elsewhere, we describe in this paper the use of the <b>logcondens</b> package and discuss functions and datasets related to log-concave density estimation contained in the package. In particular, we provide functions to (1) compute the maximum likelihood estimate (MLE) as well as a smoothed log-concave density estimator derived from the MLE, (2) evaluate the estimated density, distribution and quantile functions at arbitrary points, (3) compute the characterizing functions of the MLE, (4) sample from the estimated distribution, and finally (5) perform a two-sample permutation test using a modified Kolmogorov-Smirnov test statistic. In addition, <b>logcondens</b> makes two datasets available that have been used to illustrate log-concave density estimation.

Sequential Detection and Estimation of Change-Points

The problem of sequential detection and estimation of a change-point is considered. The ‘large parameter’ approach for solving this problem is proposed. A two-stage method is designed according to this approach, which includes the nonparametric version of the CUSUM procedure for sequential change-point detection and the modified Kolmogorov-Smirnov test for the retrospective estimation of the detected change-point. The asymptotic effectiveness of this method is proved for dependent observations (Theorems 2.1 and 3.1) when the large parameter infinitely increases. Monte Carlo study of this method for the Gaussian case (changes in mean and dispersion) is performed. The a priori theoretical lower bounds are proved for new performance measures in sequential change-point detection and retrospective estimation (Theorems 5.1 and 5.2) and the asymptotic optimality of the proposed method is demonstrated.

Comparison of selected statistical distributions for modelling the diameter distributions in near-natural Abies–Fagus forests in the Świętokrzyski National Park (Poland)

The aim of the study is to compare selected theoretical distributions (normal, lognormal, Weibull, gamma, logistic, and exponential) in describing the tree diameter (DBH) distributions of mixed near-natural forests consisting of fir Abies alba Mill. and beech Fagus sylvatica L. growing in various vertical structures. Tree DBH data were collected between 1997 and 2008 from 51 sample plots established in the Świetokrzyski National Park in Poland. The empirical data represent differentiated DBH distributions, ranging from almost symmetric to extremely asymmetric ones. The chi-square test and the modified Kolmogorov–Smirnov test were chosen for the goodness-of-fit testing. In addition to the test statistics, the bias (B), the root mean square error (RMSE) and the graphical method (quantile–quantile plots) were used. In one-storied stands, the most suitable distributions were the normal and logistic distributions; in two-storied and multilayered stands, the Weibull and gamma distribution were the most suitable; and in selection stands, the exponential distribution was the most appropriate to describe the DBH distribution. The order of precision of the tested distributions (from the highest to the lowest) was Weibull, gamma, logistic, normal, exponential, and lognormal. The normal and exponential distribution should be applied only to one-storied and selection forests, respectively. The least suitable distribution for DBH distribution modelling was the lognormal one.

Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov–Smirnov test statistic. Part II: Experiment and application

Optimal maintenance decision analysis is heavily dependent on the accuracy of condition indicators. A condition indicator that is subject to such varying operating conditions as load is unable to provide precise condition information of the monitored object for making optimal operational maintenance decisions even if the maintenance program is established within a rigorous theoretical framework. For this reason, the performance of condition monitoring techniques applied to rotating machinery under varying load conditions has been a long-term concern and has attracted intensive research interest. Part I of this study proposed a novel technique based on adaptive autoregressive modeling and hypothesis tests. The method is able to automatically search for the optimal time-series model order and establish a compromised autoregressive model fitting based on the healthy gear motion residual signals under varying load conditions. The condition of the monitored gearbox is numerically represented by a modified Kolmogorov–Smirnov test statistic. Part II of this study is devoted to applications of the proposed technique to entire lifetime condition detection of three gearboxes with distinct physical specifications, distinct load conditions, and distinct failure modes. A comprehensive and thorough comparative study is conducted between the proposed technique and several counterparts. The detection technique is further enhanced by a proposed method to automatically identify and generate fault alerts with the aid of the Wilcoxon rank-sum test and thus requires no supervision from maintenance personnel. Experimental analysis demonstrated that the proposed technique applied to automatic identification and generation of fault alerts also features two highly desirable properties, i.e. few false alerts and early alert for incipient faults. Furthermore, it is found that the proposed technique is able to identify two types of abnormalities, i.e. strong ghost components abruptly appearing in and disturbing the nominal operating process and the breakage of gear teeth, whereas conventional condition indicators are usually not capable of detecting the presence of the former.

Transformations for Testing the Fit of the Inverse-Gaussian Distribution

Use of the MVUE for the inverse-Gaussian distribution has been recently proposed by Nguyen and Dinh [Nguyen, T. T., Dinh, K. T. (2003). Exact EDF goodnes-of-fit tests for inverse Gaussian distributions. Comm. Statist. (Simulation and Computation) 32(2):505–516] where a sequential application based on Rosenblatt's transformation [Rosenblatt, M. (1952). Remarks on a multivariate transformation. Ann. Math. Statist. 23:470–472] led the authors to solve the composite goodness-of-fit problem by solving the surrogate simple goodness-of-fit problem, of testing uniformity of the independent transformed variables. In this note, we observe first that the proposal is not new since it was proposed in a rather general setting in O'Reilly and Quesenberry [O'Reilly, F., Quesenberry, C. P. (1973). The conditional probability integral transformation and applications to obtain composite chi-square goodness-of-fit tests. Ann. Statist. I:74–83]. It is shown on the other hand that the results in the paper of Nguyen and Dinh (2003) are incorrect in their Sec. 4, specially the Monte Carlo figures reported. Power simulations are provided here comparing these corrected results with two previously reported goodness-of-fit tests for the inverse-Gaussian; the modified Kolmogorov–Smirnov test in Edgeman et al. [Edgeman, R. L., Scott, R. C., Pavur, R. J. (1988). A modified Kolmogorov-Smirnov test for inverse Gaussian distribution with unknown parameters. Comm. Statist. 17(B): 1203–1212] and the A 2 based method in O'Reilly and Rueda [O'Reilly, F., Rueda, R. (1992). Goodness of fit for the inverse Gaussian distribution. T Can. J. Statist. 20(4):387–397]. The results show clearly that there is a large loss of power in the method explored in Nguyen and Dinh (2003) due to an implicit exogenous randomization.

An evaluation of diagnostic tests and their roles in validating forest biometric models

Model validation is an important part of model development. It is performed to increase the credibility and gain sufficient confidence about a model. This paper evaluated the usefulness of 10 statistical tests, five parametric and five nonparametric, in validating forest biometric models. The five parametric tests are the paired t test, the Χ2 test, the separate t test, the simultaneous F test, and the novel test. The five nonparametric tests are the Brown-Mood test, the Kolmogorov–Smirnov test, the modified Kolmogorov–Smirnov test, the sign test, and the Wilcoxon signed-rank test. Nine benchmark data sets were selected to evaluate the behavior of these tests in model validation; three were collected from Alberta and six were published elsewhere. It was shown that the usefulness of statistical tests in model validation is very limited. None of the tests seems to be generic enough to work well across a wide range of models and data. Each model passed one or more tests, but not all of them. Because of this, caution should be exercised when choosing a statistical test or several tests together to try to validate a model. It is important to reduce and remove any potential personal bias in selecting a favorite test, which can influence the outcome of the results.

A modified Kolmogorov-Smirnov test for a rectangular distribution with unknown parameters: Computation of the distribution of the test statistic

A recursive scheme for the calculation of the distribution of the test statistic of a modified Kolmogorov-Smirnov-test for a rectangular distribution with unknown parameters is given.

Spatio-temporal segmentation based on region merging

This paper proposes a technique for spatio-temporal segmentation to identify the objects present in the scene represented in a video sequence. This technique processes two consecutive frames at a time. A region-merging approach is used to identify the objects in the scene. Starting from an oversegmentation of the current frame, the objects are formed by iteratively merging regions together. Regions are merged based on their mutual spatio-temporal similarity. We propose a modified Kolmogorov-Smirnov test for estimating the temporal similarity. The region-merging process is based on a weighted, directed graph. Two complementary graph-based clustering rules are proposed, namely, the strong rule and the weak rule. These rules take advantage of the natural structures present in the graph. Experimental results on different types of scenes demonstrate the ability of the proposed technique to automatically partition the scene into its constituent objects.

EFFECTIVENESS OF THE COMPARATIVE RELIABILITY ASSESSMENT TECHNIQUES EVALUATING QUALITY &amp; RELIABILITY IN ENGINEERING DESIGN

In this paper a new generalization of the Wilcoxon test is proposed for the comparative reliability evaluation of alternative engineering designs. Using Monte Carlo simulations the performance of the new test is assessed against the results provided by four other two-sample tests for censored reliability data, i.e., the Gehan-Wilcoxon, Peto-Prentice, Logrank and modified Kolmogorov-Smirnov tests. The results of the simulations suggest that the Wilcoxon alternatives based on weight functions that are reliability function estimates, such as the Peto-Prentice and the Bohoris-Wilcoxon, are the most preferable for routine use.

Conditional power for arbitrary survival curves to decide whether to extend a clinical trial

This article describes a computer simulation methodology to calculate conditional power for comparing two arbitrary survival curves as an aid in deciding whether or not to extend a clinical trial. The method is a modification of that by Halpern and Brown, which computes unconditional power for comparing arbitrary survival curves at the beginning of a study. The advantage of this method is that it permits conditional power calculations for comparisons of distribution-free survival curves. Power is computed for two commonly used statistical tests, the log-rank test and Gehan's generalization of the Wilcoxon test, and for a modified Kolmogorov-Smirnov test, which is particularly sensitive to crossing survival curves. This method for estimating conditional power should be useful in the situation in which a decision must be made regarding the benefit of continuing a clinical trial. The application of this method is shown using VA Cooperative Study No. 90, “Prognosis and Outcome Following Heart Valve Replacement.”

Non‐Weibull behavior observed in a model‐generated global surface wind field frequency distribution

The frequency distribution of the surface wind speeds at each 4.5°×7.5° latitude‐longitude grid point produced by the National Center for Atmospheric Research community climate model is examined. A modified Kolmogorov‐Smirnov (KS) test was used to ascertain the extent of Weibull behavior for perpetual January and July model runs. The modified KS test has been applied to 400 days of both perpetual January and July model runs using a 0.5‐day time sample. A global map of the KS statistic for each of the January and July control runs has been generated. These maps are presented for both the ocean and land wind fields. For the January oceanic winds, 29.2% of the frequency distributions were non‐Weibull at the 95% confidence level. Over land, 35.4% of the wind speed frequency distributions were judged to be non‐Weibull. For the July wind speed data, 32.7% of the ocean data sets were judged to be non‐Weibull, while for winds over land, 30.2% were found to be non‐Weibull. Large areas of Eurasia experience non‐Weibull behavior during the January run. The main oceanic latitudinal zones associated with a non‐Weibull character are from 5° to 30° in each hemisphere, a feature that is most evident in the July run. The monsoonal winds over the Indian Ocean are almost entirely Weibull. The non‐Weibull character of surface wind field frequency distributions may explain, in part, the apparent inability of some surface wind data sets to drive an ocean circulation model through inexact wind forcing.

Modified Kolmogorov-Smirnov Test Procedures with Application to Arbitrarily Right-Censored Data

The classical Kolmogorov one-sample goodness-of-fit and Smirnov two-sample test procedures are modified in an attempt to obtain increased power when applied to uncensored data. Both are then generalized for use with arbitrarily right-censored data. Motivation for the formulation of the generalized procedures is provided heuristically by appealing to the basic concept upon which the procedures for uncensored data are based; a theoretical motivation is provided by asymptotic weak convergence results. The size and power of the generalized Smirnov two-sample procedure are evaluated for small and moderate sample sizes using Monte Carlo simulations. Results of the simulations are also used to make comparisons with the Gehan-Wilcoxon and logrank two-sample test procedures. The generalized Smirnov procedure is found to maintain the size of the test in nearly all the cases studied, although it is conservative in small samples of heavily censored data. It is found to be more powerful than both the Gehan-Wilcoxon and the logrank procedures for the non-Lehmann alternatives considered.

Some Modified Kolmogorov-Smirnov Tests of Approximate Hypotheses and their Properties

The paradox of almost certain rejection of the null hypothesis in the Chi Square test-of-fit, when many observations are used, has been pointed out by Cochran [4], and largely removed by Lehmann and Hodges [7]. The same paradox arises in most tests of goodness-of-fit. In this paper the Kolmogorov-Smirnov tests are modified to remove this difficulty and some properties of this modification are investigated. In particular, a rigorous method for choosing sample size (Theorem 3.2 and corollaries) is presented. Given independent random variables $X_1, \cdots, X_n$ with common distribution function $F$, suppose that we desire to determine whether or not $F$ is in some class $\mathscr{H}_0$. If we are only interested in whether $F$ is close, in some sense, to some distribution function in $\mathscr{H}_0$, we can let $\mathscr{H}^\ast_0 \supset \mathscr{H}_0$, where $\mathscr{H}^\ast_0$ is the class of distribution functions "close" to those in $\mathscr{H}_0$, and test the more reasonable hypothesis that $F \epsilon \mathscr{H}^\ast_0$. In what follows we consider tests based on the uniform metric $d_1$, given by $d_1(F, H) = \sup_x |F(x) - H(x)|$, where $\mathscr{H}_0$ consists of a single distribution function $F_0$.