Statistical Testing Approach Research Articles

A weight-adjusted Peto?s test when cause of death is not assigned

A new statistical testing approach using a weighted logrank statistic is developed for rodent tumorigenicity assays that have a single terminal sacrifice but not cause-of-death data. Instead of using cause-of-death assignment by pathologists, the number of fatal tumors is estimated by a constrained nonparametric maximum likelihood estimation method. For data lacking cause-of-death information, the Peto test is modified with estimated numbers of fatal tumors and a Fleming–Harrington-type weight, which is based on an estimated tumor survival function. A bootstrap resampling method is used to estimate the weight function. The proposed testing method with the weight adjustment appears to improve the performance in various situations of single-sacrifice animal experiments. A Monte Carlo simulation study for the proposed test is conducted to assess size and power of the test. This testing approach is illustrated using a real data set.

Multi-class clustering and prediction in the analysis of microarray data

DNA microarray technology provides tools for studying the expression profiles of a large number of distinct genes simultaneously. This technology has been applied to sample clustering and sample prediction. Because of a large number of genes measured, many of the genes in the original data set are irrelevant to the analysis. Selection of discriminatory genes is critical to the accuracy of clustering and prediction. This paper considers statistical significance testing approach to selecting discriminatory gene sets for multi-class clustering and prediction of experimental samples. A toxicogenomic data set with nine treatments (a control and eight metals, As, Cd, Ni, Cr, Sb, Pb, Cu, and AsV with a total of 55 samples) is used to illustrate a general framework of the approach. Among four selected gene sets, a gene set Ω I formed by the intersection of the F-test and the set of the union of one-versus-all t-tests performs the best in terms of clustering as well as prediction. Hierarchical and two modified partition ( k-means) methods all show that the set Ω I is able to group the 55 samples into seven clusters reasonably well, in which the As and AsV samples are considered as one cluster (the same group) as are the Cd and Cu samples. With respect to prediction, the overall accuracy for the gene set Ω I using the nearest neighbors algorithm to predict 55 samples into one of the nine treatments is 85%.

Sample size calculation for multiple testing in microarray data analysis

Microarray technology is rapidly emerging for genome-wide screening of differentially expressed genes between clinical subtypes or different conditions of human diseases. Traditional statistical testing approaches, such as the two-sample t-test or Wilcoxon test, are frequently used for evaluating statistical significance of informative expressions but require adjustment for large-scale multiplicity. Due to its simplicity, Bonferroni adjustment has been widely used to circumvent this problem. It is well known, however, that the standard Bonferroni test is often very conservative. In the present paper, we compare three multiple testing procedures in the microarray context: the original Bonferroni method, a Bonferroni-type improved single-step method and a step-down method. The latter two methods are based on nonparametric resampling, by which the null distribution can be derived with the dependency structure among gene expressions preserved and the family-wise error rate accurately controlled at the desired level. We also present a sample size calculation method for designing microarray studies. Through simulations and data analyses, we find that the proposed methods for testing and sample size calculation are computationally fast and control error and power precisely.

A New Testing Approach for Comparing the Overall Homogeneity of Survival Curves

AbstractThe assessment of overall homogeneity of time‐to‐event curves is a key element in survival analysis. The currently commonly used methods, e.g., log‐rank and Wilcoxon tests, may have a significant loss of statistical testing power under certain circumstances. In this paper a new statistical testing approach is developed to compare the overall homogeneity of survival curves. The proposed new method has greater power than the commonly used tests to detect overall differences between crossing survival curves. The small‐sample performance of the new test is investigated under a variety of situations by means of Monte Carlo simulations. Furthermore, the applicability of the proposed testing approach is illustrated by a real data example from a kidney dialysis trial. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A Note on the Mixed Geographically Weighted Regression Model*

Abstract. A mixed, geographically weighted regression (GWR) model is useful in the situation where certain explanatory variables influencing the response are global while others are local. Undoubtedly, how to identify these two types of the explanatory variables is essential for building such a model. Nevertheless, It seems that there has not been a formal way to achieve this task. Based on some work on the GWR technique and the distribution theory of quadratic forms in normal variables, a statistical test approach is suggested here to identify a mixed GWR model. Then, this note mainly focuses on simulation studies to examine the performance of the test and to provide some guidelines for performing the test in practice. The simulation studies demonstrate that the test works quite well and provides a feasible way to choose an appropriate mixed GWR model for a given data set.

Dose–Response and Thresholds in Mutagenicity Studies: A Statistical Testing Approach

The analysis of dose-response relationships is an important objective in toxicology, and one in which both modelling and testing approaches are used. One particular question is whether a threshold exists at low doses. The concept of a pragmatic threshold is used, i.e. low doses with biologically unimportant effects are assumed to be threshold doses. "Biologically unimportant" means, in statistical terms, a lower effect than the effect of the negative control, or at least a just-tolerable margin delta higher than the effect of the negative control. Therefore, threshold doses can be tested in terms of a one-sided hypothesis of equivalence. A new approach is proposed, assuming, at the least, that the low dose is a threshold dose, and the highest dose is superior to the negative control. By analogy to the k-fold rule commonly used in mutagenicity studies, tests on ratio-to-control are used. The a priori definition of the threshold margin is inherently needed. A further approach proposes the analysis of dose-response relationships by means of order-restricted inference (the so-called trend test). A modification of a multiple-contrast test is used, in which only those contrasts are included that are sensitive for no effects at low doses. A further modification treats the complicated, but real, problem of simultaneous existence of a threshold, a monotonic increase, and a downturn effect at high dose(s). A parametric procedure is considered, together with an extension for proportions. The important problem of a priori sample size definition is discussed. The approaches are demonstrated by means of examples based on real data.

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

AbstractA 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.

Topology selection in unrooted molecular phylogenetic tree by minimum model-based complexity method.

In reconstruction of phylogenetic trees from molecular data, it has been pointed out that multifurcate phylogenetic trees are difficult to be correctly reconstructed by the conventional methods like maximum likelihood method(ML). In order to resolve this problem, we have been engaged in developing a new phylogenetic tree reconstruction method, based on the minimum complexity principle widely used in the inductive inference. Our method, which we call "minimum model-based complexity (MBC) method", has been proved so far to be efficient in estimating multifurcate branching when the tree is described in the form of rooted one. In this study, we make further investigations about the efficiency of MBC method in estimating the multifurcation in unrooted phylogenetic trees. To do so, we conduct computer simulation in which the estimations by MBC method are compared with those by ML, AIC and statistical test approach. The results show that MBC method also provides good estimations even in the case of multifurcate unrooted trees and suggest that it could be generally used for reconstruction of phylogenetic tree having arbitrary multifurcations.

Compressed video processing for cut detection

One of the challenging problems in video databases is the organisation of video information. Segmenting a video into a number of clips and characterising each clip has been suggested as one mechanism for organising video information. This approach requires a suitable method to automatically locate cut points (boundaries between consecutive camera shots in a video). Several existing techniques solve this problem using uncompressed video. Since video is increasingly being captured, moved, and stored in compressed form, there is a need for detecting shot boundaries directly in compressed video. The authors address this issue and show certain feature extraction steps in MPEG compressed video that allow the implementation of most of the existing cut detection methods developed for uncompressed video for MPEG video stream. They also examine the performance of three tests for cut detection by viewing the problem of cut detection as a statistical hypothesis testing problem. As the experimental results indicate, the statistical hypothesis testing approach permits fast and accurate detection of video cuts.

A statistical hypothesis testing approach to the determination of supportable aircraft separation standards

This paper deals with the setting of a statistical hypothesis testing approach to the determination of aircraft separation standards that can be supported within a given Flight Information Region. Given a minimal safety distance to be maintained between two aircraft, we derive a criterion that must be obeyed by their radar plots in order to meet the required separation at a known level of confidence. Conversely, given that a minimal safety distance is maintained between two radar plots, one can find the actual separation that can be guaranteed between both aircraft. The results described here can help to implement automated conflict alert and minimum safe altitude warning facilities.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Government Regulation and Structural Change in the Corporate Acquisitions Market: The Impact of the Williams Act

This paper presents evidence on how the Williams Act affected the corporate acquisitions market. The acquisition process is modeled and three hypotheses about the Act's effects are discussed. These hypotheses imply differing restrictions on how the Act changes the model's parameters. Parameter changes are estimated but we are unable to reliably discriminate between two of the three hypotheses using the classical statistical testing approach, though the third hypothesis is reliably rejected. Bayesian analysis using a diffuse prior is employed to make formal probability comparisons among the hypotheses. The most probable hypothesis, according to the results, implies that the Williams Act reduced the expected gross present value of acquisition attempts.

Statistical methods for assessing environmental effects on human genetic disorders

AbstractMethods are presented for assessing interactions and other effects between genetic and environmental factors for human disease or cancer susceptibility. Statistical estimation and testing approaches are based on a simple multinomial sampling model for the case‐control sampling scenario. It is noted that logistic regression methods can facilitate computation of likelihood‐based statistics in this setting. Additional models for collapsibility over genotypes within the genetic factor are considered. Monte Carlo comparisons show that the method appears to retain nominal significance levels at total sample sizes above 100. At smaller sample sizes, a goodness‐of‐fit statistic is suggested for testing the interactive effect between the genetic and environmental factors.

Diffusion indexes and a statistical test for predicting turning points in business cycles

This paper presents a non-econometric statistical procedure for testing the significance of turning points in a sample diffusion index of leading indicators, allowing one to make inferences with respect to turning points of the corresponding business cycle. The procedure is applied utilizing 30 leading indicators in the prediction of peaks and troughs in the U.S. business cycle between 1969 and 1982. For this time period, the procedure correctly predicts the four peaks and the four troughs in the U.S. business cycle with a lead time range of from zero to twelve months, although false turns with respect to the prediction of peaks were recorded. This procedure compares very favorable with the Neftci non-econometric statistical test approach for predicting turning points in business cycles. Further, this procedure may be used in conjunction with smoothing and weighting techniques for improving predictions from leading indicators.

On Statistical Testing

The statistical testing approaches of Hypothesis Testing (Fisher) and Significance Testing (Neyman-Pearson) are briefly reviewed. Highly related notions of alpha-values, P-values, and magnitude-of-effect are discussed. A statistical testing approach that is a hybrid of Hypothesis Testing and Significance Testing is then advanced. This approach takes into consideration the two decision-error probabilities as well as an alternative hypothesis characterization of interest.

On Statistical Testing

The statistical testing approaches of Hypothesis Testing (Fisher) and Significance Testing (Neyman-Pearson) are briefly reviewed. Highly related notions of alpha-values, P-values, and magnitude-of-effect are discussed. A statistical testing approach that is a hybrid of Hypothesis Testing and Significance Testing is then advanced. This approach takes into consideration the two decision-error probabilities as well as an alternative hypothesis characterization of interest.