Note on a binomial test against sectoral preference of circular observations

A binomial test is proposed to test the nullhypothesis of uniform distribution of circular observations against the alternative of sectoral preference where the sector in which the observations are expected to cluster must be chosen prior to sampling. This binomial test against sectoral preference is illustrated by an example from psychopharmacology. The method is modified for comparing the sectoral proportions of two independent as well as two paired samples of circular observations.     

An omnibus consistent adaptive percentile modified Wilcoxon rank sum test with applications in gene expression studies

Summary We present an adaptive percentile modified Wilcoxon rank sum test for the two‐sample problem. The test is basically a Wilcoxon rank sum test applied on a fraction of the sample observations, and the fraction is adaptively determined by the sample observations. Most of the theory is developed under a location‐shift model, but we demonstrate that the test is also meaningful for testing against more general alternatives. The test may be particularly useful for the analysis of massive datasets in which quasi‐automatic hypothesis testing is required. We investigate the power characteristics of the new test in a simulation study, and we apply the test to a microarray experiment on colorectal cancer. These empirical studies demonstrate that the new test has good overall power and that it succeeds better in finding differentially expressed genes as compared to other popular tests. We conclude that the new nonparametric test is widely applicable and that its power is comparable to the power of the Baumgartner‐Weiß‐Schindler test.     

Exact Tests for Comparing Two Paired Proportions with Incomplete Data

Various asymptotic test procedures have been developed previously for testing the equality of two binomial proportions with partially incomplete paired data. Test procedures that discard incomplete observations have been shown to be less powerful than those procedures that utilize all available observations. On the other hand, asymptotic test procedures that utilize all available observations may not be reliable in small‐sample problems or sparse data structures. In this article, unconditional exact test procedures are proposed for testing the equality of two paired binomial proportions with partially incomplete paired data under a random mechanism. The proposed unconditional exact test methods are illustrated with real data from a neurological study. Empirical studies are conducted to investigate the performance of these and other test procedures with respect to size and power. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multi-Sample Slippage Test for Ordered Observations

A multi-sample slippage test based on ordered observations has been given. The test statistic is based on the sum of ranks of the sample. The probability distribution of the test statistic has been worked out for small sample and it turns out to be chi-square distribution for large sample. The analytical procedure has been explained by a numerical example.     

A multiple testing procedure for clinical trials.

A multiple testing procedure is proposed for comparing two treatments when response to treatment is both dichotomous (i.e., success or failure) and immediate. The proposed test statistic for each test is the usual (Pearson) chi-square statistic based on all data collected to that point. The maximum number (N) of tests and the number (m1 + m2) of observations collected between successive tests is fixed in advance. The overall size of the procedure is shown to be controlled with virtually the same accuracy as the single sample chi-square test based on N(m1 + m2) observations. The power is also found to be virtually the same. However, by affording the opportunity to terminate early when one treatment performs markedly better than the other, the multiple testing procedure may eliminate the ethical dilemmas that often accompany clinical trials.     

How well do multivariate data sets match? The advantages of a Procrustean superimposition approach over the Mantel test

The Mantel test provides a means to test the association between distance matrices and has been widely used in ecological and evolutionary studies. Recently, another permutation test based on a Procrustes statistic (PROTEST) was developed to compare multivariate data sets. Our study contrasts the effectiveness, in terms of power and type I error rates, of the Mantel test and PROTEST. We illustrate the application of Procrustes superimposition to visually examine the concordance of observations for each dimension separately and how to conduct hypothesis testing in which the association between two data sets is tested while controlling for the variation related to other sources of data. Our simulation results show that PROTEST is as powerful or more powerful than the Mantel test for detecting matrix association under a variety of possible scenarios. As a result of the increased power of PROTEST and the ability to assess the match for individual observations (not available with the Mantel test), biologists now have an additional and powerful analytical tool to study ecological and evolutionary relationships.     

Detection of rare major genes in lipid levels

Summary A statistical test of polygenic inheritance (TPI) against the alternative of a rare major gene is presented. It is designed for a random sample of quantitative observations on index cases and siblings of those index cases (probands) selected on the basis of the observed measurements of these probands. The test focuses on an increase of the variance of siblings of probands over its value under polygenic inheritance, such an increase being expected in the presence of a major gene producing a shift of the quantitative observations. Certain data on lipids are then analyzed by this test. A major gene can tentatively be confirmed for triglycerides but not for cholesterol. In addition, the values of all index cases are subjected to an analysis of a mixture of normal distributions (NOCOMP computer program), resulting in a significant second component for triglycerides but not for cholesterol. For both TPI and NOCOMP, the exponent in a power transformation is estimated by maximum likelihood simultaneously with all other parameters, so that these analysis methods are robust against a wide range of skewness in the data, which is demonstrated by manipulation of the observations and their reanalyis.     

A simple nonparametric test for linkage with sib-pair censored event time observations

Consider the case that individual phenotype and genotype observations were collected from a large or moderate number of pedigrees. Some of the pedigrees have multi-generation nuclear families. For each nuclear family, the phenotype trait value of each sibling is the time to onset for a specific event (e.g., disease). Often, this event time may be right censored, that is, an individual is event-free at the study examination time point. In this article, we propose a purely nonparametric test for testing if the distribution of a Haseman-Elston distance measure between two siblings' event times is independent of their mean genetic sharing identical by descent at a genetic marker based on such incomplete observations from all the nuclear families. The new test can be implemented easily and is illustrated with a data set from the Genetic Analysis Workshop 12. The validity of the new test is examined via a simulation study.     

A new statistical test of fitness set data from reciprocal transplant experiments involving intermediate phenotypes

Experimental biologists use reciprocal transplant experiments (RTEs) involving divergent forms to test hypotheses about fitness trade-offs across, and local adaptation to, native environments. Additional evolutionary hypotheses about diversifying selection, the evolution of specialization, and the coexistence of specialists and generalists are only testable when the RTE also includes intermediate (or alternatively generalist) forms. Environmental variation makes such RTEs challenging, and so strategies that increase their effectiveness are useful. Here, we focus on improvements to the efficiency of RTEs involving intermediate forms with respect to the experimental design and the analysis of the resulting data. We provide a likelihood ratio-based test that offers increased statistical power and robustness relative to another test involving nonlinear regression, when used both for simulated data sets and for data from a study of two divergent fish species and their hybrids transplanted between two lake habitats. The test can be used with unequal numbers of observations, unequal variances, and binomial-type survival data and other nonnormal data. Simulations suggest that having equal numbers of experimental units in each phenotype-environment combination is reasonable. The intentional pairing of observations between environmental conditions (by using clones, full sibs, or half-sibs) is beneficial when paired observations have fitnesses that are negatively related between conditions but is detrimental with positive relatedness. Our methods can be extended to study more than two divergent forms.     

A test of transmission/disequilibrium for quantitative traits in pedigree data, by multiple regression.

The transmission/disequilibrium (TD) test (TDT), proposed, by Spielman et al., for binary traits is a powerful method for detection of linkage between a marker locus and a disease locus, in the presence of allelic association. As a test for linkage disequilibrium, the TDT makes the assumption that any allelic association present is due to linkage. Allison proposed a series of TD-type tests for quantitative traits and calculated their power, assuming that the marker locus is the disease locus. All these tests assume that the observations are independent, and therefore they are applicable, as a test for linkage, only for nuclear-family data. In this report, we propose a regression-based TD-type test for linkage between a marker locus and a quantitative trait locus, using information on the parent-to-offspring transmission status of the associated allele at the marker locus. This method does not require independence of observations, thus allowing for analysis of pedigree data as well, and allows adjustment for covariates. We investigate the statistical power and validity of the test by simulating markers at various recombination fractions from the disease locus.     

Development of sequential multiple comparison procedure for dose response test

We propose a multiple comparison procedure to identify the minimum effective dose level by sequentially comparing each dose level with the zero dose level in the dose finding test. If we can find the minimum effective dose level at an early stage in the sequential test, it is possible to terminate the procedure in the dose finding test after a few group observations up to the dose level. Thus, the procedure is viable from an economical point of view when high costs are involved in obtaining the observations. In the procedure, we present an integral formula to determine the critical values for satisfying a predefined type I familywise error rate. Furthermore, we show how to determine the required sample size in order to guarantee the power of the test in the procedure. In practice, we compare the power of the test and the required sample size for various configurations of the population means in simulation studies and adopt our sequential procedure to the dose response test in a case study.     

A chi-square goodness-of-fit analysis of dependent resource selection data

The chi2 goodness-of-fit test is commonly used for testing if animals use resources in proportion to availability. This method assumes independence of resource selection among animals. In reality, this assumption is violated if animals display antisocial or gregarious behavior. Data from a study of sharp-tailed grouse in eastern Washington suggested some dependency among observations. Realizing that this dependency can have a great influence on inference for resource selection data, we develop a technique to incorporate information on dependent observations through a simple adjustment of the usual goodness-of-fit statistic. We also demonstrate how confidence intervals on proportional use may be modified for dependent observations. Simulation is used to compare our method to other methods.     

A nonparametric version of Williams' test for a randomized block design

A large-sample nonparametric version of Williams' test for comparing increasing doses of a substance with a zero-dose control response is given for observations from a randomized block experimental design. The method is based on Friedman-type ranks. Williams' test and the nonparametric equivalent for a one-way design are briefly described. The validity of the new method is shown and a numerical example is given.     

Nonparametric methods for analyzing incomplete nondecreasing repeated measurements

In comparing the effectiveness of two treatments, suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject. A class of univariate one-sided global asymptotically distribution-free tests is proposed to test the equality of the two treatments. The test procedures allow different patterns of missing observations in the two groups to be compared, although the missing data mechanism is required to be independent of the observations in each treatment group. Test-based point and interval estimators of the global treatment difference are given. Multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study. The proposed methods are illustrated by an example from a bladder cancer study.     

A new location-scale test based on a combination of the ideas of Levene and Lepage

Lepage's test combines the Wilcoxon rank-sum and the Ansari-Bradley statistics. We propose to replace the latter statistic by a Wilcoxon rank-sum calculated after Levene's transformation. We use the medians for this transformation, i.e. absolute deviations from sample medians are calculated. The new location-scale test can be carried out as a permutation test based on permutations of the original observations, the Levene transformation has to be applied for each permutation in an intermediate step to calculate the test statistic. Simulations indicate that the new test can be more powerful than an O'Brien-type test and Lepage's test, the latter is the standard nonparametric location-scale test. The new test is illustrated using real data about colony sizes of yellow-eyed penguins and an SAS program to perform the test is freely available.     

Testing equality of survival functions based on both paired and unpaired censored data

We introduce two test procedures for comparing two survival distributions on the basis of randomly right-censored data consisting of both paired and unpaired observations. Our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data. One generalization adapts the Prentice-Wilcoxon score, while the other adapts the Akritas score. The use of these particular scoring systems in pooled rank tests with randomly right-censored paired data has been advocated by several researchers. Our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores. Permutation versions of tests for right-censored paired data and for two independent right-censored samples that use the proposed scoring systems are obtained as special cases of our test procedures. Simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log-logistic distributions for the survival times. We also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data. The tests are applied to skin graft data previously reported elsewhere.     

Proposal of k Sample Tests for Bivariate Censored Data for Nondecreasing Ordered Alternatives

Tests are introduced which are designed to test for a nondecreasing ordered alternative among the survival functions of k populations consisting of multiple observations on each subject. Some of the observations could be right censored. A simulation study is conducted comparing the proposed tests on the basis of estimated power when the underlying distributions are multivariate normal. Equal sample sizes of 20 with 25% censoring, and 40 with both 25% and 50% censoring are considered for 3 and 4 populations. All of the tests hold their α‐values well. A recommendation is made as to the best overall test for the situations considered.     

Potassium current kinetics in Myxicola axons. Effects of conditioning prepulses

In Myxicola giant axons the time constants for activation of the potassium conductance (GK) after prepulses less depolarized than a test pulse are comparable to the time constants for turn off of GK after prepulses more depolarized than the same test pulse. The absolute magnitude of the steady-state level of GK is also independent of prepulse amplitude in Myxicola. The results are contrasted with recent observations on voltage-clamped frog nodes.     

Sensitivity analysis for m-estimates, tests, and confidence intervals in matched observational studies

Huber's m-estimates use an estimating equation in which observations are permitted a controlled level of influence. The family of m-estimates includes least squares and maximum likelihood, but typical applications give extreme observations limited weight. Maritz proposed methods of exact and approximate permutation inference for m-tests, confidence intervals, and estimators, which can be derived from random assignment of paired subjects to treatment or control. In contrast, in observational studies, where treatments are not randomly assigned, subjects matched for observed covariates may differ in terms of unobserved covariates, so differing outcomes may not be treatment effects. In observational studies, a method of sensitivity analysis is developed for m-tests, m-intervals, and m-estimates: it shows the extent to which inferences would be altered by biases of various magnitudes due to nonrandom treatment assignment. The method is developed for both matched pairs, with one treated subject matched to one control, and for matched sets, with one treated subject matched to one or more controls. The method is illustrated using two studies: (i) a paired study of damage to DNA from exposure to chromium and nickel and (ii) a study with one or two matched controls comparing side effects of two drug regimes to treat tuberculosis. The approach yields sensitivity analyses for: (i) m-tests with Huber's weight function and other robust weight functions, (ii) the permutational t-test which uses the observations directly, and (iii) various other procedures such as the sign test, Noether's test, and the permutation distribution of the efficient score test for a location family of distributions. Permutation inference with covariance adjustment is briefly discussed.     

The pinwheel flap nipple and barrier areola graft reconstruction

The pinwheel flap with a snug barrier areola graft appears to be an efficacious modification of Little's quadripod flap for nipple reconstruction. Further, long-term evaluation is needed to test the validity of these observations over several years.