Exact,Distribution Free Confidence Intervals for Late Effects in Censored Matched Pairs

When comparing censored survival times for matched treated and control subjects, a late effect on survival is one that does not begin to appear until some time has passed. In a study of provider specialty in the treatment of ovarian cancer, a late divergence in the Kaplan–Meier survival curves hinted at superior survival among patients of gynecological oncologists, who employ chemotherapy less intensively, when compared to patients of medical oncologists, who employ chemotherapy more intensively; we ask whether this late divergence should be taken seriously. Specifically, we develop exact, permutation tests, and exact confidence intervals formed by inverting the tests, for late effects in matched pairs subject to random but heterogeneous censoring. Unlike other exact confidence intervals with censored data, the proposed intervals do not require knowledge of censoring times for patients who die. Exact distributions are consequences of two results about signs, signed ranks, and their conditional independence properties. One test, the late effects sign test, has the binomial distribution; the other, the late effects signed rank test, uses nonstandard ranks but nonetheless has the same exact distribution as Wilcoxon's signed rank test. A simulation shows that the late effects signed rank test has substantially more power to detect late effects than do conventional tests. The confidence statement provides information about both the timing and magnitude of late effects (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-sample rank tests for detecting changes that occur in a small proportion of the treated population

In the course of studying a biological phenomenon thought to be a precursor to chromosome breakage, researchers have found that treatments sometimes produce a higher proportion of "outliers" than do controls. Our examples pertain to smokers and patients undergoing chemotherapy, although the statistical methods developed here would apply to subjects exposed to any other health hazard. We formulate the problem in a nonparametric setting. Locally most powerful rank tests are obtained for mixture alternatives. In one instance, the approximate scores test has the simple form of counting the number of treatment responses above a combined sample percentile. Our test statistics are compared to the Wilcoxon and normal scores tests using empirical power studies and asymptotic efficiencies.     

The Baumgartner-Weiss-Schindler test for the detection of differentially expressed genes in replicated microarray experiments

MOTIVATION: An important application of microarray experiments is to identify differentially expressed genes. Because microarray data are often not distributed according to a normal distribution nonparametric methods were suggested for their statistical analysis. Here, the Baumgartner-Weiss-Schindler test, a novel and powerful test based on ranks, is investigated and compared with the parametric t-test as well as with two other nonparametric tests (Wilcoxon rank sum test, Fisher-Pitman permutation test) recently recommended for the analysis of gene expression data. RESULTS: Simulation studies show that an exact permutation test based on the Baumgartner-Weiss-Schindler statistic B is preferable to the other three tests. It is less conservative than the Wilcoxon test and more powerful, in particular in case of asymmetric or heavily tailed distributions. When the underlying distribution is symmetric the differences in power between the tests are relatively small. Thus, the Baumgartner-Weiss-Schindler is recommended for the usual situation that the underlying distribution is a priori unknown. AVAILABILITY: SAS code available on request from the authors.     

An Exact Paired Rank Test

An exact rank test for two dependent samples based on overall mid‐ranks is discussed which can be applied to metric as well as to ordinal data. The exact conditional distribution of the test statistic given the observed vector of rank differences is determined. A recursion formula is given as well as a fast shift algorithm in SAS/IML code. Moreover, it is demonstrated that the paired rank test can be more powerful than other tests for paired samples by means of a simulation study. Finally, the test is applied to a psychiatric trial with longitudinal ordinal data.     

The treatment of isolated genera

Problems presented by genera, or small groups of genera, which have been given family rank are reviewed, and the genera are divided into a number of categories according to the closeness of their affinity to other genera or families. Satellite genera that stand in close relation to families should be united with them. Binary families, that have been divided into two (or more) related families, should be re–united. Families connected by linking genera, should, logically, be united but practical considerations usually prevent this. Clusters of diverse but more or less distantly related genera present unusual problems, being treated either as several, often monogeneric families or as a loosely structured family. Truly isolated genera must be given family and often ordinal rank.     

Estimating Location Parameters Using Censored Rank Statistics

In this paper censored data rank location estimators are obtained by using censored one-sample rank test statistics of the location parameter and censored two-sample rank test statistics of the shift of location parameter. Also, methods for constructing censored small sample confidence intervals and asymptotic confidence intervals for the location are considered. Generalizations of the solutions from uncensored one-sample and two-sample rank tests are utilized.     

A simple approach to estimate similarity in ecosystem analysis

A simple rank similarity index is proposed to use in estimation of ecological community similarities. The analysis of similarities is based on hypergeometric probabilities of the coincidence of dominant species in the samples. When 4 dominant species are ranked in samples, two sets of ranks can be compared in 133 different ways. In the case of total similarity rank similarity index M=10 and for dissimilarity M=0. Critical levels of M are given for total amount of species from 10 to 300. The proposed approach useful in rapid similarity analysis of planktonic communities.     

Fitting a sinusoid to biological rhythm data using ranks

Biological data are frequently collected with small numbers of observations from several subjects. Often a linear model is fitted to the data by averaging over subjects. Frequently there are considerable between-subject differences, and due allowance should be made for these when the model is fitted by parametric techniques. In this paper it is proposed that the model should be fitted by using the within-subject ranks of the observations. The technique is applied to the problem of estimating the 'cosinor' diagram for biological rhythm data. An example involving melatonin levels, in which there are considerable between-subject differences, is considered. The results obtained by use of the ranks are compared with those of a parametric analysis which makes allowance for the between-subject differences. The results are very similar, but the rank analysis requires much less computation.     

Caveat emptor: rank transform methods and interaction

When distributional assumptions for analysis of variance are suspect, and nonparametric methods are unavailable, ecologists frequently employ rank transformation (RT) methods. The technique replaces observations by their ranks, which are then analysed using standard parametric tests. RT methods are widely recommended in statistics texts and in manuals for packages like SAS and IMSL. They are robust and powerful for the analysis of additive factorial designs. Recently, however, RT methods have been found to be grossly inappropriate for use with non-additive models. This severe limitation remains largely unreported outside of the theoretical statistics literature. Our goal is to explain this shortcoming of RT methods.     

Lower cardiovascular responsiveness in men with a positive family history of hypertension who remain normotensive in middle age

Within the framework of a primary preventive study in 760 research workers aged 30-59, laboratory examinations of cardiovascular responsiveness to upright posture, cold and mental stress (Stroop word-colour interference test and ranking of three-digit numbers) were performed. Twenty men with essential hypertension (Stage I-II) not treated with antihypertensive drugs were selected from this population (Group 3) and matched with normotensive subjects with a negative (Group 1) and positive (Group 2) family history of hypertension, according to age, weight, neuroticism and Type A behaviour. Hypertensive men showed higher pressor responses to cold and mental stress tests than normotensive ones. Significantly lower anticipation and test responses were found in Group 2 as compared with Group 1 and 3, i.e. in those subjects who remained normotensive to higher age in spite of having a positive family history of hypertension. This fact suggests an important--intrinsic or modulating--role of cardiovascular responsiveness to physiological and psychological challenges in the manifestation of the genetic disposition for essential hypertension.     

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.     

Trying to See Red Through Stickleback Photoreceptors: Functional Substitution of Receptor Sensitivities

A key to understanding animal behavior is knowledge of the sensory information animals extract from their environment. For visually motivated tasks, the information animals obtain through their eyes is often assumed to be essentially the same as that perceived by humans. However, known differences in structure and processing among the visual systems of different animals clearly indicate that the world seen by each is different. A well‐characterized difference between human and other animal visual systems is the number of types and spectral sensitivities of their photoreceptors. We are developing a technique, functional substitution, that exploits knowledge of these differences to portray for human subjects, colors as they would appear through the photoreceptors of another animal. In a specific application, we ask human subjects to rank hues of male threespine stickleback (Gasterosteus aculeatus) throats viewed through stickleback photopigments. We compare these ranks to ranks of the same throat hues viewed through normal human photoreceptors. We find essentially no difference between the two sets of rankings. This suggests that any differences in human and stickleback rankings of such hues would result from differences in post‐receptoral neural processing. Using a previously developed model of stickleback neural processing, we established another ranking of the hues which was again essentially the same as the rankings produced by the human subjects. A growing literature indicates that stickleback do rank such hues in the evaluation of males as potential mates or threats. Although our results do not demonstrate that humans and stickleback use the same mechanisms to assess color, our experiments significantly failed to show that stickleback and human rankings of throat hues should be different. Nevertheless, a comparison of all these rankings to ranks derived from subjective color scoring by human observers suggests that color scoring may utilize other cues and should thus be used cautiously.     

Comparison of social ranks based on worm-running and aggressive behaviour in young domestic fowl

Worm-running is behaviour in which a chick runs carrying a worm-like object while flock mates follow and attempt to grab the object from its beak. We hypothesised that social ranks based on worm-running frequency are stable over time and are positively correlated with social ranks based on success in aggressive interactions when older. At 8-12 days of age, we scored worm-running in 17 groups of 12 female White Leghorn chicks during three 10-min tests. Based on instantaneous scans at 5-s intervals, the bird carrying the 'worm' most often was placed in rank one and so on down the rank order. These tests were repeated at 68-70 days of age. An aggression index for each bird was calculated as the number of aggressive acts given, divided by the number given and received, during three 1-h observation periods when the birds were 68-70 days. Ranks obtained in worm-running tests were positively correlated over the two age periods (P < 0.05) but were not correlated with ranks based on the aggression index (P > 0.05). Our results indicate that worm-running ranks are not predictive of success in aggressive interactions. Instead, worm-running fits some criteria for play.     

Social rank and body size as determinants of positional behavior inPan troglodytes

A yearlong study of the positional behavior ofPan troglodytes at the Mahale Mountains National Park yielded 571 hr of observation.Cant (1987) articulated four predictions concerning the relationship between body weight/branch diameter and positional behavior based on the classic suspensory-ape paradigm. He noted that only two were supported by orangutan data. Three of these four hypothesis were not supported by chimpanzee data, as follows: there was no significant difference between the three largest males and the four smallest males in (1) branch diameters (5.8 cm vs 5.2 cm) nor (2) in the percentage of arm-hanging (13.6% vs 12.1%); and (3) large males did not arm-hang significantly more often than small males in any of three support diameter categories. The fourth hypothesis, that arm-hanging should be more common among smaller branches, was supported: arm-hanging as a percentage of all posture rose from 2.5% to 8.3% to 24% as stratum size decreased from >10 cm to <3 cm. The possibility that the first three hypotheses failed because of confounding effects of a correlation between body size and social rank was examined. Multiple regressions were done on 6600 2-min instantaneous observations on focal individuals. With social rank effects factored out, larger individuals preferentially utilized smaller, rather than larger supports. When positional mode frequencies were compared between large and small males matched for social rank, large males exhibited a lower frequency of arm-hanging than small males. An unexpected result was that social rank more consistently predicted branch diameter choice than body size. The most profound trend was for high ranking males to use larger supports, even though they spent more time in the terminal branches. These results suggest that (1) suspensory behavior is functionally related to small branch diameters; (2) chimpanzees do not prefer smaller branches, rather they are forced into them by food choice limitations; and (3) social rank more profoundly affects chimpanzee behavior than body weight.     

Effect of a Treatment with Naphthaleneacetic Acid on the Arrangement of Lateral Roots in Onion (Allium cepa L): General Pattern and Coordination between Ranks

Lateral roots in Allium cepa arise in longitudinal rows opposite the protoxylem poles of adventitious roots. The number, spacing within ranks and positional relationship to laterals in different ranks were analysed in control roots and those treated with an auxin (α-naphthaleneacetic acid). Treatment increased numbers of laterals per rank and distributed the more evenly in all ranks. Laterals of control roots were concentrated in two neighbouring ranks. Auxin-treated roots showed a more regular distribution of laterals between ranks and close spacing of laterals along each rank. Comparisons with theoretical random distributions suggest a dispersed spacing model for lateral root arrangement with mutual repulsion between successive lateral roots within each rank both in control and auxintreated roots. On the other hand, there is some interaction between laterals in different ranks in 0.1 mM NAA-treated roots.     

A word-oriented approach to alignment validation

MOTIVATION: Multiple sequence alignment at the level of whole proteomes requires a high degree of automation, precluding the use of traditional validation methods such as manual curation. Since evolutionary models are too general to describe the history of each residue in a protein family, there is no single algorithm/model combination that can yield a biologically or evolutionarily optimal alignment. We propose a 'shotgun' strategy where many different algorithms are used to align the same family, and the best of these alignments is then chosen with a reliable objective function. We present WOOF, a novel 'word-oriented' objective function that relies on the identification and scoring of conserved amino acid patterns (words) between pairs of sequences. RESULTS: Tests on a subset of reference protein alignments from BAliBASE showed that WOOF tended to rank the (manually curated) reference alignment highest among 1060 alternative (automatically generated) alignments for a majority of protein families. Among the automated alignments, there was a strong positive relationship between the WOOF score and similarity to the reference alignment. The speed of WOOF and its independence from explicit considerations of three-dimensional structure make it an excellent tool for analyzing large numbers of protein families. AVAILABILITY: On request from the authors.     

Are the linnean and phylogenetic nomenclatural systems combinable? Recommendations for biological nomenclature

A combination approach between the rules and recommendations from the Linnean (rank-based) and phylogenetic nomenclature is proposed, with a review of the debate. Advantages and drawbacks of both systems are discussed. Too often the debates are biased and unconstructive, and there is a need for dialogue and compromise. Our recommendations for the future of biological classification, to be considered by new editions of all codes of nomenclature, would enable the Linnean and the phylogenetic nomenclatural systems to coexist, or be combined. (1) We see it as essential that species binomen, including the formal rank of genus, are retained, and (2) species should continue to be linked to type specimens. (3) The use of other formal ranks should be minimized; however, we suggest retaining the classical supergeneric ranks (family, class, order, phylum, kingdom) for purely practical reasons. (4) For these ranks and any formally defined clades, type taxa (species, genera) should be replaced by phylogenetic definitions that explicitly hypothesize monophyly. (5) In contrast, species monophyly should not be required, because theory predicts that many species are not monophyletic. (6) It should be stressed that equal ranks do not imply comparable evolutionary histories.     

Optimal unified approach for rare-variant association testing with application to small-sample case-control whole-exome sequencing studies

We propose in this paper a unified approach for testing the association between rare variants and phenotypes in sequencing association studies. This approach maximizes power by adaptively using the data to optimally combine the burden test and the nonburden sequence kernel association test (SKAT). Burden tests are more powerful when most variants in a region are causal and the effects are in the same direction, whereas SKAT is more powerful when a large fraction of the variants in a region are noncausal or the effects of causal variants are in different directions. The proposed unified test maintains the power in both scenarios. We show that the unified test corresponds to the optimal test in an extended family of SKAT tests, which we refer to as SKAT-O. The second goal of this paper is to develop a small-sample adjustment procedure for the proposed methods for the correction of conservative type I error rates of SKAT family tests when the trait of interest is dichotomous and the sample size is small. Both small-sample-adjusted SKAT and the optimal unified test (SKAT-O) are computationally efficient and can easily be applied to genome-wide sequencing association studies. We evaluate the finite sample performance of the proposed methods using extensive simulation studies and illustrate their application using the acute-lung-injury exome-sequencing data of the National Heart, Lung, and Blood Institute Exome Sequencing Project.     

Grooming Between Male Chimpanzees at Ngogo,Kibale National Park. II. Influence of Male Rank and Possible Competition for Partners

Allogrooming contributes to the development and maintenance of social relationships, including those that involve alliances, in many primate species. Variation in relatedness, dominance rank, and other factors can produce variation in the value of others as grooming partners. Several models have been developed to account for variation in the distribution of grooming in relation to dominance ranks. These start from the premise that individuals are attracted to high-ranking partners, but time limits, direct competition, and prior grooming engagement between high-ranking individuals can constrain access to them. Sambrook et al. (1995) formalized some of these models and showed the importance of taking group size variation into account when assessing them. Chimpanzees form multimale communities in which males are the philopatric sex. Males commonly associate and groom with each other; they also form dominance hierarchies and form alliances that influence dominance ranks and mating success. Both male rank and the rank distance between partners are significantly correlated with the distribution of grooming between males in an extremely large chimpanzee community at Ngogo, Kibale National Park, Uganda, that has more males than any other known community. High-ranking males had more grooming partners than mid- or low-ranking males. Grooming predominantly went up the dominance hierarchy, but was also concentrated among males that were close in rank. Rank and rank distance apparently both affected grooming independently of reciprocity in grooming and independently of the frequency with which males associated in temporary parties. However, the data do not clearly indicate how constraints on access to partners might have operated. Published data from a smaller chimpanzee community at Mahale show no rank or rank distance effect on male grooming. These results and earlier, conflicting findings on the association between dominance rank and grooming in male chimpanzees indicate that variation in group size, i.e., the number of males per community, probably influences the strength of any such effects, as happens for grooming between females in several cercopithecine species. Data on coalitions at Ngogo support the argument that high-ranking males are valuable social partners, and similarity in strategies of alliance formation may influence the distribution of grooming.     

Testing the correlation between beta diversity and differences in productivity among global ecoregions,biomes, and biogeographical realms

Considerable amount of research on the relationships between species diversity and productivity at different spatial, ecological, and taxonomic scales has been conducted. However, the overall trend of the correlation at the global scale still remains sketchy and the causal relationship between species diversity and productivity needs further exploration. This is especially true with beta diversity since most studies carried out use alpha diversity as the general term for species diversity. In this study we use the MODIS NDVI as the surrogate of productivity, and the WWF ecoregion systems and its species distribution information to test correlations between beta diversity and differences in productivity at various taxonomic ranks on a global scale. Matrix correlation is performed between species composition measured as beta diversities using Sørensen similarity index and MODIS NDVI/productivity measured as Bhattacharyya distances through Mantel permutation tests. The correlation coefficients and Mantel test significance levels are reported at the global ecoregion, biogeographical realm, and biome levels respectively. Significant correlations are found at all three taxonomic ranks. Results from realm and biome tests suggest that the highest correlations are reached at the temperate regions when species rank is used. Our findings suggest that species' natural spatial boundaries, such as the biogeographical realms or biogeographic kinship play a critical role in shaping the correlation patterns between beta diversity and productivity differences at the global scale.