Likelihood-based tests of topologies in phylogenetics

Likelihood-based statistical tests of competing evolutionary hypotheses (tree topologies) have been available for approximately a decade. By far the most commonly used is the Kishino-Hasegawa test. However, the assumptions that have to be made to ensure the validity of the Kishino-Hasegawa test place important restrictions on its applicability. In particular, it is only valid when the topologies being compared are specified a priori. Unfortunately, this means that the Kishino-Hasegawa test may be severely biased in many cases in which it is now commonly used: for example, in any case in which one of the competing topologies has been selected for testing because it is the maximum likelihood topology for the data set at hand. We review the theory of the Kishino-Hasegawa test and contend that for the majority of popular applications this test should not be used. Previously published results from invalid applications of the Kishino-Hasegawa test should be treated extremely cautiously, and future applications should use appropriate alternative tests instead. We review such alternative tests, both nonparametric and parametric, and give two examples which illustrate the importance of our contentions.     

An Adaptive Location‐Scale Test

Increasing locations are often accompanied by an increase in variability. In this case apparent heteroscedasticity can indicate that there are treatment effects and it is appropriate to consider an alternative involving differences in location as well as in scale. As a location‐scale test the sum of a location and a scale test statistic can be used. However, the power can be raised through weighting the sum. In order to select values for this weighting an adaptive design with an interim analysis is proposed: The data of the first stage are used to calculate the weights and with the second stage's data a weighted location‐scale test is carried out. The p‐values of the two stages are combined through Fisher's combination test. With a Lepage‐type location‐scale test it is illustrated that the resultant adaptive test can be more powerful than the ‘optimum’ test with no interim analysis. The principle to calculate weights, which cannot be reasonably chosen a priori, with the data of the first stage may be useful for other tests which utilize weighted statistics, too. Furthermore, the proposed test is illustrated with an example from experimental ecology.     

Designing and analyzing clinical trials with composite outcomes: consideration of possible treatment differences between the individual outcomes

When the individual outcomes within a composite outcome appear to have different treatment effects, either in magnitude or direction, researchers may question the validity or appropriateness of using this composite outcome as a basis for measuring overall treatment effect in a randomized controlled trial. The question remains as to how to distinguish random variation in estimated treatment effects from important heterogeneity within a composite outcome. This paper suggests there may be some utility in directly testing the assumption of homogeneity of treatment effect across the individual outcomes within a composite outcome. We describe a treatment heterogeneity test for composite outcomes based on a class of models used for the analysis of correlated data arising from the measurement of multiple outcomes for the same individuals. Such a test may be useful in planning a trial with a primary composite outcome and at trial end with final analysis and presentation. We demonstrate how to determine the statistical power to detect composite outcome treatment heterogeneity using the POISE Trial data. Then we describe how this test may be incorporated into a presentation of trial results with composite outcomes. We conclude that it may be informative for trialists to assess the consistency of treatment effects across the individual outcomes within a composite outcome using a formalized methodology and the suggested test represents one option.     

Testing for Poisson Zero Inflation in Disease Mapping

When analyzing mortality data due to rare diseases in small areas, it is common to find several health zones with no mortality cases. In these circumstances, the classical homogeneous model based on the Poisson distribution used to estimate the relative risks within each area may encounter lack of fit due to a disproportionately large frequency of zeros. To cope with these zeros, the zero inflated Poisson model can be used. In this paper, we propose a test for detecting zero inflation in the context of disease mapping which is based on bootstrap techniques. The test is illustrated using male mortality data due to brain cancer in Navarra, Spain. In addition, comparisons with other tests for Poisson zero inflation such as the score test and the likelihood ratio test are carried out in terms of empirical power and size using the brain cancer scenario. The proposed bootstrap test has good power and size and works well when detecting the excess of zeros in small area data sets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sample reproducibility of genetic association using different multimarker TDTs in genome-wide association studies: characterization and a new approach

Multimarker Transmission/Disequilibrium Tests (TDTs) are very robust association tests to population admixture and structure which may be used to identify susceptibility loci in genome-wide association studies. Multimarker TDTs using several markers may increase power by capturing high-degree associations. However, there is also a risk of spurious associations and power reduction due to the increase in degrees of freedom. In this study we show that associations found by tests built on simple null hypotheses are highly reproducible in a second independent data set regardless the number of markers. As a test exhibiting this feature to its maximum, we introduce the multimarker 2-Groups TDT (mTDT(2G)), a test which under the hypothesis of no linkage, asymptotically follows a χ2 distribution with 1 degree of freedom regardless the number of markers. The statistic requires the division of parental haplotypes into two groups: disease susceptibility and disease protective haplotype groups. We assessed the test behavior by performing an extensive simulation study as well as a real-data study using several data sets of two complex diseases. We show that mTDT(2G) test is highly efficient and it achieves the highest power among all the tests used, even when the null hypothesis is tested in a second independent data set. Therefore, mTDT(2G) turns out to be a very promising multimarker TDT to perform genome-wide searches for disease susceptibility loci that may be used as a preprocessing step in the construction of more accurate genetic models to predict individual susceptibility to complex diseases.     

Extension of the rank sum test for clustered data: two-group comparisons with group membership defined at the subunit level

The Wilcoxon rank sum test is widely used for two-group comparisons for nonnormal data. An assumption of this test is independence of sampling units both between and within groups. In ophthalmology, data are often collected on two eyes of an individual, which are highly correlated. In ophthalmological clinical trials, randomization is usually performed at the subject level, but the unit of analysis is the eye. If the eye is used as the unit of analysis, then a modification to the usual Wilcoxon rank sum variance formula must be made to account for the within-cluster dependence. For some clustered data designs, where the unit of analysis is the subunit, group membership may be defined at the subunit level. For example, in some randomized ophthalmologic clinical trials, different treatments may be applied to fellow eyes of some patients, while the same treatment may be applied to fellow eyes of other patients. In general, binary eye-specific covariates may be present (scored as exposed or unexposed) and one wishes to compare nonnormally distributed outcomes between exposed and unexposed eyes using the Wilcoxon rank sum test while accounting for the clustering. In this article, we present a corrected variance formula for the Wilcoxon rank sum statistic in the setting of eye (subunit)-specific covariates. We apply it to compare ocular itching scores in ocular allergy patients between eyes treated with active versus placebo eye drops, where some patients receive the same eye drop in both eyes, while other patients receive different eye drops in fellow eyes. We also present comparisons between the clustered Wilcoxon test and each of the signed rank tests and mixed model approaches and show dramatic differences in power in favor of the clustered Wilcoxon test for some designs.     

NUCLEIC ACID SEQUENCE PHYLOGENY AND RANDOM OUTGROUPS

Abstract— When divergent taxa are used to root networks, it is assumed that the character stales in the outgroup have historical similarity to those in the ingroup. Yet, if the data are nucleic acid sequences, the character stales shared by a divergent outgroup may be based not on history but on random similarity. A simple procedure is proposed to test this possibility. In the absence of an appropriate outgroup, root position can be estimated with the use of an asymmetrical character transformation matrix. If the matrix is sufficiently biased, it can supply the polarity information usually derived from an outgroup. This outgroup test and rooting procedure are demonstrated with ADH sequences from the genus Drosophila .     

Test for increasing convex order in multivariate response

Trend test based on cross-classified data in dose-response has been a central problem in medicine. Most of existing test methods are known to only fit to binary response variables. However, the approaches for binary response tables may suffer from the lack of a clear choice for dichotomization. For multivariate response with ordered categories, some studies have been done for simple stochastic order, likelihood ratio order and so on. However, methods of statistical inference on increasing convex order for more than two multinomial populations have not been fully developed. For testing the increasing convex order alternative, this article provides a model-free test method which can be used in the case of two-way tables and stratified data. Two real examples will be used to illustrate how to apply our test method.     

Accounting for nonignorable verification bias in assessment of diagnostic tests

A "gold" standard test, providing definitive verification of disease status, may be quite invasive or expensive. Current technological advances provide less invasive, or less expensive, diagnostic tests. Ideally, a diagnostic test is evaluated by comparing it with a definitive gold standard test. However, the decision to perform the gold standard test to establish the presence or absence of disease is often influenced by the results of the diagnostic test, along with other measured, or not measured, risk factors. If only data from patients who received the gold standard test were used to assess the test performance, the commonly used measures of diagnostic test performance--sensitivity and specificity--are likely to be biased. Sensitivity would often be higher, and specificity would be lower, than the true values. This bias is called verification bias. Without adjustment for verification bias, one may possibly introduce into the medical practice a diagnostic test with apparent, but not truly, high sensitivity. In this article, verification bias is treated as a missing covariate problem. We propose a flexible modeling and computational framework for evaluating the performance of a diagnostic test, with adjustment for nonignorable verification bias. The presented computational method can be utilized with any software that can repetitively use a logistic regression module. The approach is likelihood-based, and allows use of categorical or continuous covariates. An explicit formula for the observed information matrix is presented, so that one can easily compute standard errors of estimated parameters. The methodology is illustrated with a cardiology data example. We perform a sensitivity analysis of the dependency of verification selection process on disease.     

The role of hair in swimming of laboratory mice: implications for behavioural studies in animals with abnormal hair

Animal swimming tests, such as the forced swim test, are extensively used in biomedical research to study rodent behaviour. Hair and skin exposed to water may be an important factor affecting the performance in this test. Since various hair and skin abnormalities are not uncommon in genetically modified or drug-treated laboratory animals, this test may be inappropriate for these animals. Because on occasions it is necessary to screen their swimming behaviour, in the present study we aimed to assess the role of hair in swimming of laboratory rodents in the forced swim test, widely used in behavioural research. For this, we shaved laboratory mice (129S1 strain) and compared their swimming patterns with those of unshaven controls. Overall, shaving mice did not affect their swimming behaviours in the 5 min forced swim test. Our results indicate that hair condition is not an important factor in the forced swim test for this mouse strain, and suggest that this test may have wider utility for behavioural analyses of mice with abnormal hair.     

Testing homogeneity in Weibull-regression models

In survival studies with families or geographical units it may be of interest testing whether such groups are homogeneous for given explanatory variables. In this paper we consider score type tests for group homogeneity based on a mixing model in which the group effect is modelled as a random variable. As opposed to hazard-based frailty models, this model presents survival times that conditioned on the random effect, has an accelerated failure time representation. The test statistics requires only estimation of the conventional regression model without the random effect and does not require specifying the distribution of the random effect. The tests are derived for a Weibull regression model and in the uncensored situation, a closed form is obtained for the test statistic. A simulation study is used for comparing the power of the tests. The proposed tests are applied to real data sets with censored data.     

The rapid fluorescent focus inhibition test is a suitable method for batch potency testing of inactivated rabies vaccines

The European Pharmacopoeia proposes two methods for potency determination of inactivated rabies vaccines for veterinary use: The first one is a classical mouse challenge test, which is imprecise, time-consuming, and causes severe distress to the test animals. Alternatively, the potency may be determined serologically by measuring the neutralizing antibody titers induced after vaccination of mice by using a rapid fluorescent focus inhibition test (RFFIT). Although this method is faster and less painful for the animals, it is not widely used yet, and only little data exist concerning the comparability of both methods.We have therefore performed a comparative study, in which we demonstrated a good correlation between the challenge test results and the mean titers determined by RFFIT. Furthermore, all vaccine batches failing the challenge test were also recognized as insufficient in the serological assay. This publication further describes the influence of different vaccine administration routes on the resulting antibody titers, and it proposes various modifications to the serological assay protocol which could improve its overall practicability. Finally, we recommend that the serological assay be used for the potency testing of inactivated rabies vaccines.     

A test for linkage and association in general pedigrees: the pedigree disequilibrium test

Family-based tests of linkage disequilibrium typically are based on nuclear-family data including affected individuals and their parents or their unaffected siblings. A limitation of such tests is that they generally are not valid tests of association when data from related nuclear families from larger pedigrees are used. Standard methods require selection of a single nuclear family from any extended pedigrees when testing for linkage disequilibrium. Often data are available for larger pedigrees, and it would be desirable to have a valid test of linkage disequilibrium that can use all potentially informative data. In this study, we present the pedigree disequilibrium test (PDT) for analysis of linkage disequilibrium in general pedigrees. The PDT can use data from related nuclear families from extended pedigrees and is valid even when there is population substructure. Using computer simulations, we demonstrated validity of the test when the asymptotic distribution is used to assess the significance, and examined statistical power. Power simulations demonstrate that, when extended pedigree data are available, substantial gains in power can be attained by use of the PDT rather than existing methods that use only a subset of the data. Furthermore, the PDT remains more powerful even when there is misclassification of unaffected individuals. Our simulations suggest that there may be advantages to using the PDT even if the data consist of independent families without extended family information. Thus, the PDT provides a general test of linkage disequilibrium that can be widely applied to different data structures.     

A global test for groups of genes: testing association with a clinical outcome

MOTIVATION: This paper presents a global test to be used for the analysis of microarray data. Using this test it can be determined whether the global expression pattern of a group of genes is significantly related to some clinical outcome of interest. Groups of genes may be any size from a single gene to all genes on the chip (e.g. known pathways, specific areas of the genome or clusters from a cluster analysis). RESULT: The test allows groups of genes of different size to be compared, because the test gives one p-value for the group, not a p-value for each gene. Researchers can use the test to investigate hypotheses based on theory or past research or to mine gene ontology databases for interesting pathways. Multiple testing problems do not occur unless many groups are tested. Special attention is given to visualizations of the test result, focussing on the associations between samples and showing the impact of individual genes on the test result. AVAILABILITY: An R-package globaltest is available from http://www.bioconductor.org     

Characterization of moorland vegetation and the prediction of bird abundance using remote sensing

Aims To characterize and identify upland vegetation composition and height from a satellite image, and assess whether the resulting vegetation maps are accurate enough for predictions of bird abundance. Location South‐east Scotland, UK. Methods Fine‐taxa vegetation data collected using point samples were used for a supervised classification of a Landsat 7 image, while linear regression was used to model vegetation height over the same image. Generalized linear models describing bird abundance were developed using field‐collected bird and vegetation data. The satellite‐derived vegetation data were substituted into these models and efficacy was examined. Results The accuracy of the classification was tested over both the training and a set of test plots, and showed that more common vegetation types could be predicted accurately. Attempts to estimate the heights of both dwarf shrub and graminoid vegetation from satellite data produced significant, but weak, correlations between observed and predicted height. When these outputs were used in bird abundance–habitat models, bird abundance predicted using satellite‐derived vegetation data was very similar to that obtained when the field‐collected data were used for one bird species, but poor estimates of vegetation height produced from the satellite data resulted in a poor abundance prediction for another. Conclusions This pilot study suggests that it is possible to identify moorland vegetation to a fine‐taxa level using point samples, and that it may be possible to derive information on vegetation height, although more appropriate field‐collected data are needed to examine this further. While remote sensing may have limitations compared with relatively fine‐scale fieldwork, when used at relatively large scales and in conjunction with robust bird abundance–habitat association models, it may facilitate the mapping of moorland bird abundance across large areas.     

Direct-acting mutagenic properties of some hair dyes used in New Zealand

Mutagenicity or carcinogenicity data are not publicly available on many hair dyes or dye components commonly used within New Zealand. Representative mid- to dark-warm brown hair dyes of 12 brands supplying more than 1% of the New Zealand market were tested for direct-acting mutagenicity using the bacterial 'Ames' test. Despite recent scientific advances in the development of non-mutagenic dyes, 23 of the 40 products tested gave positive results in one or both of the tester strains used. There appeared to be differences between distributors in the proportion of their hair dyes which were mutagenic. In the case of 6 out of 10 of the above dyes which had tested positive, in vitro mutagenicity or toxicity was enhanced in the presence of verapamil, suggesting that risks from hair-dye exposure may change in the case of persons using this or similar drugs. It is recognised that there are uncertainties regarding human risks from dyes which are shown to be mutagenic in in vitro tests. However, from the above results, it seems possible to produce non-mutagenic hair dyes in this color range; and in the interests of public reassurance, it may be prudent to require that such dyes be used.     

On two tests of fit for HLA data with no double blanks.

Stevens suggests a test of fit, based on Bernstein's estimators, of the Hardy-Weinberg law for the ABO system. Nam and Gart extend this test to the generalized ABO-like system and apply it to HLA data. When the recessive gene is rare, Huether and Murphy recall Haldane's point that its Bernstein's estimator is negatively biased and go on to suggest novel corrected versions of it. With the identification of more HLA antigens, it is not uncommon to find, in certain populations, that the sample data contain no double blanks; that is, every individual reacts to at least one antigen for a given locus. Gart and Nam give a simple score test of a zero true recessive-gene frequency for such situations. Here we examine the extended test of Stevens as a test of this hypothesis. We find that it is fully efficient for two codominant alleles but that when the number exceeds two its efficiency may be 50% or lower or as high as 100%, depending on the number of alleles and the pattern of gene frequencies. The tests are applied to a set of HLA data.     

Active lymphatic pumping and sheep lung lymph flow

Active (intrinsic) lymphatic pumping may be an important factor determining lymph flow from the lungs. Unfortunately, in most experiments, it is very difficult to determine the influence of active pumping vs. passive factors on lymph flow. However, 1) the pumping activity (stroke volume and frequency) of isolated lymphatic segments varies nonlinearly with transmural pressure, and 2) the lung lymph flow from awake sheep varies nonlinearly with lymphatic outflow pressure. Accordingly, if lymphatic pumping significantly influences lung lymph flow, then it should be possible to describe the sheep lung lymph flow vs. outflow pressure data with the pumping activity data. To test this, we used published lymphatic pumping activity data to develop a mathematical model of the lymphatic pump for a segment of lymphatic vessel. Flow vs. outflow pressure relationships obtained from simulations with this model were very similar to the data from sheep. Our results indicate that both passive factors and active lymphatic pumping contribute to lymph flow, and our model may allow investigators to distinguish the effects of active pumping vs. passive factors in the regulation of lymph flow.     

Joint analysis for genome-wide association studies in family-based designs

In family-based data, association information can be partitioned into the between-family information and the within-family information. Based on this observation, Steen et al. (Nature Genetics. 2005, 683-691) proposed an interesting two-stage test for genome-wide association (GWA) studies under family-based designs which performs genomic screening and replication using the same data set. In the first stage, a screening test based on the between-family information is used to select markers. In the second stage, an association test based on the within-family information is used to test association at the selected markers. However, we learn from the results of case-control studies (Skol et al. Nature Genetics. 2006, 209-213) that this two-stage approach may be not optimal. In this article, we propose a novel two-stage joint analysis for GWA studies under family-based designs. For this joint analysis, we first propose a new screening test that is based on the between-family information and is robust to population stratification. This new screening test is used in the first stage to select markers. Then, a joint test that combines the between-family information and within-family information is used in the second stage to test association at the selected markers. By extensive simulation studies, we demonstrate that the joint analysis always results in increased power to detect genetic association and is robust to population stratification.     

Use of the score test as a goodness-of-fit measure of the covariance structure in genetic analysis of longitudinal data

Model selection is an essential issue in longitudinal data analysis since many different models have been proposed to fit the covariance structure. The likelihood criterion is commonly used and allows to compare the fit of alternative models. Its value does not reflect, however, the potential improvement that can still be reached in fitting the data unless a reference model with the actual covariance structure is available. The score test approach does not require the knowledge of a reference model, and the score statistic has a meaningful interpretation in itself as a goodness-of-fit measure. The aim of this paper was to show how the score statistic may be separated into the genetic and environmental parts, which is difficult with the likelihood criterion, and how it can be used to check parametric assumptions made on variance and correlation parameters. Selection of models for genetic analysis was applied to a dairy cattle example for milk production.