robustness and power of analysis of covariance applied to ordinal scaled data as arising in randomized controlled trials in clinical trials comparing two treatments ordinal scales of three four or five points are often used to assess severity both prior to and after treatment analysis of covariance is an attractive technique however the data clearly violate the normality assumption and in the presence of small samples and large sample theory may not apply the robustness and power of various versions of parametric analysis of covariance applied to small samples of ordinal scaled data are investigated through computer simulation subjects are randomized to one of two competing treatments and the pre treatment or baseline assessment is used as the covariate we compare two parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regressions slopes and the two independent samples t test on difference scores under the null hypothesis of no difference in adjusted treatment means we estimated actual significance levels by comparing observed test statistics to appropriate critical values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypotheses the model which assumes homogeneous slopes and the t test on difference scores were robust in the presence of three four and five point ordinal scales the hierarchical approach which first tests for homogeneity of regression slopes and then fits separate slopes if there is significant non homogeneity produced significance levels that exceeded the nominal levels especially when the sample sizes were small the model which assumes homogeneous regression slopes produced the highest power among competing tests for all of the configurations investigated the t test on difference scores also produced good power in the presence of small samples

local empirical likelihood inference for varying coefficient density ratio models based on case control data in this article we develop a varying coefficient density ratio model for case control studies the case and control samples come from two different distributions under the model assumption the ratio of the two densities is related to the linear combination of covariates with varying coefficients through a known function a special case is the exponential tilt model where the log ratio of the two densities is a linear function of covariates we propose a local empirical likelihood el approach to estimate the nonparametric coefficient functions under some regularity assumptions the proposed estimators are shown to be consistent and asymptotically normally distributed the sieve empirical likelihood ratio selr test statistic for detecting whether the varying coefficients are really constant and other related hypotheses is constructed and it follows approximately a chi squared distribution we introduce a modified bootstrap procedure to estimate the null distribution of the selr when sample size is s

hypothesis testing in a mixture case control model summary we consider a problem of testing mixture proportions using two sample data one from group one and the other from a mixture of groups one and two with unknown proportion for being in group two various statistical applications including microarray study infectious epidemiological studies case control studies with contaminated controls clinical trials allowing nonresponders genetic studies for gene mutation and fishery applications can be formulated in this setup under the assumption that the log ratio of probability density functions from the two groups is linear in the observations we propose a generalized score test statistic to test the mixture proportion under some regularity conditions it is shown that this statistic converges to a weighted chi squared random variable under the null hypothesis of 0 where the weight depends only on the sampling fraction of both groups the permutation method is used to provide more reliable finite sample approximation simulation results and two real data applications are presented

empirical likelihood ratio confidence regions than are those based on student s t statistic an effective method is presented for computing empirical profile likelihoods for the mean of a vector random variable the method is a reduction by convex duality to an unconstrained minimization of a convex function on a low dimensional domain algorithms exist for finding the unique global minimum at a superlinear rate of convergence a byproduct is a noncombinatorial algorithm for determining whether a given point lies within the convex hull of a finite set of points the multivariate empirical likelihood regions are justified for functions of several means such as variances correlations and regression parameters and for statistics with linear estimating equations an algorithm is given for computing profile empirical likelihoods for these statistics

on the relationship between nlc width and linear nlc width in this paper we consider nlc width nlct width and linear nlc width bounded graphs we show that the set of all complete binary trees has unbounded linear nlc width and that the set of all co graphs has unbounded nlct width since trees have nlct width 3 and co graphs have nlc width 1 it follows that the family of linear nlc width bounded graph classes is a proper subfamily of the family of nlct width bounded graph classes and that the family of nlct width bounded graph classes is a proper subfamily of the family of nlc width bounded graph classes

exemplary data set sample size calculation for wilcoxon mann whitney tests zhao rahardja and qu consider sample size calculation for wilcoxon mann whitney wmw tests for data with ties and present a straightforward formula we observe that the exemplary data set approach usually applied in more complex situations has a close relationship to the zhao rahardja qu method for wmw sample size estimation and they are asymptotically equivalent therefore the exemplary data set approach can be used to easily obtain estimates similar to those that the closed formula gives we illustrate application of both methods for a wmw sample size estimation example and also extend the simulation study presented by zhao et al we find that the zhao rahardja qu formula and by extension the exemplary data set method can give estimates just as accurate as those obtained using either the kolassa approach via nquery advisor or the o brien castelloe approach via sas 9 2 proc power for 1 1 and 1 2 allocation ratios however the latter two methods can be more accurate for a ratio of 1 4 or 1 19 finally we note the general utility of the exemplary data set approach for sample size estimation even in other situations where closed form sample size formulae exist

logarithmic transformations in anova a method is presented for choosing an additive constant c when transforming data x to y log x c the method preserves type i error probability and power in anova under the assumption that the x c for some c are log normally distributed the method has advantages similar to those of rank transformations namely it is easy to use and is resistant to extreme observations since the special case c infinity corresponds in anova to y x the method is a useful generalization of least squares

robustness and power of analysis of covariance applied to data distorted from normality by floor effects homogeneous regression slopes we investigate through computer simulations the robustness and power of two group analysis of covariance test applied to small samples distorted normality by floor effects when the regression slopes are homogeneous we consider four parametric analysis of covariance tests that vary according to the treatment of the homogeneity of regression slopes and two t tests on unadjusted means and on difference scores under the null hypothesis of no difference in means we estimated actual significance levels by comparing observed test statistics to appropriate values from the f and t distributions for nominal significance levels of 0 10 0 05 0 02 and 0 01 we estimated power by similar comparisons under various alternative hypothesis the hierarchical approach that adjusts for non homogeneous slopes if found significant the test that assumes homogeneous regression slopes and the test that estimates separate regression slopes in each treatment were robust in general each test produced power at least equal to that expected from normal theory the textbook approach which does not test for mean differences when there is significant non homogeneity was conservative but also had good power the t tests were robust but had poorer power properties than the above procedures

linear rank width and linear clique width of trees we show that for every forest t the linear rank width of t is equal to the path width of t and the linear clique width of t equals the path width of t plus two provided that t contains a path of length three it follows that both linear rank width and linear clique width of forests can be computed in linear time using our characterization of linear rank width of forests we determine the set of minimal excluded acyclic vertex minors for the class of graphs of linear rank width at most k

determining the appropriate sample size for nonparametric tests for location shift for the case in which two independent samples arc to be compared using a nonparametric test for location shift we propose a bootstrap technique for estimating the sample sizes required to achieve a specified power the estimator called boot uses information from a small pilot experiment for the special case of the wilcoxon test a simulation study is conducted to compare boot to two other sample size estimators one method called anpv is based on the assumption that the underlying distribution is normal with a variance estimated from the pilot data the other method called noether adapts the sample size formula of noether for use with a location shift alternative the boot and noether sample size estimators are particularly appropriate for this nonparametric setting because they do not require assumptions about the shape of the underlying continuous probability distribution the simulation study shows that a sample size estimates can have large uncertainty b boot is at least as accurate as an

an analysis of transformations revisited rebutted abstract in a paper written in 1964 box and cox described a method for estimating transformations and showed how in suitable cases valuable increases in simplicity and efficiency were possible since that time this technique has enjoyed wide practical use and considerable success however a recent theoretical paper by bickel and doksum 1981 seems to suggest that serious dangers are associated with the employment of this method and speaks of instability and cost of estimation of the transformation these difficulties seem to be associated with 1 examples which common sense would rule out namely situations where the effect of transformation on the data is almost linear so that it is a matter of indifference which transformation is used 2 the idea that it makes sense to state conclusions in terms of a number measured on an arbitrary scale 3 failure to take proper account of the jacobian of the transformation

on certain properties for some classes of starlike functions abstract let f z z a2z2 be analytic in the unit disk u z z 1 by using the method of differential subordinations we give a criterion for a function f z to be in a certain class l a b of starlike functions for functions f z l a b a subordination relation for f z z is also given

power and sample size calculations for discrete bounded outcome scores we consider power and sample size calculations for randomized trials with a bounded outcome score bos as primary response adjusted for a priori chosen covariates we define bos to be a random variable restricted to a finite interval typically a bos has a j or u shaped distribution hindering traditional parametric methods of analysis when no adjustment for covariates is needed a non parametric test could be chosen however there is still a problem with calculating the power since the common location shift alternative does not hold in general for a bos in this paper we consider a parametric approach and assume that the observed bos is a coarsened version of a true bos which has a logit normal distribution in each treatment group allowing correction for covariates a two step procedure is used to calculate the power firstly the power function is defined conditionally on the covariate values secondly the marginal power is obtained by averaging the conditional power with respect to an assumed distribution for the covariates using monte carlo integration a simulation study evaluates the performance of our method which is also applied to the ecass 1 stroke study

an information matrix test for logistic regression models based on case control data summary we propose an information matrix based goodness of fit statistic to test the validity of the logistic regression model based on case control data by extending the information matrix test of white 1982 for detecting one sample parametric model misspecification to the semiparametric profile likelihood setting under a two sample semiparamnetric model which is equivalent to the assumed logistic regression model the proposed test statistic requires a high dimensional matrix inversion but is otherwise easily computed and has an asymptotic chi squared distribution this test statistic is an alternative to the kolmogorov smirnov type statistic of qin zhang 1997 and the chi squared type statistic of zhang 1999 and needs neither to employ a bootstrap method to evaluate its critical values nor to group the combined sample data into a finite number of mutually exclusive categories even when the underlying population distribution is continuous we demonstrate that the proposed test statistic and its asymptotic distribution may be obtained by fitting the prospective logistic regression model to case control data we present some results on simulation and on the analysis of three real datasets

estimating the power of the two sample wilcoxon test for location shift summary traditional methods for calculating the power of a statistical test for location shift require knowledge of the shape of the underlying probability distribution the distribution shape however may be unknown this paper describes a bootstrap method for using observed data or pilot data to approximate the power no assumptions need be made about the shape of the underlying continuous probability distribution simulation evidence shows that when applied to the wilcoxon two sample test for location shift the suggested method is reliable the evidence also shows that it is more accurate than a benchmark traditional approach the bootstrap method is applied to a real data example the analysis demonstrates how the method can be used to determine sample sizes and how to choose the more powerful of two alternative tests for location shift

a linear recognition algorithm for cographs cographs are the graphs formed from a single vertex under the closure of the operations of union and complement another characterization of cographs is that they are the undirected graphs with no induced paths on four vertices cographs arise naturally in such application areas as examination scheduling and automatic clustering of index terms furthermore it is known that cographs have a unique tree representation called a cotree using the cotree it is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general such problems include chromatic number clique determination clustering minimum weight domination isomorphism minimum fill in and hamiltonicity in this paper we present a linear time algorithm for recognizing cographs and constructing their cotree representation

robustness of the two independent samples t test when applied to ordinal scaled data one may encounter the application of the two independent samples t test to ordinal scaled data for example data that assume only the values 0 1 2 3 from small samples this situation clearly violates the underlying normality assumption for the t test and one cannot appeal to large sample theory for validity in this paper we report the results of an investigation of the t test s robustness when applied to data of this form for samples of sizes 5 to 20 our approach consists of complete enumeration of the sampling distributions and comparison of actual levels of significance with the significance level expected if the data followed a normal distribution we demonstrate under general conditions the robustness of the t test in that the maximum actual level of significance is close to the declared level

calculation of power and sample size with bounded outcome scores the two sample wilcoxon rank sum test is the most popular non parametric test for the comparison of two samples when the underlying distributions are not normal although the underlying distributions need not be known in detail to calculate the null distribution of the test statistic parametric assumptions are often made to determine the power of the test or the sample size we encountered difficulties with this approach in the planning of a recent clinical trial in stroke patients it is shown that for power and sample size estimation it can be dangerous to apply the classical formulae routinely especially with outcome scores having a u shaped or a j shaped distribution as an example we have taken the barthel index a quality of life outcome measure in stroke patients further we have investigated alternative methods by means of monte carlo simulation the distributional characteristics of the estimated powers were compared our findings suggest more appropriate computer software is necessary for the calculation of power and sample size when efficacy is measured by a non parametric method

lex bfs and partition refinement with applications to transitive orientation interval graph recognition and consecutive ones testing by making use of lexicographic breadth rst search lex bfs and partition renement with pivots we obtain very simple algorithms for some well known problems in graph theory we give a o n mlogn algorithm for transitive orientation of a comparability graph and simple linear algorithms to recognize interval graphs convex graphs y semichordal graphs and matrices that have the consecutive ones property previous approaches to these problems used dicult preprocessing steps such as computing pq trees or modular decomposition the algorithms we give are easy to understand and straightforward to prove they do not make use of sophisticated data structures and the complexity analysis is straightforward c 2000 elsevier science b v all rights reserved

power transformations to symmetry summary power transformations for achieving distributional symmetry are discussed estimates of the transformation power are based on general measures of symmetry they are shown to be consistent and asymptotically normal use of the skewness coefficient as a measure of symmetry is shown to be optimal in an important special case the methods are compared to the likelihood methods of box cox 1964 and alternative methods of hinkley 1975 1977 the box cox method or a robust adaptation of it carroll 1980 bickel doksum 1981 is found to be the generally most suitable method

repeatability of paired counts the bland and altman technique is widely used to assess the variation between replicates of a method of clinical measurement it yields the repeatability i e the value within which 95 per cent of repeat measurements lie the valid use of the technique requires that the variance is constant over the data range this is not usually the case for counts of items such as cd4 cells or parasites nor is the log transformation applicable to zero counts we investigate the properties of generalized differences based on box cox transformations for an example in a data set of hookworm eggs counted by the kato katz method the square root transformation is found to stabilize the variance we show how to back transform the repeatability on the square root scale to the repeatability of the counts themselves as an increasing function of the square mean root egg count i e the square of the average of square roots as well as being more easily interpretable the back transformed results highlight the dependence of the repeatability on the sample volume used

certain subclasses of p valent functions involving the dziok srivastava operator using the methods of differential subordination we investigate some inclusion relationships of certain subclasses of analytic and p valent functions which are defined by means of dziok srivastava operator

smoothed empirical likelihood confidence intervals for quantiles standard empirical likelihood confidence intervals for quantiles are identical to sign test intervals they have relatively large coverage error of size n 1 2 even though they are two sided intervals we show that smoothed empirical likelihood confidence intervals for quantiles have coverage error of order n 1 and may be bartlett corrected to produce intervals with an error of order only n 2 necessary and sufficient conditions on the smoothing parameter in order for these sizes of error to be attained are derived the effects of smoothing on the positions of endpoints of the intervals are analysed and shown to be only of second order

sample size calculations for ordered categorical data many clinical trials yield data on an ordered categorical scale such as very good good moderate poor under the assumption of proportional odds such data can be analysed using techniques of logistic regression in simple comparisons of two treatments this approach becomes equivalent to the mann whitney test in this paper sample size formulae consistent with an eventual logistic regression analysis are derived the influence on efficiency of the number and breadth of categories will be examined effects of misclassification and of stratification are discussed and examples of the calculations are given

statistical tests based on transformed data abstract the problem of testing hypotheses in linear models when the original data have been transformed is considered it is assumed that the transformation involves an unknown parameter that has to be estimated from the data for certain important testing problems it is found that the asymptotic level and power is as if had been assumed known asymptotic efficiency results show that when the box cox transformation is used tests based on transformed data have good power properties simulation results for transformed two sample and linear regression testing problems show this to be true for moderate to small sample sizes as well in particular an trimmed t test based on averages of trimmed transformed variables performs very well in both light tailed and heavy tailed skew models when compared with the usual t test and rank tests

the use of bootstrap methods for estimating sample size and analysing health related quality of life outcomes health related quality of life hrqol measures are increasingly used in trials as primary outcome measures investigators are now asking statisticians for advice on how to plan and analyse studies using such outcomes hrqol outcomes like the sf 36 are usual measured on an ordinal scale although most investigators assume that there exists an underlying continuous latent variable and that the actual measured outcomes the ordered categories reflect contiguous intervals along this continuum the ordinal scaling of hrqol measures means they tend to generate data that have discrete bounded and skewed distributions thus standard methods of analysis that assume normality and constant variance may not be appropriate for this reason conventional statistical advice would suggest non parametric methods be used to analyse hrqol data the bootstrap is one such computer intensive non parametric method for estimating sample sizes and analysing data we describe three methods of estimating sample sizes for two group cross sectional comparisons of hrqol outcomes we then compared the power of the three methods for a two group cross sectional study design using bootstrap simulation the results showed that under the location shift alternative hypothesis conventional methods of sample size estimation performed well particularly whitehead s method whitehead s method is recommended if the hrqol outcome has a limited number of discrete values 7 and or the expected proportion of cases at either of the bounds is high if a pilot data set is readily available then bootstrap simulation will provide a more accurate and reliable estimate than conventional methods finally we used the bootstrap for hypothesis testing and the estimation of standard errors and confidence intervals for parameters in an example data set we then compared and contrasted the bootstrap with standard methods of analysing hrqol outcomes in the data set studied with the sf 36 outcome the use of the bootstrap for estimating sample sizes and analysing hrqol data produces results similar to conventional statistical methods these results suggest that bootstrap methods are not more appropriate for analysing hrqol outcome data than standard methods

estimate of standard deviation for a log transformed variable using arithmetic means and standard deviations analyses of study variables are frequently based on log transformations to calculate the power for detecting the between treatment difference in the log scale we need an estimate of the standard deviation of the log transformed variable however in many situations a literature search only provides the arithmetic means and the corresponding standard deviations without individual log transformed data to directly calculate the sample standard deviation we need alternative methods to estimate it this paper presents methods for estimating and constructing confidence intervals for the standard deviation of a log transformed variable given the mean and standard deviation of the untransformed variable it also presents methods for estimating the standard deviation of change from baseline in the log scale given the means and standard deviations of the untransformed baseline value on treatment value and change from baseline simulations and examples are provided to assess the performance of these estimates

choice of test for comparing two groups with particular application to skewed outcomes we consider a clinical trial where a skewed outcome variable is to be compared between two groups while comparison of sample means may lack power we show that power also depends on the nature of the anticipated treatment effect for any given distribution in the control arm there is a family of true distributions in the intervention arm for which the most powerful test is a comparison of arithmetic means similar results hold for a comparison of geometric means and approximately for the wilcoxon rank sum test and a comparison of medians we discuss how these methods could be used in planning the analysis of a clinical trial in which the intervention effect alters the shape of the distribution these ideas are illustrated by a trial in community psychiatry where the primary outcome days in hospital was highly skewed but the intervention was mainly expected to reduce the frequency of values in the tail we show that a comparison of sample means is a reasonable choice in this case despite the skewness

a modified wilcoxon test for non negative distributions with a clump of zeros comparing two samples with a continuous non negative score e g a utility score over 0 1 with a substantial proportion say 50 per cent scoring 0 presents distributional problems for most standard tests a wilcoxon rank test can be used but the large number of ties reduces power i propose a new test the wilcoxon rank sum test performed after removing an equal and maximal number of 0 s from each sample this test recovers much of the power compared with a directional modification of a two part test proposed by lachenbruch the truncated wilcoxon has similar power when the non zero scores are independent of the proportion of zeros but unlike the two part test the truncated wilcoxon is relatively unaffected when these processes are dependent

on empirical likelihood for a semiparametric mixture model summary plant and animal studies of quantitative trait loci provide data which arise from mixtures of distributions with known mixing proportions previous approaches to estimation involve modelling the distributions parametrically we propose a semiparametric alternative which assumes that the log ratio of the component densities satisfies a linear model with the baseline density unspecified it is demonstrated that a constrained empirical likelihood has an irregularity under the null hypothesis that the two densities are equal a factorisation of the likelihood suggests a partial empirical likelihood which permits unconstrained estimation of the parameters and which is shown to give consistent and asymptotically normal estimators regardless of the null the asymptotic null distribution of the log partial likelihood ratio is chi squared theoretical calculations show that the procedure may be as efficient as the full empirical likelihood in the regular set up the usefulness of the robust methodology is illustrated with a rat study of breast cancer resistance genes

some power considerations when deciding to use transformations conventional wisdom suggests that for small data sets having substantial skew one should attempt to determine the correct distributional form if possible and apply statistical methods appropriate for that distribution transformations such as the log or square root are often used if an appropriate distributional form cannot be determined a distribution free procedure such as a rank transformation or a randomization test procedure can be used to better appreciate the effect of such alternatives on both the type i error and power of detecting differences between treatment groups simulation studies were conducted for responses having specific gamma g r theta and log normal ln m v distributions the gamma and log normal distributions were selected so that they had the same first two moments a simple two group design was assumed the reference group always had an average disease level mu 3 0 mu r theta for gamma mu m for log normal and the treatment group always had means whose reductions ranged from 0 per cent to 50 per cent the effect of distributional type and the degree of skewness was investigated by varying the population parameter values six statistical test procedures were compared for the gamma distributions all test procedures were robust relative to the type i error the ump test based on a ratio of sample means produced the greatest power for all combinations of n r and rt the power losses associated with the randomization test the t test on original scale and the t test on the square root scale were very small 3 per cent to 6 per cent in absolute value for n 10 and 15 and less than 2 per cent for group sizes of 25 or more the power loss associated with the t test on the log scale was much larger ranging from 5 per cent to 10 per cent smaller power than the t test on original scale the wilcoxon rank test produced similar results to that of the log t test for small samples the power for the shifted log x c test increased monotonically to the asymptotic value of the orig t test the same five test procedures based on differences in sample means were then compared for the corresponding log normal distributions the ump test that is log x produced the highest power there was very little power lost for the sqrt t test the loss in power varied between 2 per cent and 5 per cent for the rank test abstract truncated at 400 words

a bootstrap semiparametric homogeneity test for the distributions of multigroup proportional data with applications to analysis of quality of life outcomes in clinical trials this article is concerned about the test for the difference in the distributions of multigroup proportional data which is motivated by the problem of comparing the distributions of quality of life qol outcomes among different treatment groups in clinical trials the proportional data such as qol outcomes assessed by answers to questions on a questionnaire are bounded in a closed interval such as 0 1 with continuous observations in 0 1 and in addition excess observations taking the boundary values 0 and or 1 common statistical procedures used in practice such as t and rank based tests may not be very powerful since they ignore the specific feature of the proportional data in this article we propose a three component mixture model for the proportional data and a density ratio model for the distributions of continuous observations in 0 1 a semiparametric test statistic for the homogeneity of distributions of multigroup proportional data is derived based on the empirical likelihood ratio principle and shown to be asymptotically distributed as a chi squared random variable under null hypothesis a nonparametric bootstrap procedure is proposed to further improve the performance of the semiparametric test simulation studies are performed to evaluate the empirical type i error and power of the proposed test procedure and compare it with likelihood ratio tests lrts under parametric distribution assumptions rank based kruskal wallis test and wald type test the proposed test procedure is also applied to the analysis of qol outcomes from a clinical trial on colorectal cancer that motivated our study

testing the mean of skewed distributions abstract johnson proposed some modified t tests to assess the mean of asymmetrical distributions the tests were suggested for any parent distribution ranging from the normal to a distribution as asymmetric as an exponential distribution for sample sizes as small as 13 in many practical situations the skewness of the parent distribution can be greater than those studied by johnson and the sample sizes can be quite small possibly as small as 10 due to the cost of the sampling procedures in these cases johnson s test can be quite inaccurate sutton suggested a composite test to improve johnson s upper tailed t test in this article a new test procedure is proposed for the upper tailed test for the mean of positively skewed distributions which requires only a little more effort than johnson s test a monte carlo study investigates the new procedure s properties for a variety of positively skewed distributions with small sample sizes it is shown that the new test procedure is more accurate and more powe

a semiparametric two component compound mixture model and its application to estimating malaria attributable fractions summary malaria remains a major epidemiologic problem in many developing countries malaria is defined as the presence of parasites and symptoms usually fever due to the parasites in endemic areas an individual may have symptoms attributable either to malaria or to other causes from a clinical viewpoint it is important to correctly diagnose an individual who has developed symptoms so that the appropriate treatments can be given from an epidemiologic and economic viewpoint it is important to determine the proportion of malaria affected cases in individuals who have symptoms so that policies on intervention program can be developed once symptoms have developed in an individual the diagnosis of malaria can be based on the analysis of the parasite levels in blood samples however even a blood test is not conclusive as in endemic areas many healthy individuals can have parasites in their blood slides therefore data from this type of study can be viewed as coming from a mixture distribution with the components corresponding to malaria and nonmalaria cases a unique feature in this type of data however is the fact that a proportion of the nonmalaria cases have zero parasite levels therefore one of the component distributions is itself a mixture distribution in this article we propose a semiparametric likelihood approach for estimating the proportion of clinical malaria using parasite level data from a group of individuals with symptoms our approach assumes the density ratio for the parasite levels in clinical malaria and nonclinical malaria cases can be modeled using a logistic model we use empirical likelihood to combine the zero and nonzero data the maximum semiparametric likelihood estimate is more efficient than existing nonparametric estimates using only the frequencies of zero and nonzero data on the other hand it is more robust than a fully parametric maximum likelihood estimate that assumes a parametric model for the nonzero data simulation results show that the performance of the proposed method is satisfactory the proposed method is used to analyze data from a malaria survey carried out in tanzania

comparison of two treatments with skewed ordinal responses in clinical studies the proportional odds model is widely used to compare treatment efficacies when the responses are categorically ordered however this model has been shown to be inappropriate when the proportional odds assumption is invalid mainly because it is unable to control the type i error rate in such circumstances to remedy this problem the latent normal model was recently promoted and has been demonstrated to be superior to the proportional odds model however the application of the latent normal model is limited to compare treatments with similar underlying distributions except possibly their means and variances when the underlying distributions are very different in skewness both of the aforementioned procedures suffer from the undesirable inflation of the type i error rate to solve the problem for clinical studies with ordinal responses we provide a viable solution that relies on the use of the latent weibull distribution which is a member of the log location scale family the proposed model is able to control the type i error rate regardless of the degree of skewness of the treatment responses in addition the power of the test also outperforms that of the latent normal model the testing procedure draws on newly developed theoretical results related to latent distributions from the location scale family the testing procedure is illustrated with two clinical examples

semiparametric estimation and inference for distributional and general treatment effects summary there is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome the paper considers evaluating the effect of treatment on the entire distribution and general functions of this effect for distributional treatment effects fully non parametric and fully parametric approaches have been proposed the fully non parametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions we develop a semiparametric instrumental variable method based on the empirical likelihood approach our method can be applied to general outcomes and general functions of outcome distributions and allows us to predict a subject s latent compliance class on the basis of an observed outcome value in observed assignment and treatment received groups asymptotic results for the estimators and likelihood ratio statistic are derived a simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully non parametric estimators the method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices

approximating the power of wilcoxon s rank sum test against shift alternatives three methods of approximating the power of wilcoxon s rank sum test against shift alternatives are studied they are obtained by using a gaussian assumption edgeworth expansion or bootstrap it is assumed that a historical data set is available to use in estimating the shape of the distribution the methods are compared through simulation across several different distributional types the results indicate that the bootstrap generally gives the most reliable approximation however the edgeworth expansion has the practical advantage that a lower bound on the power can be roughly approximated the methods are illustrated on muscle strength data from patients with osteogenesis imperfecta published in 1999 by john wiley sons ltd this is us government work and is in the public domain in the united states

univalent solutions of briot bouquet differential equations let and be complex numbers and let h z be regular in the unit disc u in this article the authors study the briot bouquet differential equation q z frac zq z beta q z gamma h z sufficient conditions are obtained for both the regularity and univalency of the solution in u in addition applications of these results to differential subordinations integral operators and univalent functions are given

sample size determination for some common nonparametric tests abstract the article discusses the problem of determining the number of observations required by some common nonparametric tests so that the tests have power at least 1 against alternatives that differ sufficiently from the hypothesis being tested it is shown that the number of observations depends on certain simple probabilities a method is suggested for fixing the value of the appropriate probability when determining sample size

sample size calculation for the wilcoxon mann whitney test adjusting for ties in this paper we study sample size calculation methods for the asymptotic wilcoxon mann whitney test for data with or without ties the existing methods are applicable either to data with ties or to data without ties but not to both cases while the existing methods developed for data without ties perform well the methods developed for data with ties have limitations in that they are either applicable to proportional odds alternatives or have computational difficulties we propose a new method which has a closed form formula and therefore is very easy to calculate in addition the new method can be applied to both data with or without ties simulations have demonstrated that the new sample size formula performs very well as the corresponding actual powers are close to the nominal powers

computer intensive methods for tests about the mean of an asymmetrical distribution abstract for one sided tests about the mean of a skewed distribution the t test is asymptotically robust for validity however it can be quite inaccurate and inefficient with small sample sizes results presented here confirm that a procedure due to johnson should be preferred to the t test when the parent distribution is asymmetrical because it reduces the probability of type i error in cases where the t test has an inflated type i error rate and it is more powerful in other situations but if the skewness is severe and the sample size is small then johnson s test can also be appreciably inaccurate for such situations computer intensive test procedures using bootstrap resampling are proposed and with an extensive monte carlo study it is shown that these procedures are remarkably robust and can result in reduced probabilities of type i and type ii errors compared to johnson s test

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

estimation of intervention effect using paired interval censored data with clumping below lower detection limit outcome variables that are semicontinuous with clumping at zero are commonly seen in biomedical research in addition the outcome measurement is sometimes subject to interval censoring and a lower detection limit ldl this gives rise to interval censored observations with clumping below the ldl level of antibody against influenza virus measured by the hemagglutination inhibition assay is an example the interval censoring is due to the assay s technical procedure the clumping below ldl is likely a result of the lack of prior exposure in some individuals such that they either have zero level of antibodies or do not have detectable level of antibodies given a pair of such measurements from the same subject at two time points a binary fold increase endpoint can be defined according to the ratio of these two measurements as it often is in vaccine clinical trials the intervention effect or vaccine immunogenicity can be assessed by comparing the binary endpoint between groups of subjects given different vaccines or placebos we introduce a two part random effects model for modeling the paired interval censored data with clumping below the ldl based on the estimated model parameters we propose to use monte carlo approximation for estimation of the fold increase endpoint and the intervention effect bootstrapping is used for variance estimation the performance of the proposed method is demonstrated by simulation we analyze antibody data from an influenza vaccine trial for illustration

graphs of linear clique width at most 3 abstract a graph has linear clique width at most k if it has a clique width expression using at most k labels such that every disjoint union operation has an operand which is a single vertex graph we give the first characterisation of graphs of linear clique width at most 3 and we give the first polynomial time recognition algorithm for graphs of linear clique width at most 3 in addition we present new characterisations of graphs of linear clique width at most 2 we also give a layout characterisation of graphs of bounded linear clique width a similar characterisation was independently shown by gurski and by lozin and rautenbach

correction of the p value after multiple coding of an explanatory variable in logistic regression we propose a method and a program to determine a significance level for a series of codings of an explanatory variable in logistic regression dichotomous and box cox transformations are considered three methods of correcting the significance level are studied the bonferroni method efron s method which uses the correlation between successive tests and the exact calculation by numerical integration using all correlations a simulation study has led to a strategy for the choice and number of the different codings of the variable this method is illustrated using the data of a study of the relation between cholesterol and dementia

sympercents symmetric percentage differences on the 100 loge scale simplify the presentation of log transformed data the results of analyses on log transformed data are usually back transformed and interpreted on the original scale yet if natural logs are used this is not necessary the log scale can be interpreted as it stands a difference of natural logs corresponds to a fractional difference on the original scale the agreement is exact if the fractional difference is based on the logarithmic mean the transform y 100 log e x leads to differences standard deviations and regression coefficients of y that are equivalent to symmetric percentage differences standard deviations and regression coefficients of x several simple clinical examples show that the 100 log e scale is the natural scale on which to express percentage differences the term sympercent or s is proposed for them sympercents should improve the presentation of log transformed data and lead to a wider understanding of the natural log transformation

tests of the null hypothesis in case control studies the relative merits of the likelihood ratio statistic the wald statistic and the score statistic are examined by an empirical evaluation based on matched case control data a mixture model for the relative odds function is used the likelihood ratio statistic is relatively constant for reasonable values of the mixture parameter but the wald statistic is unstable the score statistic is shown to be independent of the mixture parameter an exact expression is derived for the change in the score statistic upon deletion of risk sets and an approximation is numerically evaluated

optimal sample size planning for the wilcoxon mann whitney test there are many different proposed procedures for sample size planning for the wilcoxon mann whitney test at given type i and type ii error rates and respectively most methods assume very specific models or types of data to simplify calculations eg ordered categorical or metric data location shift alternatives etc we present a unified approach that covers metric data with and without ties count data ordered categorical data and even dichotomous data for that we calculate the unknown theoretical quantities such as the variances under the null and relevant alternative hypothesis by considering the following synthetic data approach we evaluate data whose empirical distribution functions match the theoretical distribution functions involved in the computations of the unknown theoretical quantities then well known relations for the ranks of the data are used for the calculations in addition to computing the necessary sample size n for a fixed allocation proportion t n1 n where n1 is the sample size in the first group and n n1 n2 is the total sample size we provide an interval for the optimal allocation rate t which minimizes the total sample size n it turns out that for certain distributions a balanced design is optimal we give a characterization of such distributions furthermore we show that the optimal choice of t depends on the ratio of the two variances which determine the variance of the wilcoxon mann whitney statistic under the alternative this is different from an optimal sample size allocation in case of the normal distribution model

alternative estimation procedures for pr x y in categorized data summary consider two independent random variables x and y the functional r pr x y or x pr x y pr y x is of practical importance in many situations including clinical trials genetics and reliability in this paper several approaches to estimation of x when x and y are presented in discretized categorical form are analyzed and compared asymptotic formulas for the variances of the estimators are derived use of the bootstrap to estimate variances is also discussed computer simulations indicate that the choice of the best estimator depends on the value of x the underlying distribution and the sparseness of the data it is shown that the bootstrap provides a robust estimate of variance several examples are treated

the log transformation is special the logarithmic log transformation is a simple yet controversial step in the analysis of positive continuous data measured on an interval scale situations where a log transformation is indicated will be reviewed this paper contends that the log transformation should not be classed with other transformations as it has particular advantages problems with using the data themselves to decide whether or not to transform will be discussed it is recommended that log transformed analyses should frequently be preferred to untransformed analyses and that careful consideration should be given to use of a log transformation at the protocol design stage