modeling tumor onset and multiplicity using transition models with latent variables summary we describe a method for modeling carcinogenicity from animal studies where the data consist of counts of the number of tumors present over time the research is motivated by applications to transgenic rodent studies which have emerged as an alternative to chronic bioassays for screening possible carcinogens in transgenic mouse studies the endpoint of interest is frequently skin papilloma with weekly examinations determining how many papillomas each animal has at a particular point in time it is assumed that each animal has two unobservable latent variables at each time point the first indicates whether or not the tumors are in a multiplying state and the second is the potential number of additional tumors if the tumors are in a multiplying state the product of these variables follows a zero inflated poisson distribution and the em algorithm can be used to maximize the observed data pseudo likelihood based on the latent variables a generalized estimating equations robust variance estimator adjusts for dependency among outcomes within individual animals the method is applied to testing for a dose related trend in both tumor incidence and multiplicity in carcinogenicity studies

on simultaneous assessment of sensitivity and specificity when combining two diagnostic tests diagnostic tests are seldom adopted in isolation few tests have high sensitivity and specificity simultaneously in these cases one can increase either the sensitivity or the specificity by combining two component tests under either the either positive rule or the both positive rule however there is a tradeoff between sensitivity and specificity when these rules are applied we propose three statistical procedures to simultaneously assess the sensitivity and specificity when combining two component tests measurements of interest include rate difference and rate ratio our empirical results demonstrate that i the asymptotic test procedures for both measurements and approximate test procedure for rate difference possess inflated type i error rate ii the exact test procedures for both measurements possess deflated type i error rate and iii the approximate unconditional test procedure for rate ratio becomes an reliable alternative and nicely controls the actual type i error rate in small to moderate sample sizes moreover the approximate unconditional test procedure is computationally less intensive than the exact unconditional test procedure we illustrate our methodologies with a real example from a residual nasopharyngeal carcinoma rnp study

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

a mixture model for occupational exposure mean testing with a limit of detection sul lhiary information from detectable exposure measurements randomly sampled from a left truncated log normal distribution may be used to evaluate the distribution of nondetectable values that fall below all analytic limit of detection if the proportion of nondetects is larger than expected under log normality alternative models to account for these unobserved data should be considered we discuss one such model that incorporates a mixture of true zero exposures and a log normal distribution with possible left censoring previously considered ill a different context by manitou and halsey 1995 biometrics 51 1570 1578 a particular relationship is demonstrated between maximum likelihood parameter estimates based on this mixture model and those assuming either left tnlllcated or left censored data these results emphasize the heed for caution when choosing a model to fit data involving nondetectable values a one sided likelihood ratio test for colli paring illeall exposure under the mixture model to an occupational exposure limit is then developed and evaluated via simulations all example demonstrates the potential impact of specifying an incorrect model for the ilondetectable value

global qualitative analysis for a ratio dependent predator prey model with delay abstract a ratio dependent predator prey model with time lag for predator is proposed and analyzed mathematical analyses of the model equations with regard to boundedness of solutions nature of equilibria permanence and stability are analyzed we note that for a ratio dependent system local asymptotic stability of the positive steady state does not even guarantee the so called persistence of the system and therefore does not imply global asymptotic stability it is found that an orbitally asymptotically stable periodic orbit exists in that model some sufficient conditions which guarantee the global stability of positive equilibrium are given

a differential equation model of hiv infection of cd4 t cells with cure rate abstract a differential equation model of hiv infection of cd4 t cells with cure rate is studied we prove that if the basic reproduction number r 0 1 the hiv infection is cleared from the t cell population and the disease dies out if r 0 1 the hiv infection persists in the host we find that the chronic disease steady state is globally asymptotically stable if r 0 1 furthermore we also obtain the conditions for which the system exists an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

development of a formal likelihood function for improved bayesian inference of ephemeral catchments 1 the application of formal bayesian inferential approaches in hydrologic modeling is often criticized for requiring explicit assumptions to be made about the distribution of the errors via the likelihood function these assumptions can be adequate in some situations but often little attention is paid to the selection of an appropriate likelihood function this paper investigates the application of bayesian methods in modeling ephemeral catchments we consider two modeling case studies including a synthetically generated data set and a real data set of an arid australian catchment the case studies investigate some typical forms of the likelihood function which have been applied widely by previous researchers as well as introducing new implementations aimed at better addressing likelihood function assumptions in dry catchments the results of the case studies indicate the importance of explicitly accounting for model residuals that are highly positively skewed due to the presence of many zeros zero inflation arising from the dry spells experienced by the catchment specifically the form of the likelihood function was found to significantly impact the calibrated parameter posterior distributions which in turn have the potential to greatly affect the uncertainty estimates in each application the likelihood function that explicitly accounted for the nonconstant variance of the errors and the zero inflation of the errors resulted in 1 equivalent or better fits to the observed discharge in both timing and volume 2 superior estimation of the uncertainty as measured by the reliability and sharpness metrics and 3 more linear quantile quantile plots indicating the errors were more closely matched to the assumptions of this form of the likelihood function

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

bootstrap confidence intervals for medical costs with censored observations medical costs data with administratively censored observations often arise in cost effectiveness studies of treatments for life threatening diseases mean of medical costs incurred from the start of a treatment until death or a certain time point after the implementation of treatment is frequently of interest in many situations due to the skewed nature of the cost distribution and non uniform rate of cost accumulation over time the currently available normal approximation confidence interval has poor coverage accuracy in this paper we propose a bootstrap confidence interval for the mean of medical costs with censored observations in simulation studies we show that the proposed bootstrap confidence interval had much better coverage accuracy than the normal approximation one when medical costs had a skewed distribution when there is light censoring on medical costs 25 per cent we found that the bootstrap confidence interval based on the simple weighted estimator is preferred due to its simplicity and good coverage accuracy for heavily censored cost data censoring rate 30 per cent with larger sample sizes n 200 the bootstrap confidence intervals based on the partitioned estimator has superior performance in terms of both efficiency and coverage accuracy we also illustrate the use of our methods in a real example

differential invariants for quasi linear and semi linear wave type equations abstract in this paper we consider the class of wave type equations u tt f x t u u xx g x t u u x u t and two special cases of it we derive the equivalence transformations for these equations and using these transformations we obtain differential invariants and invariant equations we employ these invariants or and invariant equations to classify all equations of this general class that can be mapped into a simple linear hyperbolic or into an elliptic equation additional applications are presented

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

stable periodic traveling waves for a predator prey model with non constant death rate and delay abstract in this paper we will consider a predator prey model with a non constant death rate and distributed delay described by a partial integro differential system the main goal of this work is to prove that the partial integro differential system has periodic orbitally asymptotically stable solutions in the form of periodic traveling waves i e n x t n t x p x t p t x where 0 is the angular frequency and is the vector number of the plane wave which propagates in the direction of the vector with speed c and n x t and p x t are the spatial population densities of the prey and the predator species respectively in order to achieve our goal we will use singular perturbation s techniques

on linearization of hyperbolic equations using differential invariants abstract in this paper we consider the general class of hyperbolic equations u x t f x t u u x u t we use equivalence transformations to derive differential invariants for this class and for two subclasses then we employ these invariants to construct equations that can be linearized via local mappings further applications of the differential invariants are given

limit cycles for competitor competitor mutualist lotka volterra systems abstract it is known that a limit cycle or periodic coexistence can occur in a competitor competitor mutualist lotka volterra system x 1 x 1 r 1 a 11 x 1 a 12 x 2 a 13 x 3 x 2 x 2 r 2 a 21 x 1 a 22 x 2 a 23 x 3 x 3 x 3 r 3 a 31 x 1 a 32 x 2 a 33 x 3 where r i a i j are positive real constants x liang j jiang the dynamical behavior of type k competitive kolmogorov systems and its applications to 3 dimensional type k competitive lotka volterra systems nonlinearity 16 2003 785 801 in this paper we shall construct an example with at least two limit cycles and furthermore we will show that the number of periodic orbits and hence a fortiori of limit cycles is finite it is also shown that contrary to three dimensional competitive lotka volterra systems nontrivial periodic coexistence does occur even if none of the three species can resist invasion from either of the others in this case new amenable conditions are given on the coefficients under which the system has no nontrivial periodic orbits these conditions imply that the positive equilibrium if it exists is globally asymptotically stable

lie algebraic solutions of linear fokker planck equations nonstationary solutions of linear fokker planck equations with arbitrary drift and diffusion coefficients are derived using lie algebraic techniques the time evolution operator is given as a product of exponentials of the differential operators appearing in the equations

a score test for zero inflation in a poisson distribution when analyzing poisson count data sometimes a lot of zeros are observed when there are too many zeros a zero inflated poisson distribution can be used a score test is presented to test whether the number of zeros is too large for a poisson distribution to fit the data well

assessing the effect of interventions in the context of mixture distributions with detection limits many quantitative assay measurements of metabolites of environmental toxicants in clinical investigations are subject to left censoring due to values falling below assay detection limits moreover when observations occur in both unexposed individuals and exposed individuals who reflect a mixture of two distributions due to differences in exposure metabolism response to intervention and other factors the measurements of these biomarkers can be bimodally distributed with an extra spike below the limit of detection therefore estimating the effect of interventions on these biomarkers becomes an important and challenging problem in this article we present maximum likelihood methods to estimate the effect of intervention in the context of mixture distributions when a large proportion of observations are below the limit of detection the selection of the number of components of mixture distributions was carried out using both bootstrap based and cross validation based information criterion we illustrate our methods using data from a randomized clinical trial conducted in qidong people s republic of china

dynamics of the modified michaelis menten system abstract the theory of cooperative and competitive systems is used to study the dynamical behaviour of the modified michaelis menten system conditions for convergence to equilibria and existence of stable closed orbits are given improving previous results obtained in r a smith some modified michaelis menten equations having stable closed orbits proc roy soc edinburgh sect a 109 1988 341 359

zero inflated poisson regression with an application to defects in manufacturing zero inflated poisson zip regression is a model for count data with excess zeros it assumes that with probability p the only possible observation is 0 and with probability 1 p a poisson random variable is observed for example when manufacturing equipment is properly aligned defects may be nearly impossible but when it is misaligned defects may occur according to a poisson distribution both the probability p of the perfect zero defect state and the mean number of defects in the imperfect state may depend on covariates sometimes p and are unrelated other times p is a simple function of such as p l 1 t for an unknown constant t in either case zip regression models are easy to fit the maximum likelihood estimates mle s are approximately normal in large samples and confidence intervals can be constructed by inverting likelihood ratio tests or using the approximate normality of the mle s simulations suggest that the confidence intervals based on likelihood ratio test

comparisons of two part models with competitors two part models arise when there is a clump of 0 observations in a distribution of continuous non negative responses several methods for comparing two such distributions are available these include the straightforward application of the z test or t test the wilcoxon mann whitney rank sum test the kolmogorov smirnov test and three tests that use a 2 degree of freedom chi 2 test based on the sum of the test for equality of proportions and a conditional chi 2 test for the continuous responses this conditional test may be the z test the rank sum test or the chi 2 corresponding to the kolmogorov smirnov test this study compares the size and power of several of these methods all tests have the appropriate distribution under the null hypothesis if the distribution of the continuous part has finite moments if it does not the z test has no power to detect any alternatives it is found that the 2 d f tests are superior to the others when the larger proportion of 0 values corresponds to the population with the larger mean if the reverse holds the difference in the proportion of zeros reinforces the difference in means and some single part models the rank sum or kolmogorov smirnov do best in those cases the two part models are not far behind although statistically significantly poorer with respect to power published in 2001 by john wiley sons ltd

equivalence and symmetries for variable coefficient linear heat type equations i a systematic and unified approach to transformations and symmetries of a class of variable coefficient heat type linear partial differential equations pdes is presented the complete symmetry group classification is re performed in the current context a useful criterion which is necessary and sufficient for being reducible to the standard heat equation by point transformations is established a similar criterion is also valid for the equations to have a four or six dimensional symmetry group nontrivial symmetry groups in this situation the basis elements are listed in terms of coefficients a number of illustrative examples are given in particular some applications from the recent literature are re examined in our new approach multidimensional parabolic pdes of heat and schrodinger type are also considered

a method for the equivalence group and its infinitesimal generators we give an effective method for the systematic determination of the equivalence group for any family of differential equations and for the determination of the infinitesimal generators of this group this is achieved by viewing the equivalence group as a projected subgroup related to the full symmetry group of the equation in which the coefficients specifying the family element in the equation are also considered as dependent variables the method is extended to provide the exact number of fundamental invariants of the equation without any prior calculation of these invariants it is then applied to review a number of results obtained in the recent literature on the subject of invariant functions of differential equations the method is also applied probably for the first time to a case of nonlinear equation

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

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

second order differential invariants of a family of diffusion equations an equivalence transformation algebra for a class of nonlinear diffusion equations is found after having obtained the second order differential invariants with respect to we get some results which allow us to linearize a subclass of the equations considered

a score test for testing a zero inflated poisson regression model against zero inflated negative binomial alternatives count data often show a higher incidence of zero counts than would be expected if the data were poisson distributed zero inflated poisson regression models are a useful class of models for such data but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the poisson distribution we therefore provide a score test for testing zero inflated poisson regression models against zero inflated negative binomial alternatives

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

two part statistics with paired data in epidemiology we often study data from a mixed distribution i e with a clump of observations at zero and positive continuous data lachenbruch developed statistics for this kind of data for independent samples these tests are the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution this paper concerns the adaptation of these tests to paired samples like lachenbruch we developed two statistics which tend to a two degree of freedom 2 distribution these two part statistics are the sum of mcnemar s test for testing the equality of proportions of zero values and the wilcoxon signed rank test or the paired student s test for testing the equality of the distribution of positive values we studied the behaviour of these tests for various proportions of zeros and mean values of the continuous distribution all tests are efficient when the smaller proportion of zero values corresponds to the population with the larger mean in all other situations the two part statistics are superior to the others these methods are applied to a matched case control study of lower limb venous insufficiency copyright 2004 john wiley sons ltd

the likelihood ratio test for the two component normal mixture problem power and sample size analysis we find through simulation and modeling an approximation to the alternative distribution of the likelihood ratio test for two component mixtures in which the components have different means but equal variances we consider the range of mixing proportions from 0 5 through 95 our simulation results indicate a dependence of power on the mixing proportion when pi less than 2 and pi greater than 80 our model results indicated that the alternative distribution is approximately noncentral chi square possibly with 2 degrees of freedom using this model we estimate a sample of 40 is needed to have 50 power to detect a difference between means equal to 3 0 for mixing proportions between 2 and 8 the sample size increases to 50 when the mixing proportion is 90 or 1 and 82 when the mixing proportion is 95 or 05 this paper contains a complete table of sample sizes needed for 50 80 and 90 power

singular invariant equation for the 1 1 fokker planck equation semi invariants for the linear parabolic equations with two independent variables time variable t and space variable x and one dependent variable u are derived under the transformation of the independent variables by using the infinitesimal method we also obtain the joint invariant equation for the above mentioned equation under equivalence transformation in fact we prove a necessary and sufficient condition for a 1 1 parabolic equation to be reducible via a local equivalence transformation to the one dimensional classical heat equation this result provides practical criteria for reduction finally examples of 1 1 fokker planck equations from applications are given to verify the results obtained

performance of analytical methods for overdispersed counts in cluster randomized trials sample size degree of clustering and imbalance many different methods have been proposed for the analysis of cluster randomized trials crts over the last 30 years however the evaluation of methods on overdispersed count data has been based mostly on the comparison of results using empiric data i e when the true model parameters are not known in this study we assess via simulation the performance of five methods for the analysis of counts in situations similar to real community intervention trials we used the negative binomial distribution to simulate overdispersed counts of crts with two study arms allowing the period of time under observation to vary among individuals we assessed different sample sizes degrees of clustering and degrees of cluster size imbalance the compared methods are i the two sample t test of cluster level rates ii generalized estimating equations gee with empirical covariance estimators iii gee with model based covariance estimators iv generalized linear mixed models glmm and v bayesian hierarchical models bayes hm variation in sample size and clustering led to differences between the methods in terms of coverage significance power and random effects estimation glmm and bayes hm performed better in general with bayes hm producing less dispersed results for random effects estimates although upward biased when clustering was low gee showed higher power but anticonservative coverage and elevated type i error rates imbalance affected the overall performance of the cluster level t test and the gee s coverage in small samples important effects arising from accounting for overdispersion are illustrated through the analysis of a community intervention trial on solar water disinfection in rural bolivia

stability in a predator prey model with crowley martin function and stage structure for prey abstract this paper is concerned with a stage structured predator prey system with crowley martin functional response by analyzing the characteristic equation the local stability of the equilibria is investigated the persistence of system and global asymptotic stability of the positive equilibrium are carried out finally several numerical simulations to illustrate the theoretical analysis are also given

methods for comparing the means of two independent log normal samples standard methods of using the t test and the wilcoxon test have deficiencies for comparing the means of two skewed log normal samples in this paper we propose two new methods to overcome these deficiencies 1 a likelihood based approach and 2 a bootstrap based approach our simulation study shows that the likelihood based approach is the best in terms of the type i error rate and power when data follow a log normal distribution

a simple direct method to find equivalence transformations of a generalized nonlinear schrodinger equation and a generalized kdv equation a simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations by using the direct method we obtain the continuous equivalence transformations of a class of nonlinear schroequations with variable coefficients and a family of nonlinear kdv equations with variable coefficients for the nonlinear schrodinger equations with variable coefficients the equivalence transformations obtained by the direct method coincide in nature with those obtained via the infinitesimal lie criterion but our computation is much simpler

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

modeling health survey data with excessive zero and k responses zero inflated poisson regression is a popular tool used to analyze data with excessive zeros although much work has already been performed to fit zero inflated data most models heavily depend on special features of the individual data to be specific this means that there is a sizable group of respondents who endorse the same answers making the data have peaks in this paper we propose a new model with the flexibility to model excessive counts other than zero and the model is a mixture of multinomial logistic and poisson regression in which the multinomial logistic component models the occurrence of excessive counts including zeros k where k is a positive integer and all other values the poisson regression component models the counts that are assumed to follow a poisson distribution two examples are provided to illustrate our models when the data have counts containing many ones and sixes as a result the zero inflated and k inflated models exhibit a better fit than the zero inflated poisson and standard poisson regressions

invariants of two and three dimensional hyperbolic equations abstract we consider linear hyperbolic equations of the form u t t i 1 n u x i x i i 1 n x i x 1 x n t u x i t x 1 x n t u t u x 1 x n t u we derive equivalence transformations which are used to obtain differential invariants for the cases n 2 and n 3 motivated by these results we present the general results for the n dimensional case it appears at least for n 2 that this class of hyperbolic equations admits differential invariants of order one but not of order two we employ the derived invariants to construct interesting mappings between equivalent equations

comparison of several independent population means when their samples contain log normal and possibly zero observations summary in this paper we consider the problem of testing the mean equality of several independent populations that contain log normal and possibly zero observations we first showed that the currently used methods in statistical practice including the nonparametric kruskal wallis test the standard anova f test and its two modified versions the welch test and the brown forsythe test could have poor type i error control then we propose a likelihood ratio test that is shown to have much better type i error control than the existing methods finally we analyze two real data sets that motivated our study using the proposed test

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

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

power and sample size requirements for two part models two part models assume the data has a probability mass at zero and a continuous response for values greater than 0 we construct tests based on the proportion of zeros and the difference among the positive values of a response giving rise to a two degree of freedom chi 2 test this note gives the non centrality parameter and finds the power for the test the power is compared to the simulation results in a recent paper we derive sample size calculations we note that some modifications of this procedure may provide better tests if the non zero responses are discrete published in 2001 by john wiley sons ltd

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

semiparametric estimation of the distribution of episodically consumed foods measured with error dietary data collected from 24 hour dietary recalls are observed with significant measurement errors in the nonparametric curve estimation literature much of the effort has been devoted to design

stable periodic orbits for a predator prey model with delay abstract in this paper we consider a predator prey model with time lag which improves upon that proposed by cavani and farkas 1994 acta math hungar 63 3 213 229 we show that when the model has exactly one non trivial unstable and hyperbolic equilibrium there exists a stable periodic orbit

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

global stability and periodic solution of the viral dynamics it is well known that the mathematical models provide very important information for the research of human immunodeficiency virus type 1 and hepatitis c virus hcv however the infection rate of almost all mathematical models is linear the linearity shows the simple interaction between the t cells and the viral particles in this paper we consider the classical mathematical model with saturation response of the infection rate by stability analysis we obtain sufficient conditions on the parameters for the global stability of the infected steady state and the infection free steady state we also obtain the conditions for the existence of an orbitally asymptotically stable periodic solution numerical simulations are presented to illustrate the results

permanence of general stage structured consumer resource models much of the existing stage structured consumer resource models ignore the permanence in this paper we consider the permanence for a series of staged structured consumer resource models with the function response of so called prey dependence resource dependence type we show that the systems are permanent if and only if the adult consumer s recruitment rate at the peak of resource abundance is more than its death rate our results indicate that the large consumer s maturation time delay will directly lead to its extinction furthermore our arguments for the main results give a light for permanence in the general stage structured consumer resource systems

symmetry properties of one and two dimensional fokker planck equations the authors study symmetry properties of some fokker planck fp equations in the one dimensional case when symmetry groups turn out to be six parameter ones this allows us to find changes of variables to reduce such fp equations to the one dimensional heat equation they present seven well known fp equations which are reduced to the heat equation they also study the symmetry and obtain some exact solutions of the kramers equation

a wald test comparing medical costs based on log normal distributions with zero valued costs medical cost data often exhibit strong skewness and sometimes contain large proportions of zero values such characteristics prevent the analysis of variance anova f test and other frequently used standard tests from providing the correct inferences when the comparison of means is of interest one solution to the problem is to introduce a parametric structure based on log normal distributions with zero values and then construct a likelihood ratio test while such a likelihood ratio test possesses excellent type i error control and power its implementation requires a rather complicated iterative optimization program in this paper we propose a wald test with simple computation we then conduct a monte carlo simulation to compare the type i error rates and powers of the proposed wald test with those of the likelihood ratio test our simulation study indicates that although the likelihood ratio test slightly outperforms the wald test the performance of the wald test is also satisfactory especially when the sample sizes are reasonably large finally we illustrate the use of the proposed wald test by analysing a clinical study assessing the effects of a computerized prospective drug utilization intervention on in patient charges

equivalence transformations and differential invariants of a generalized nonlinear schrodinger equation by using lie s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear schrodinger equations with variable coefficients we construct the differential invariants of order 1 starting from a special equivalence subalgebra we apply these latter ones to find the most general subclass of variable coefficient nonlinear schrodinger equations which can be mapped by means of an equivalence transformation of to the well known cubic schrodinger equation we also provide the explicit form of the transformation

stable periodic orbits for a class of three dimensional competitive systems abstract it is shown that for a dissipative three dimensional competitive and irreducible system of ordinary differential equations having a unique equilibrium point at which point the jacobian matrix has negative determinant either the equilibrium point is stable or there exists an orbitally stable periodic orbit if in addition the system is analytic then there exists an orbitally asymptotically stable periodic orbit when the equilibrium is unstable the additional assumption of analyticity can be replaced by the assumption that the equilibrium point and every periodic orbit are hyperbolic in this case the morse smale conditions hold and the flow is structurally stable

symmetry classification and exact solutions of the one dimensional fokker planck equation with arbitrary coefficients of drift and diffusion symmetry properties of the one dimensional fokker planck equations with arbitrary coefficients of drift and diffusion are investigated it is proved that the group symmetry of these equations can be one two four or six parametric and corresponding criteria are obtained the changes of the variables reducing fokker planck equations to the heat equation and schrodinger equation with certain potentials are determined using the substructure of the invariance algebra of the rayleigh process equation we obtain the differential invariants and construct some classes of the exact solutions of this equation

a mixture model with detection limits for regression analyses of antibody response to vaccine antibody concentration values as determined by quantitative assays often are left censored due to detection limits or limits established for purpose of specificity standard analyses which assume the data arise from a single lognormal response distribution may not be appropriate when more observations are censored than would be expected under such a model interference from maternal antibodies due to vaccination at an early age for example could result in a high proportion of nonresponders to vaccine a mixture model consisting of a censored lognormal distribution and a point distribution located below the detection limit is proposed for such situations antibody data from a study of measles vaccine are used to illustrate the utility of this approach and the interpretation of the model parameters

analyzing excessive no changes in clinical trials with clustered data this article considers clinical trials in which the efficacy measure is taken from several sites within each patient such as the alveolar bone height of the tooth sites or bone mineral densities of the lumbar spine sites since usually only a small portion of these sites will exhibit changes the conventional method using per patient average gives a diluted result due to excessive no changes in the data different methods have been proposed for this type of data in the case where the observations are mutually independent this includes the popular two part model lachenbruch 2001 statistics in medicine 20 1215 1234 2002 statistical methods in medical research 11 297 302 which is related to the composite approach for discrete and continuous data in shih and quan 1997 statistics in medicine16 1225 1239 2001 statistica sinica 11 53 62 in this article we model the data with excessive zeros no changes in clustered data using a mixture of distributions and taking into account possible measurement errors this mixture model includes the two part model as a special case when one component of the mixture degenerates

differential invariants for systems of linear hyperbolic equations in this paper we consider a general class of systems of two linear hyperbolic equations motivated by the existence of the laplace invariants for the single linear hyperbolic equation we adopt the problem of finding differential invariants for the system we derive the equivalence group of transformations for this class of systems the infinitesimal method which makes use of the equivalence group is employed for determining the desired differential invariants we show that there exist four differential invariants and five semi invariants of first order applications of systems that can be transformed by local mappings to simple forms are provided

confidence intervals for the mean of diagnostic test charge data containing zeros in this paper we consider the problem of interval estimation for the mean of diagnostic test charges diagnostic test charge data may contain zero values and the nonzero values can often be modeled by a log normal distribution under such a model we propose three different interval estimation procedures a percentile t bootstrap interval based on sufficient statistics and two likelihood based confidence intervals for theoretical properties we show that the two likelihood based one sided confidence intervals are only first order accurate and that the bootstrap based one sided confidence interval is second order accurate for two sided confidence intervals all three proposed methods are second order accurate a simulation study in finite sample sizes suggests all three proposed intervals outperform a widely used minimum variance unbiased estimator mvue based interval except for the case of one sided lower end point intervals when the skewness is very small among the proposed one sided intervals the bootstrap interval has the best coverage accuracy for the two sided intervals when the sample size is small the bootstrap method still yields the best coverage accuracy unless the skewness is very small in which case the bias corrected ml method has the best accuracy when the sample size is large all three proposed intervals have similar coverage accuracy finally we analyze with the proposed methods one real example assessing diagnostic test charges among older adults with depression

a predator prey system with stage structure for predator abstract this paper studies the asymptotoc behavior of a predator prey model with stage structure it is found that an orbitally asymptotically stable periodic orbit exists in that model when time delay due to gestation of predator and time delay from crowding effect of prey are incorporated we establish the condition for the permanence of populations and sufficient conditions under which positive equilibrium of the model is globally stable

a two part model for reference curve estimation subject to a limit of detection reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation estimation of reference curves can be complicated by a technical limit of detection lod that censors the measurement from the left as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty we discuss issues with common approaches to the lod problem in the context of our pubertal hormone study and propose a two part model that addresses those issues one part of the proposed model specifies the probability of a measurement exceeding the lod as a function of age the other part of the model specifies the conditional distribution of a measurement given that it exceeds the lod again as a function of age information from the two parts can be combined to estimate the identifiable portion i e above the lod of a reference curve and to calculate the relative standing of a given measurement above the lod unlike some common approaches to lod problems the two part model is free of untestable assumptions involving unobservable quantities flexible for modeling the observable data and easy to implement with existing software the method is illustrated with hormone data from the third national health and nutrition examination survey

positive periodic solutions for a class of delay differential equations abstract in this paper we employ fixed point theorem and functional equation theory to study the existence of positive periodic solutions of the delay differential equation x t t x t t x 2 t t x t t x t moreover new explicit conditions for the related population growth models are also given

global dynamics of a predator prey model with stage structure for the predator the global properties of a predator prey model with nonlinear functional response and stage structure for the predator are studied using lyapunov functions and lasalle s invariance principle it is found that under hypotheses which ensure the uniform persistence of the system and the existence of a unique positive steady state a feasible a priori lower bound condition on the abundance of the prey population ensures the global asymptotic stability of the positive steady state a condition which leads to the extinction of the predators is indicated we also obtain results on the existence and stability of periodic solutions in particular when 4 2 fails to hold and the unique positive steady state e becomes unstable the coexistence of prey and predator populations is ensured for initial populations not on the one dimensional stable manifold of e albeit with fluctuating population sizes

existence of periodic orbits for high dimensional autonomous systems abstract we give a result on existence of periodic orbits for autonomous differential systems with arbitrary finite dimension it is based on a poincare bendixson property enjoyed by a new class of monotone systems introduced in l a sanchez cones of rank 2 and the poincare bendixson property for a new class of monotone systems j differential equations 216 2009 1170 1190 a concrete application is done to a scalar differential equation of order 4

four limit cycles for a three dimensional competitive lotka volterra system with a heteroclinic cycle abstract for three dimensional competitive lotka volterra systems zeeman m l zeeman hopf bifurcations in competitive three dimensional lotka volterra systems dynamics and stability of systems 8 1993 189 217 identified 33 stable equivalence classes among these only classes 26 31 may have limit cycles it is known that all these classes may possess two limit cycles and in classes 27 and 29 three limit cycles have been constructed it has been conjectured that the maximum number of limit cycles is three in this paper we disprove the conjecture by constructing four limit cycles in the three dimensional competitive lotka volterra system with a heteroclinic cycle class 27 in zeeman s classification furthermore in the case of a heteroclinic cycle on the boundary of the carrying simplex of three dimensional competitive lotka volterra systems we show that i the conditions a there is a pair of purely imaginary eigenvalues at a positive equilibrium b the first focal values vanishes and c the second focal values vanishes do not imply that the heteroclinic cycle is neutrally stable and hence they do not imply that the interior equilibrium is a center ii the conditions a there is a pair of purely imaginary eigenvalues at a positive equilibrium b the first focal value vanishes and c the heteroclinic cycle is neutrally stable do not imply the second focal value vanishes and hence they do not imply that the interior equilibrium is a center this refutes a conjecture by hofbauer and so j hofbauer j w h so multiple limit cycles for three dimensional lotka volterra equations appl math lett 7 1994 65 70

positive periodic solutions of infinite delay functional differential equations depending on a parameter in this paper we employ the upper and lower solutions method to study the existence of positive periodic solutions to a system of infinite delay equations with a email protected t a t x t email protected t x t

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

invariants of a family of third order ordinary differential equations we consider a family of third order ordinary differential equations odes with the cubic nonlinearity in second order derivative which is closed with respect to contact transformations using lie s infinitesimal method we construct the basis of differential invariants for this family of equations and the operators of invariant differentiation invariants provide a simple way of finding the equations which may be equivalent to a given nonlinear ode and the transformation connecting two equivalent equations some examples are given to illustrate the results obtained in the paper

global stability in a viral infection model with lytic and nonlytic immune responses this paper investigates the global stability of a viral infection model with lytic and nonlytic immune responses if the basic reproductive ratio of the virus is less than or equal to one by the lasalle s invariance principle and center manifold theorem the disease free steady state is globally asymptotically stable if the basic reproductive ratio of the virus is greater than one then the virus persists in the host and the disease steady state is locally asymptotically stable furthermore by the method of lyapunov function the global stability of the disease steady state is established at the same time if we neglect the efficacy of the lytic component using a geometrical approach we obtain a different type of conditions for the global stability of the disease steady state

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

sample size and statistical power assessing the effect of interventions in the context of mixture distributions with detection limits often in randomized clinical trials and observational cohort studies a non negative continuously distributed response variable is measured in treatment and control groups in the presence of true zeros for the response variable a two part zero inflated log normal model which assumes that the data has a probability mass at zero and a continuous response for values greater than zero is usually recommended however in some environmental health and human immunodeficiency virus hiv studies quantitative assays for metabolites of toxicants or quantitative hiv rna measurements are subject to left censoring due to values falling below the limit of detection ld here a zero inflated log normal mixture model is often suggested since true zeros are indistinguishable from left censored values due to the ld when the probabilities of true zeros in the two groups are not restricted to be equal the information contributed by values falling below ld is used only to estimate the probability of true zeros in the context of mixture distributions we derived the required sample size to assess the effect of a treatment in the context of mixture models with equal and unequal variances based on the left truncated log normal distribution methods for calculation of statistical power are also presented we calculate the required sample size and power for a recent study estimating the effect of oltipraz on reducing urinary levels of the hydroxylated metabolite aflatoxin m1 afm1 in a randomized placebo controlled double blind phase iia chemoprevention trial in qidong china a monte carlo simulation study is conducted to investigate the performance of the proposed methods copyright 2006 john wiley sons ltd