discharge rates of medicare stroke patients to skilled nursing facilities bayesian logistic regression with unobserved heterogeneity abstract we determine factors both hospital specific and market area specific associated with hospitals propensities for discharging medicare stroke patients to skilled nursing facilities snf s in california and florida logistic regression is generalized to the case of a betabinomial hierarchical model in which covariate information is included in the hyperparameters of the second stage beta distribution it is found that the posterior mean of the proportion discharged to snf is approximately a weighted average i e shrinkage estimator of the logistic regression estimator and the observed rate we develop fully bayesian inference that takes into account uncertainty about the hyperparameters and we find that this also allows us to test for overdispersion in a natural way the number of observed zeros i e hospitals that sent no stroke patients to a snf is excessive compared to the number expected from a standard logistic regression model and is fit better by the hierarchical betabinomial mod

scaling variables and asymptotic expansions in damped wave equations abstract we study the long time behavior of small solutions to the nonlinear damped wave equationeu u a u n u u u r 0 whereeis a positive not necessarily small parameter we assume that the diffusion coefficienta converges to positive limitsa as and that the nonlinearity n u u u vanishes sufficiently fast asu 0 introducing scaling variables and using various energy estimates we compute an asymptotic expansion of the solutionu in powers of 1 2as and we show that this expansion is entirely determined up to the second order by a linear parabolic equation which depends only on the limiting valuesa in particular this implies that the small solutions of the damped wave equation behave for large like those of the parabolic equation obtained by settinge 0

existence and stability of propagating fronts for an autocatalytic reaction diffusion system we study a one dimensional reaction diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic a b 2b and a cubic a 2b 3b autocatalysis the parameters of this system are in the ratio d d b d a of the diffusion constants of the reactant a and the autocatalyst b and the relative activity ii of the cubic reaction first for all values of d 0 and k greater than or equal to 0 we prove the existence of a family of propagating fronts or travelling waves describing the advance of the reaction in particular in the quadratic case k 0 we recover the results of billingham and needham phil trans r sec london a 334 1991 1 24 then if d is close to 1 and k is sufficiently small we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted sobolev spaces this extends part of the results that are known for the scalar equation to which our system reduces when d 1 c 1998 elsevier science b v

interval estimation of risk difference for data sampled from clusters risk difference rd is an important measure in epidemiological studies where the probability of developing a disease for individuals in an exposed group for example is compared with that in a control group there are varying cluster sizes in each group and the binary responses within each cluster cannot be assumed independent under the cluster sampling scenario lui statistical estimation of epidemiological risk wiley ca 2004 7 27 discusses four methods for the construction of a confidence interval for the rd in this paper we introduce two very simple methods one method is based on an estimator of the variance of a ratio estimator sampling techniques 3rd edn wiley new york 1977 30 67 and the other method is based on a sandwich estimator of the variance of the regression estimator using the generalized estimating equations approach of zeger and liang biometrics 1986 42 121 130 these two methods are then compared by simulation in terms of maintaining nominal coverage probability and average coverage length with the four methods discussed by lui statistical estimation of epidemiological risk wiley ca 2004 7 27 simulations show at least as good properties of these two methods as those of the others the method based on an estimate of the variance of a ratio estimator performs best overall it involves a very simple variance expression and can be implemented with a very few computer codes therefore it can be considered as an easily implementable alternative

non uniqueness of quantized yang mills theories we consider quantized yang mills theories in the framework of causal perturbation theory which goes back to epstein and glaser in this approach gauge invariance is expressed by a simple commutator relation for the s matrix the most general coupling which is gauge invariant to first order contains a two parametric ambiguity in the ghost sector a divergence and a coboundary coupling may be added we prove not completely that the higher orders with these two additional couplings are also gauge invariant moreover we show that the ambiguities of the n point distributions restricted to the physical subspace are only a sum of the divergences in the sense of vector analysis it turns out that the theory without divergence and coboundary coupling is the simplest one in a quite technical sense the proofs for the n point distributions containing coboundary couplings are given up to third or fourth order only whereas the statements about the divergence coupling are proved for all orders

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

on the transition from the ginzburg landau equation to the extended fisher kolmogorov equation abstract the ginzburg landau gl equation generically describes the behaviour of small perturbations of a marginally unstable basic state in systems on unbounded domains in this paper we consider the transition from this generic situation to a degenerate co dimension 2 case in which the gl approach is no longer valid instead of studying a general underlying model problem we consider a two dimensional system of coupled reaction diffusion equations in one spatial dimension we show that near the degeneration the behaviour of small perturbations is governed by the extended fisher kolmogorov efk equation at leading order the relation between the gl equation and the efk equation is quite subtle but can be analysed in detail the main goal of this paper is to study this relation which we do asymptotically the asymptotic analysis is compared to numerical simulations of the full reaction diffusion system as one approaches the co dimension 2 point we observe that the stable stationary periodic patterns predicted by the gl equation evolve towards various different families of stable stationary but not necessarily periodic so called multi bump solutions in the literature these multi bump patterns are shown to exist as solutions of the efk equation but there is no proof of the asymptotic stability of these solutions our results suggest that these multi bump patterns can also be asymptotically stable in large classes of model problems

maximum likelihood estimation of the parameters of the prior distributions of three variables that strongly influence reproductive performance in cows ovulation detection rate pregnancy rate and embryo loss rate greatly affect the reproductive performance of cows a previous model described the separate effects of these variables on the resulting calving patterns and assumed that the variables have the same value for all cows belonging to the same herd this is not a realistic biological assumption so the beta distribution is used to introduce between cow variation in the three variables two approaches are used to find maximum likelihood estimates of the parameters of these prior beta distributions the first considers sequences of ovulations artificial inseminations and pregnancies separately for both ovulation detection rate and pregnancy rate this approach considers the number of successes of each event for a particular cow e g in the case of an ovulation a success is a detection and conditions on the total number of occurrences of that event in the cow so that beta binomial distributions are considered however for embryo loss rate the number of pregnancies required until a particular cow calves is considered so that a beta geometric distribution results if the cow is removed before she calves a censored sequence will result the second approach considers the sequences of ovulations artificial inseminations pregnancies and embryo losses together which will stop only when the cow calves otherwise if she is removed before that time a censored sequence will result in this case a joint distribution with three independent prior beta distributions is considered the results of the analysis of data from 22 herds are discussed

the impact of litter effects on dose response modeling in teratology the fitting of dose response models to teratology data involving littermates in order to generate estimates of teratogenic risk is receiving increasing attention as a potential alternative to the safety factor approach to risk estimation in this paper we utilize the beta binomial distribution to introduce varying degrees of intralitter correlation and for purposes of illustration consider a logistic dose response model that describes the logit of risk as a straight line function of ln dose the biases and exact and asymptotic variances of the maximum likelihood estimators of the intercept and slope are studied by simulation as a function of the intralitter correlation structure

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

the incorporation of historical control information in tests of proportions simulation study of tarone s procedure empirical bayes procedures for incorporating historical control information in bioassay carcinogenesis studies are receiving attention in the literature in general the empirical bayes methods fail to take into account the error in estimating the parameters of a prior distribution the implications of this are studied for the beta prior of tarone 1982 biometrics 38 215 220 using simulations we show that the skewness in the maximum likelihood estimators for the parameters of the beta prior increases the false positive rate in the test of dose related trend

ward identities and renormalization of general gauge theories we introduce the concept of general gauge theory which includes yang mills models we use the framework of the causal approach and show that the anomalies can appear only in the vacuum sector of the identities obtained from the gauge invariance condition by applying derivatives with respect to the basic fields for the yang mills model we provide these identities in the lowest orders of the perturbation theory and prove that they are valid the investigation of higher orders of the perturbation theory is still an open problem

pattern generating travelling waves in a discrete multicellular system with lateral inhibition abstract on a one dimensional string of cells the juxtacrine signalling model for delta notch lateral inhibition by collier et al j r collier n a m monk p k maini j h lewis pattern formation by lateral inhibition with feedback a mathematical model of delta notch intercellular interaction j theoret biol 183 1996 429 446 exhibits a predominant alternating pattern of cells expressing either delta or notch as well as many aperiodic patterns despite this multistationarity in the idealised situation of no noise travelling waves invading the unstable homogeneous state only generate the predominant alternating pattern in their wake all over the lattice however this robustness is totally lost in the presence of stochastic noise because the invaded initial state is unstable using linear approximations around the initial homogeneous state and around the final patterned state we are able to derive analytically all essential properties of the wave the shape of the wave front the unique alternating pattern generated by the wave and the asymptotic speed of the wave front we show that the asymptotic wave speed equals the theoretical minimum wave speed the latter agrees extremely well with the value estimated from numerical simulations thus in this system travelling waves are pulled by the leading edge of the front

estimation bias using the beta binomial distribution in teratology kupper et al 1986 biometrics 42 85 98 considered the fitting of dose response regressions to litter proportions in teratology experiments they found that the estimators which maximise the beta binomial likelihood become biased when the intralitter correlation is incorrectly assumed to be homogeneous this paper considers the nature of this bias and its implications for the analysis of litter proportions in toxicology

profile likelihood based confidence interval of the intraclass correlation for binary outcome data sampled from clusters the intraclass correlation in binary outcome data sampled from clusters is an important and versatile measure in many biological and biomedical investigations properties of the different estimators of the intraclass correlation based on the parametric semi parametric and nonparametric approaches have been studied extensively mainly in terms of bias and efficiency see for example ridout et al biometrics 1999 55 137 148 paul et al journal of statistical computation and simulation 2003 73 507 523 and lee statistical modelling 2004 4 113 126 but little attention has been paid to extending these results to the problem of the confidence intervals in this article we generalize the results of the four point estimators by constructing asymptotic confidence intervals obtaining closed form asymptotic and sandwich variance expressions of those four point estimators it appears from simulation results that the asymptotic confidence intervals based on these four estimators have serious under coverage to remedy this we introduce the fisher s z transformation approach on the intraclass correlation coefficient the profile likelihood approach based on the beta binomial model and the hybrid profile variance approach based on the quadratic estimating equation for constructing the confidence intervals of the intraclass correlation for binary outcome data as assessed by monte carlo simulations these confidence interval approaches show significant improvement in the coverage probabilities moreover the profile likelihood approach performs quite well by providing coverage levels close to nominal over a wide range of parameter combinations we provide applications to biological data to illustrate the methods copyright 2012 john wiley sons ltd

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

power and sample size estimation for the wilcoxon rank sum test with application to comparisons of c statistics from alternative prediction models the wilcoxon mann whitney wmw u test is commonly used in nonparametric two group comparisons when the normality of the underlying distribution is questionable there has been some previous work on estimating power based on this procedure lehmann 1998 nonparametrics in this article we present an approach for estimating type ii error which is applicable to any continuous distribution and also extend the approach to handle grouped continuous data allowing for ties we apply these results to obtaining standard errors of the area under the receiver operating characteristic curve auroc for risk prediction rules under h 1 and for comparing auroc between competing risk prediction rules applied to the same data set these results are based on sas callable functions to evaluate the bivariate normal integral and are thus easily implemented with standard software

confidence intervals for the risk ratio under cluster sampling based on the beta binomial model in cohort studies the risk ratio rr is one of the most commonly used epidemiologic indices to quantify the effect of a suspected risk factor on the probability of developing a disease when we employ cluster sampling to collect data an interval estimator that does not account for the intraclass correlation between subjects within clusters is likely inappropriate in application of the beta binomial model to account for the intraclass correlation we develop four asymptotic interval estimators of the rr which are direct extensions of some recently developed estimators for independent binomial sampling we then use monte carlo simulation to evaluate the finite sample performance of these four interval estimators in a variety of situations we find that the estimator using the logarithmic transformation generally performs well and is preferable to the other three estimators in most of the situations considered here finally we include an example from a study of an educational intervention with emphasis on behaviour change to illustrate the use of the estimators developed in this paper

pattern forming pulled fronts bounds and universal convergence we analyze the dynamics of pattern forming fronts which propagate into an unstable state and whose dynamics is of the pulled type so that their asymptotic speed is equal to the linear spreading speed v we discuss a method that allows to derive bounds on the front velocity and which hence can be used to prove for among others the swift hohenberg equation the extended fisher kolmogorov equation and the cubic complex ginzburg landau equation that the dynamically relevant fronts are of the pulled type in addition we generalize the derivation of the universal power law convergence of the dynamics of uniformly translating pulled fronts to both coherent and incoherent pattern forming fronts the analysis is based on a matching analysis of the dynamics in the leading edge of the front to the behavior imposed by the nonlinear region behind it numerical simulations of fronts in the swift hohenberg equation are in full accord with our analytical predictions

algebraic quantum field theory perturbation theory and the loop expansion the perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory we show that the algebra of interacting fields is additive i e fully determined by its subalgebras associated to arbitrary small subregions of minkowski space we also give an algebraic formulation of the loop expansion by introducing a projective system n of observables up to n loops where 0 is the poisson algebra of the classical field theory finally we give a local algebraic formulation for two cases of the quantum action principle and compare it with the usual formulation in terms of green s functions

effective sample size for tests of censored survival data summary when survival experience of two groups is compared in the presence of arbitrary right censoring the effective sample size for determining the power of the test used is usually taken to be the number of uncensored observations this convention is examined through a monte carlo study empirical powers of the generalized savage test and generalized wilcoxon test with uncensored data are compared to those with censored data containing approximately the same number of uncensored observations large sample relative efficiencies are calculated for a lehmann family of alternatives it is shown that depending on the underlying distribution and censoring mechanism censored observations can add appreciably to the power of either test

estimating intraclass correlation for binary data summary this paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study some of the estimators are very specific while others result from general methods such as pseudo likelihood and extended quasi likelihood estimation the simulation study identifies several useful estimators one of which does not seem to have been considered previously for binary data estimators based on extended quasi likelihood are found to have a substantial bias in some circumstances

the performance of the o brien fleming multiple testing procedure in the presence of intraclass correlation assuming that all subject responses were independent o brien and fleming 1979 biometrics 35 549 556 proposed a simple and useful multiple testing procedure for clinical trials for comparing two treatments with dichotomous data differences in the methods of evaluating subject responses at each evaluation time however may induce an intraclass correlation among these responses used in calculating the o brien fleming multiple testing procedure on the basis of monte carlo simulations we note that even a small intraclass correlation among subject responses in the same analysis can substantially inflate the type i error of the o brien fleming multiple testing procedure furthermore this inflation generally increases as either the number of analyses or the underlying response probability increases we also have demonstrated that if we were able to maintain a uniform medical test procedure between the two treatments for each analysis the actual type i error of the o brien fleming multiple testing procedure may conversely become conservative

procedures for testing the homogeneity of relative difference in sparse data to quantify the excess effect of an experimental treatment over a placebo group in clinical trials we often consider use of the relative difference defined as the proportion of patients who would respond to the experimental treatment among those who would not otherwise if they were assigned to the placebo group to control the effects due to confounders on the response of interest we frequently employ stratified analysis in practice before obtaining a summary estimate of the relative difference it is desirable to assess whether this measure is constant across strata based on the beta binomial model we develop simple procedures for testing the homogeneity of relative difference for sparse data in which we have many strata but few patients per stratum using monte carlo simulations we demonstrate that the proposed test procedures can generally perform well with respect to type i error in a variety of situations we further evaluate and study the power of these test procedures finally we note some robustness in using the test procedures proposed here

existence and stability of traveling fronts in the extended fisher kolmogorov equation abstract we study traveling wave solutions to a general fourth order differential equation that is a singular perturbation of the fisher kolmogorov equation we apply the geometric method for singularly perturbed systems to show that for every positive wavespeed there exists a traveling wave also we find that there exists a critical wavespeed c which divides these solutions into monotonic c c and oscillatory c c solutions we show that the monotonic fronts are locally stable under perturbations in appropriate weighted sobolev spaces by using various energy functionals

interval estimation for the intraclass correlation in dirichlet multinomial data when the underlying distribution is discrete with a limited number of categories methods for interval estimation of the intraclass correlation which assume normality are theoretically inadequate for use on the basis of large sample theory this paper develops an asymptotic closed form interval estimate of the intraclass correlation for the case where there is a natural score associated with each category this paper employs monte carlo simulation to demonstrate that when the underlying intraclass correlation is large the traditional interval estimator which assumes normality can be misleading we find that when the number of classes is 20 the interval estimator proposed here can generally perform reasonably well in a variety of situations this paper further notes that the proposed interval estimator is invariant with respect to a linear transformation when the data are on a nominal scale an extension of the proposed method to account for this case as well as a discussion on the relationship between the intraclass correlation and a kappa type measure defined here and on the limitation of the corresponding kappa type estimator are given

instabilities and propagation properties in a fourth order reaction diffusion equation in this paper we investigate the instability and the propagation properties of a class of reaction diffusion equations of fourth order two examples are introduced the extended fisher kolmogorov equation efk and the swift hohenberg equation sh both have been studied before by related methods see for example peletier and rottschafer 2004 19 van saarloos 2003 24 but the analysis here will support the introduced linear mechanism in front selection these two equations support a patterned front solutions and the double eigenvalue mechanism is used to provide evidence for that and to determine a minimal front speed

interval estimation of generalized odds ratio in data with repeated measurements when the underlying responses are on an ordinal scale the generalized odds ratio gor defined as the ratio of the proportions of concordant and discordant pairs is a useful index to summarize the difference between two stochastically ordered distributions of an ordinal categorical variable we discuss interval estimation of the gor for ordinal data with repeated measurements on the basis of the dirichlet multinomial model we develop three asymptotic interval estimators of the gor using wald s test statistic a logarithmic transformation and a method analogous to fieller s theorem respectively to evaluate and compare the finite sample performance of these estimators we apply monte carlo simulation we find that when the number of subjects per group is not large the coverage probability of interval estimator using wald s test statistic is likely to be less than the desired confidence level by contrast the coverage probability of the other two estimators are approximately equal to or larger than the desired confidence level when the number of subjects per group is small and the intraclass correlation between repeated measurements within subjects is large we note that applying the interval estimator derived from a method analogous to fieller s theorem can lose efficiency we also note that the interval estimator using the logarithmic transformation is generally preferable to the other two estimators with respect to both the coverage probability and the average length finally on the basis of a few preliminary simulations we do find some robustness for all the estimators developed here we include an example comparing the inflammation grade after lung transplant between surgeries to illustrate the use of the proposed interval estimators

on the transition from pulled to pushed monotonic fronts of the extended fisher kolmogorov equation abstract the extended fisher kolmogorov equation u t u xx u xxxx f u with arbitrary positive f u satisfying f 0 f 1 0 has monotonic traveling fronts for 1 12 we find a simple lower bound on the speed of the fronts which allows to determine for a given reaction term when will the front of minimal speed be pushed

the non linear stability of front solutions for parabolic partial differential equations for the ginzburg landau equation and similar reaction diffusion equations on the line we show convergence of complex perturbations of front solutions towards the front solutions by exhibiting a coercive functional

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

an interval estimate for the interclass correlation in beta binomial sampling the beta binomial distribution has been frequently applied to model intraclass correlation among dichotomous responses in cluster sampling to avoid using sophisticated numerical procedures to calculate maximum likelihood estimates many authors have proposed different moment estimators most of them focused their discussion however on point estimation only in this paper we have developed a closed form interval estimate for the intraclass correlation and have shown it has asymptotically correct coverage we have further used a monte carlo simulation to evaluate the performance of the proposed interval estimation in a variety of situations we have found that when the number of clusters is moderate 50 the proposed interval estimation performs reasonably well except for the situation where the intraclass correlation is large and the underlying mean response probability is small even when the number of clusters is as small as 20 the proposed interval estimation may still be useful in the situation where the intraclass correlation is small we have also extended the proposed interval estimate to accommodate stratified sampling in which each stratum has a different mean response probability but has a common intraclass correlation

incorporating historical controls in testing for a trend in proportions abstract the testing of chemicals for carcinogenic activity in lifetime rodent bioassays has produced a large amount of data on a few strains of mice and rats because of the use of fixed protocols in repeated experiments the opportunity presents itself for using this historical data in the analysis of a current experiment what has been considered is the statistical incorporation of the historical control data into the current control group to increase the power of the test this is especially relevant when dealing with tumors of a rare type where the toxicologist will place great significance on their occurrence in a treatment group experimentally it is assumed that three groups of about 50 animals each are tested at two treatment levels and a control the response for each treatment group is assumed to be binomial further it is assumed that the probability of an animal with a tumor in the control group has a beta distribution that is determined from the historical control data several authors demp

the effect of retaining probability variation on sample size calculations for normal variates skalski 1992 biometrics 48 877 882 assumed a constant retaining probability p for all experimental units and found that the traditional ad hoc procedure of escalating sample size by the multiplicative factor ilp tends to underestimate the required sample size when p is small because this retaining probability p often depends on characteristics of different experimental units however p may vary from one unit to another in this report we have allowed p to vary among different experimental units we have noted that when the retaining probability p has a small mean but a large variance the underestimation of the required sample size for a desired precision by use of the traditional adjusted sample size formula can be even more serious than that demonstrated by skalski

a note on the effect of the intraclass correlation in the multiple reading procedure with a unanimity rule the use of multiple reading procedures to improve the performance of a diagnostic test occurs often in practice evaluation of the utility of multiple reading procedures however usually ignores the effect of the intraclass correlation this paper provides a quantitative assessment of this effect in the multiple reading procedure with a unanimity rule with respect to sensitivity specificity positive and negative predictive values we have found that when the disease prevalence is rare or moderate less than or equal to 0 20 use of the multiple reading procedure with a unanimity rule is effective in increasing the positive predictive value of a single reading procedure for the situation in which the variation of responses among different subjects and the intraclass correlation among repeated tests are small this is however not true for the situation in which the disease is rare and the variation of responses among different subjects is large even when the intraclass correlation is small or 0 furthermore when the disease is rare and the variation of responses among subjects is small a small or moderate intraclass correlation can substantially decrease the positive predictive value that one calculates under the assumption that the intraclass correlation is equal to 0 in general when the disease is rare or moderate less than or equal to 0 20 the intraclass correlation between repeated tests and the variation of responses among subjects have little effect on the negative predictive value

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

a revisit on tests for homogeneity of the risk difference lipsitz et al 1998 biometrics 54 148 160 discussed testing the homogeneity of the risk difference for a series of 2 x 2 tables they proposed and evaluated several weighted test statistics including the commonly used weighted least squares test statistic here we suggest various important improvements on these test statistics first we propose using the one sided analogues of the test procedures proposed by lipsitz et al because we should only reject the null hypothesis of homogeneity when the variation of the estimated risk differences between centers is large second we generalize their study by redesigning the simulations to include the situations considered by lipsitz et al 1998 as special cases third we consider a logarithmic transformation of the weighted least squares test statistic to improve the normal approximation of its sampling distribution on the basis of monte carlo simulations we note that as long as the mean treatment group size per table is moderate or large or 16 this simple test statistic in conjunction with the commonly used adjustment procedure for sparse data can be useful when the number of 2 x 2 tables is small or moderate or 32 in these situations in fact we find that our proposed method generally outperforms all the statistics considered by lipsitz et al finally we include a general guideline about which test statistic should be used in a variety of situations

confidence interval estimation of the intraclass correlation coefficient for binary outcome data we obtain closed form asymptotic variance formulae for three point estimators of the intraclass correlation coefficient that may be applied to binary outcome data arising in clusters of variable size our results include as special cases those that have previously appeared in the literature fleiss and cuzick 1979 applied psychological measurement 3 537 542 bloch and kraemer 1989 biometrics 45 269 287 altaye donner and klar 2001 biometrics 57 584 588 simulation results indicate that confidence intervals based on the estimator proposed by fleiss and cuzick provide coverage levels close to nominal over a wide range of parameter combinations two examples are presented

robust bayes and empirical bayes analysis with _ epsilon contaminated priors on considere deux directions dans l analyse bayesienne robuste la premiere consiste a determiner l etendue des probabilites a posteriori d un ensemble la seconde consiste a selectionner une bonne distribution a priori

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

the use of historical control information in testing for a trend in proportions a problem commonly faced in biometric applications is to test for a trend in proportions in a 2 x k contingency table in which the k columns have a natural ordering for example a test compound may be administered at increasing dose levels to groups of test animals to determine if the proportion of animals developing a tumor increases with increasing dose level cochran 1954 and armitage 1955 proposed a chi square statistic for testing for a trend in proportions for problems with a large amount of historical data a test for trend incorporating the historical data would be useful this paper develops such a test based on a statistic which is closely related to that of cochran and armitage this method for binomial proportions is analogous to the method derived by pocock 1976 for normallydistributed data the problem will be developed in the context of an animal carcinogenesis experiment consider an experiment involving r 1 groups of test animals one group serves as a control group and the remaining r groups are given a test compound at increasing dose levels dld2 dr the animals are followed for a fixed period of time and the number of animals which develop a tumor at a particular organ is recorded for each group let ni denote the number of animals in the ith group and let the number of these animals which develop a tumor during the course of the experiment be denoted by xi i 0 1 r the results of this experiment can be summarized in a 2 x r 1 table such as table 1 to test for ap increase in the proportions pi xjni with increasing dose level cochran and armitage suggested the test statistic

homotopy classes for stable connections between hamiltonian saddle focus equilibria for a class of hamiltonian systems in 4 the set of homoclinic and heteroclinic orbits which connect saddle focus equilibria is studied using a variational approach the oscillatory properties of a saddle focus equilibrium and the variational nature of the problem give rise to connections in many homotopy classes of the configuration plane punctured at the saddle foci this variational approach does not require any assumptions on the intersections of stable and unstable manifolds such as transversality moreover these connections are shown to be local minimizers of an associated action functional this result has applications to spatial pattern formation in a class of fourth order bistable evolution equations

a note on sample size determination for a nonparametric test of location sample size determination methods are considered for hypothesis testing about location parameters of two continuous distributions using independent random samples and the mann whitney wilcoxon mww test for a specified shift size and power these methods are based on the so called noether s formula derived from a normal approximation to the power of the mww test and a pilot sample from each of the distributions compared with alternate methods including the one using bootstrap similar to that of hamilton and collings 1991 the new methods are shown to be at least as good in terms of accuracy and substantially more efficient in terms of speed and variability the simpler method using linearly smoothed empirical cdf s of the pilot samples and requiring no bootstrapping is recommended for practical use extensions and adaptations for obtaining an upper confidence bound on the sample size and to general linear rank tests are indicated

quick and simple approximation of sample sizes for comparing two independent binomial distributions different sample size case given the ratio k of two sample sizes sample sizes for comparing two independent proportions can be approximated from the sample size for the equal sample size design the proposed method is compared to the method of fleiss tytun and ury 1980 biometrics 36 343 346 methods for choosing the ratio are also presented

on sample size of the kruskal wallis test with application to a mouse peritoneal cavity study summary as the nonparametric generalization of the one way analysis of variance model the kruskal wallis test applies when the goal is to test the difference between multiple samples and the underlying population distributions are nonnormal or unknown although the kruskal wallis test has been widely used for data analysis power and sample size methods for this test have been investigated to a much lesser extent this article proposes new power and sample size calculation methods for the kruskal wallis test based on the pilot study in either a completely nonparametric model or a semiparametric location model no assumption is made on the shape of the underlying population distributions simulation results show that in terms of sample size calculation for the kruskal wallis test the proposed methods are more reliable and preferable to some more traditional methods a mouse peritoneal cavity study is used to demonstrate the application of the methods

a stabilized moment estimator for the beta binomial distribution the beta binomial distribution has been proposed as a model for the incorporation of historical control data in the analysis of rodent carcinogenesis bioassays low spontaneous tumor incidences along with the small number and sizes of historical control groups combine to make the moment and maximum likelihood estimates of the beta binomial parameters deficient we therefore propose a stabilized moment estimator for one of the parameters the stabilized moment estimator is similar to the ridge regression estimator and introduces a shrinkage parameter computer simulations were run to examine the behavior of the stabilized moment estimator the effect of the stabilized moment estimator on the score test for dose related trend is considered both on simulated data and on an example from the literature

variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation we give an integral variational characterization for the speed of fronts of the nonlinear diffusion equationut uxx f u withf 0 f 1 0 andf 0 in 0 1 which permits in principle the calculation of the exact speed for arbitraryf