an evaluation of some methods for fitting dose response models to quantal response developmental toxicology data the analysis of quantal response developmental toxicology data by dose response modeling is discussed with emphasis on methods that avoid exact distributional assumptions these methods quasi likelihood bootstrapping and jackknifing are contrasted with analyses based on the beta binomial distribution for the resampling procedures dose response models are fit under a binomial likelihood a justification for this choice of estimator in resampling plans is given based on an extension of the standard results for asymptotic normality and consistency of maximum likelihood estimators this justification depends only on the true distribution of the data having the usual binomial expectation a quasi likelihood approach is also considered in which simple assumptions about the intralitter correlation structure are made quasi likelihood methods are in theory asymptotically robust to misspecification of the intralitter correlation structure the practical implications of these asymptotic results are evaluated in a simulation study

test of marginal compatibility and smoothing methods for exchangeable binary data with unequal cluster sizes exchangeable binary data are often collected in developmental toxicity and other studies and a whole host of parametric distributions for fitting this kind of data have been proposed in the literature while these distributions can be matched to have the same marginal probability and intra cluster correlation they can be quite different in terms of shape and higher order quantities of interest such as the litter level risk of having at least one malformed fetus a sensible alternative is to fit a saturated model bowman and george 1995 journal of the american statistical association 90 871 879 using the expectation maximization em algorithm proposed by stefanescu and turnbull 2003 biometrics 59 18 24 the assumption of compatibility of marginal distributions is often made to link up the distributions for different cluster sizes so that estimation can be based on the combined data stefanescu and turnbull proposed a modified trend test to test this assumption their test however fails to take into account the variability of an estimated null expectation and as a result leads to inaccurate p values this drawback is rectified in this article when the data are sparse the probability function estimated using a saturated model can be very jagged and some kind of smoothing is needed we extend the penalized likelihood method simonoff 1983 annals of statistics 11 208 218 to the present case of unequal cluster sizes and implement the method using an em type algorithm in the presence of covariate we propose a penalized kernel method that performs smoothing in both the covariate and response space the proposed methods are illustrated using several data sets and the sampling and robustness properties of the resulting estimators are evaluated by simulations

modelling and analysing exchangeable binary data with random cluster sizes correlated binary data occur very frequently in cluster sample surveys dependent repeated cancer screening teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods to analyse these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices however in many applications it is reasonable to assume that the data from the same cluster are exchangeable when all sampled clusters have equal sizes bowman and george introduced maximum likelihood estimates mles of the population parameters such as the marginal means moments and correlations of order two and higher they also extended their approach to sampled clusters with unequal sizes it seems that their extension has a gap this paper points out the source of this gap and shows that estimates introduced by bowman and george are not the mles of the parameters which are used to identify the joint distribution of correlated binary data we show that the mles of the population parameters have no closed form in general and should be calculated by numerical methods we apply our results and a generalized estimating equation procedure to a data set from a double blind randomized clinical trial comparing two antibiotics cefaclor and amoxicillin used for the treatment of acute otitis media to see the performance of the mles with small or moderate sample sizes several simulation studies are also conducted

dose response models for teratological experiments in a recent paper hereinafter referred to as rvr rai and van ryzin 1985 propose a dose response model for use in low dose extrapolation from teratological experiments involving quantal responses suppose n litters are divided into m 1 dose groups the ith group consisting of ni litters exposed to dose di o do di dn the group i 0 being a zero dose control let sij denote the size of the jth litter in the ith group j 1 ni and let rij denote the number of foetuses or pups in the litter exhibiting the toxic response of interest the model proposed by rvr assumes that the conditional distribution of rij given sij sij is binomial sij p1j where

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

bifurcations of travelling wave solutions for the nonlinear dispersion drinfel d sokolov d m n system abstract by using the bifurcation theory of planar dynamical systems to the nonlinear dispersion drinfel d sokolov d m n system the existence of solitary wave solutions kink and anti kink wave solutions compacton solutions and uncountably infinite many smooth and non smooth periodic wave solutions is proved under different regions of parametric spaces various sufficient conditions to guarantee the existence of above solutions are given some exact explicit parametric representations of the above waves are determined

likelihood inference for exchangeable binary data with varying cluster sizes ce papier etudie l estimation au maximum de vraisemblance dans des modeles satures et insatures pour des donnees binaires correlees echangeables lorsqu on dispose d un echantillon de clusters independants de tailles variables nous discutons plusieurs parametrisations de ces modeles et nous proposons l utilisation de l algorithme em pour obtenir des estimations du maximum de vraisemblance la methodologie est illustree par des applications a une etude d agregation familiale de maladie et a la construction d un essai randomise par groupe pour la prevention du cancer

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

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

computing finite time non ruin probability and some joint distributions in discrete time risk model with exchangeable claim occurrences abstract in this paper we study a discrete time risk model based on exchangeable dependent claim occurrences in particular we obtain expressions for the finite time non ruin probability and the joint distribution of the time to ruin the surplus immediately before ruin and the deficit at ruin an illustration of the results is given and some implications of the results are provided comparisons are made with the corresponding results for the classical compound binomial model of independent and identically distributed claim occurrences

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

a shared response model for clustered binary data in developmental toxicity studies summary existing distributions for modeling fetal response data in developmental toxicology such as the beta binomial distribution have a tendency of inflating the probability of no malformed fetuses and hence understating the risk of having at least one malformed fetus within a litter as opposed to a shared probability extra binomial model we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response an explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses the em algorithm can be used to estimate the model parameters results of a simulation study show that the em estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form but not so for the estimates of intralitter correlation and the litter level probability of having at least one malformed fetus the proposed model is fitted to a set of data from the u s national toxicology program for the same dose response relationship the fit based on the shared response distribution is superior to that based on the beta binomial and comparable to that based on the recently proposed q power distribution kuk 2004 applied statistics53 369 386 an advantage of the shared response model over the q power distribution is that it is more interpretable and can be extended more easily to the multivariate case to illustrate this a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation

a dose response model for teratological experiments involving quantal responses this paper introduces a dose response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size the maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm two methods of low dose extrapolation are presented one based on the litter size distribution and the other a conservative method the resulting procedures are then applied to a teratological data set from the literature

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

inference procedures for assessing interobserver agreement among multiple raters summary we propose a new procedure for constructing inferences about a measure of interobserver agreement in studies involving a binary outcome and multiple raters the proposed procedure based on a chi square goodness of fit test as applied to the correlated binomial model bahadur 1961 in studies in item analysis and prediction 158 176 is an extension of the goodness of fit procedure developed by donner and eliasziw 1992 statistics in medicine11 1511 1519 for the case of two raters the new procedure is shown to provide confidence interval coverage levels that are close to nominal over a wide range of parameter combinations the procedure also provides a sample size formula that may be used to determine the required number of subjects and raters for such studies

1 soliton solution of the d m n equation with generalized evolution abstract this paper obtains the 1 soliton solution of the nonlinear dispersive drinfel d sokolov equation with power law nonlinearity in the first case the soliton solution is without the generalized evolution the solitary wave ansatz method is used to carry out the integration subsequently the he s semi inverse variational principle is used to integrate the equation with power law nonlinearity parametric conditions for the existence of envelope solitons are given

a repeated measures concordance correlation coefficient the concordance correlation coefficient is commonly used to assess agreement between two raters or two methods of measuring a response when the data are measured on a continuous scale however the situation may arise in which repeated measurements are taken for each rater or method e g longitudinal studies in clinical trials or bioassay data with subsamples this paper proposes a coefficient for measuring agreement between two raters or two methods of measuring a response in the presence of repeated measurements we illustrate the methodology with examples comparing 1 1 hr versus 2 hr blood draws for measuring cortisol in an asthma clinical trial and 2 two measurements of percentage body fat from skinfold calipers and dual energy x ray absorptiometry

1 soliton solution of the generalized zakharov equation in plasmas by he s variational principle this paper obtains the 1 soliton solution to zakharov equation with power law and dual power law nonlinearities the he s variational principle is used to carry out the integration of this equation

statistical inference for familial disease clusters in many epidemiologic studies the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units the concept of clustering is contrasted with incidence we assume that all individuals are exchangeable except for their disease status this assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease conditional on the number of diseased cases and the distribution of the sizes of the various family units new parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering we consider models and an example that takes covariates into account ascertainment bias is described and the appropriate sampling distribution is demonstrated four numerical examples with real data illustrate these methods

tests of independence treatment heterogeneity dose related trend with exchangeable binary data abstract existing methods of testing for treatment effects for clustered binary data include the beta binomial quasilikelihood gee procedures all of these methods revolve around the mean response and the second order correlation however these two parameters alone do not fully determine the effect of treatment this article develops nonparametric likelihood ratio procedures to test for independence heterogeneity dose related trend in dose response studies involving exchangeable binary data the hypotheses of independence heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics unlike the test statistics for independence and heterogeneity the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi square however an upper bound of its p value is obtained by using a chi squared distribution a set of clustere

hypothesis testing for proportions with overdispersion summary the properties of likelihood ratio tests and simpler t tests are investigated by simulation under an assumed beta binomial model for parameter values typically found in toxicological studies it is found that likelihood ratio methods are at least as powerful as the simpler approaches and in certain situations can be significantly more powerful

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

a unified approach for analyzing exchangeable binary data with applications to developmental toxicity studies in this article we present a general procedure to analyze exchangeable binary data that may also be viewed as realizations of binomial mixtures our approach unifies existing models and is practical and computationally easy resulting from completely monotonic functions we introduce a rich family of parametric parsimonious binomial mixtures including the incomplete beta gamma normal and poisson binomial generalizing the beta binomial we show that the family is closed under convex linear combinations products and composites we also give the moments and the markov property of the family with such distributions we can perform statistical inference on correlated binary data and in particular overdispersed data we propose a regression procedure that generalizes logistic regression we provide a forward model selection procedure we run a small simulation to validate the inclusion of the binomial distribution finally we apply the proposed procedure to analyze the 2 4 5 trichlorophenoxyacetic acid and e2 data and compare the results with existing procedures copyright 2009 john wiley sons ltd

on exchangeable multinomial distributions we derive an expression for the joint distribution of exchangeable multinomial random variables which generalizes the multinomial distribution based on independent trials while retaining some of its important properties unlike de finneti s representation theorem for a binary sequence the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence using expressions for higher moments and correlations we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature and we analyse data from developmental toxicology studies the proposed analyses have been implemented in r and are available on cran in the corrbin package

the cole hopf transformation and multiple soliton solutions for the integrable sixth order drinfeld sokolov satsuma hirota equation abstract the completely integrable sixth order nonlinear drinfeld sokolov satsuma hirota equation is studied three distinct methods namely the cole hopf transformation method the tanh coth method and the exp function method are used for a reliable treatment of this equation solitons multiple soliton solutions multiple singular soliton solutions and plane periodic solutions are obtained for this equations the study highlights the power of each method

a saturated model for analyzing exchangeable binary data applications to clinical and developmental toxicity studies abstract correlated binary data occur very frequently in statistical practice in many applications it is reasonable to assume that data from the same cluster are exchangeable such data are commonly encountered in cluster sample surveys teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods of analyzing these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices the focus of these procedures is an estimation of the mean and variance parameters more information can be obtained when data are exchangeable by expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means moments and correlations of orders two and higher applications are m