on two open problems of 2 interval patterns the 2 interval pattern problem introduced in stephane vialette on the computational complexity of 2 interval pattern matching problems theoret comput sci 312 2 3 2004 223 249 models general problems with biological structures such as protein contact maps and macroscopic describers of secondary structures of ribonucleic acids given a set of 2 intervals d and a model r the problem is to find a maximum cardinality subset d of d such that any two 2 intervals in d satisfy r where r is a subset of relations on disjoint 2 intervals precedence nest and cross the problem left unanswered at present is that of whether there is a polynomial time solution for the 2 interval pattern problem when r and all the support intervals of d are disjoint in this paper we present a reduction from the clique problem to show that in this case the problem is np hard the disjoint 2 interval pattern matching problem is to decide whether a disjoint 2 interval pattern called the pattern is a substructure of another disjoint 2 interval pattern called the target in general the problem is np hard but when there are restrictions on the form of the pattern the problem can in some cases be solved in polynomial time in particular a polynomial time algorithm has been proposed gramm wabi 2004 and ieee acm tcbb 2004 for the case where the patterns are so called crossing contact maps in this paper we show that the problem is actually np hard and point out an error in the analysis of the above algorithm

a hierarchical bayesian model for combining multiple 2 x 2 tables using conditional likelihoods summary this paper introduces a hierarchical bayesian model for combining multiple 2 2 tables that allows the flexibility of different odds ratio estimates for different tables and at the same time allows the tables to borrow information from each other the proposed model however is different from a full bayesian model in that the nuisance parameters are eliminated by conditioning instead of integration the motivation is a more robust model and a faster and more stable gibbs algorithm we work out a gibbs scheme using the adaptive rejection sampling for log concave density and an algorithm for the mean and variance of the noncentral hypergeometric distribution the model is applied to a multicenter ulcer clinical trial

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

equivalence between conditional and random effects likelihoods for pair matched case control studies two approaches dominate the analysis of highly stratified data sets use of conditional likelihood and random effects models conditioning is more traditional and has attractive robustness properties contemporary random effects approaches rely more on accurate assumptions but can be applied to a larger class of problems for pair matched studies with arbitrary numbers of categorical covariates we reconcile these two approaches showing that the conditional approach has an exact interpretation as a specific type of random effects model the random effects models that provide equivalence with conditioning naturally inherit all the attractive properties of that approach and we argue they are a pragmatic model choice we also discuss desirable characteristics of the random effects model that are entirely novel and that have foundational implications for example although our model is specified entirely within a full likelihood framework its assumed random effects distribution does not need a parametric f

approximately exact inference for the common odds ratio in several 2 2 tables abstract the conditional maximum likelihood estimator mle of the common odds ratio in a sequence of independent 2 2 tables is known to be superior to the mantel haenszel estimator in terms of asymptotic efficiency and has the further advantage that its exact distribution is known however a long standing barrier to the widespread use of this estimator has been computational intractability in particular the calculation of significance levels confidence sets and power based on the exact distribution requires fast and efficient algorithms an important class of such algorithms form the basis of statxact a software package able to solve various aspects of the exact inference problem for a sequence of several 2 2 tables in real time we provide an alternative methodology by developing several useful saddlepoint approximations to the exact distribution of the conditional mle the approximations are derived from an interesting representation for hypergeometric random variables as a sum of independent

analysis of matched case control data with multiple ordered disease states possible choices and comparisons in an individually matched case control study effects of potential risk factors are ascertained through conditional logistic regression clr extension of clr to situations with multiple disease or reference categories has been made through polychotomous clr and is shown to be more efficient than carrying out separate clrs for each subgroup in this paper we consider matched case control studies where there is one control group but there are multiple disease states with a natural ordering among themselves this scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease for example according to different stages of cancer we explore several popular models for ordered categorical data in this context we first adopt a cumulative logit or equivalently a proportional odds model to account for the ordinal nature of the data the important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum specific nuisance parameters cannot be eliminated in this model via the conditional likelihood approach we discuss a mantel haenszel approach for analysing such data we point out possible difficulties with standard likelihood based approaches with the cumulative logit model when applied to case control data we then consider an alternative conditional adjacent category logit model we illustrate the methods by analysing data from a matched case control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control a simulation study compares the different ordinal methods with methods ignoring sub classification of the ordered disease states

retrospective prospective symmetry in the likelihood and bayesian analysis of case control studies summary prentice pyke 1979 established that the maximum likelihood estimate of an odds ratio in a case control study is the same as would be found by fitting a logistic regression in other words for this specific target the incorrect prospective model is inferentially equivalent to the correct retrospective model similar results have been obtained for other models and conditions have also been identified under which the corresponding bayesian property holds namely that the posterior distribution of the odds ratio is the same whether it is computed using the prospective or the retrospective likelihood in this article we demonstrate how these results follow directly from certain parameter independence properties of the models and priors and identify prior laws that support such reverse analysis for both standard and stratified designs somekeywords case controlstudy conditionalindependence hypermarkovlaw logisticregression retrospective likelihood

efficient monte carlo methods for conditional logistic regression abstract exact inference for the logistic regression model is based on generating the permutation distribution of the sufficient statistics for the regression parameters of interest conditional on the sufficient statistics for the remaining nuisance parameters despite the availability of fast numerical algorithms for the exact computations there are numerous instances where a data set is too large to be analyzed by the exact methods yet too sparse or unbalanced for the maximum likelihood approach to be reliable what is needed is a monte carlo alternative to the exact conditional approach which can bridge the gap between the exact and asymptotic methods of inference the problem is technically hard because conventional monte carlo methods lead to massive rejection of samples that do not satisfy the linear integer constraints of the conditional distribution we propose a network sampling approach to the monte carlo problem that eliminates rejection entirely its advantages over alternative saddlepoint

semiparametric bayesian modeling of random genetic effects in family based association studies we consider the inference problem of estimating covariate and genetic effects in a family based case control study where families are ascertained on the basis of the number of cases within the family however our interest lies not only in estimating the fixed covariate effects but also in estimating the random effects parameters that account for varying correlations among family members these random effects parameters though weakly identifiable in a strict theoretical sense are often hard to estimate due to the small number of observations per family a hierarchical bayesian paradigm is a very natural route in this context with multiple advantages compared with a classical mixed effects estimation strategy based on the integrated likelihood we propose a fully flexible bayesian approach allowing nonparametric modeling of the random effects distribution using a dirichlet process prior and provide estimation of both fixed effect and random effects parameters using a markov chain monte carlo numerical integration scheme the nonparametric bayesian approach not only provides inference that is less sensitive to parametric specification of the random effects distribution but also allows possible uncertainty around a specific genetic correlation structure the bayesian approach has certain computational advantages over its mixed model counterparts data from the prostate cancer genetics project a family based study at the university of michigan comprehensive cancer center including families having one or more members with prostate cancer are used to illustrate the proposed methods a small scale simulation study is carried out to compare the proposed nonparametric bayes methodology with a parametric bayesian alternative

hypothesis testing in an errors in variables model with heteroscedastic measurement errors in many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors the main goal of this paper is to consider inference on such models with error prone observations and variances of the measurement errors changing across observations we suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed aggregate data allow the estimation of the error variances maximum likelihood estimates are computed numerically via the em algorithm consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed test statistics are proposed for testing hypotheses of interest further we implement a simple graphical device that enables an assessment of the model s goodness of fit results of simulations concerning the properties of the test statistics are reported the approach is illustrated with data from the who monica project on cardiovascular disease

a general approach to analyzing epidemiologic data that contain misclassification errors misclassification is a common source of bias and reduced efficiency in the analysis of discrete data several methods have been proposed to adjust for misclassification using information on error rates i gathered by resampling the study population ii gathered by sampling a separate population or iii assumed a priori we present unified methods for incorporating these types of information into analyses based on log linear models and maximum likelihood estimation general variance expressions are developed examples from epidemiologic studies are used to demonstrate the proposed methodology

rapid calculation of shuffles of two words resume un mot c du monoide libre c d alphabet c est appele un melange de deux mots u et de c s il existe k 0 et des mots u1 uk 1 k de c tels que u u1 uk 1 k et c u1 1u2 2 uk k nous donnons ici un algorithme qui determine les melanges de deux mots sans omission ni repetition

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

binomial mixtures geometric estimation of the mixing distribution given a mixture of binomial distributions how do we estimate the unknown mixing distribution we build on earlier work of lindsay and further elucidate the geometry underlying this question exploring the approximating role played by cyclic polytopes convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given problems over the lack of identifiability of the mixing distribution in part disappear

estimation by data augmentation in regression models with continuous and discrete covariates measured with error estimation methods are considered for regression models which have both misclassified discrete covariates and continuous covariates measured with error adjusted parameter estimates are obtained using the method of data augmentation where the true values of the covariates measured with error are regarded as missing data validation data on the covariates are assumed to be available the distinction between internal and external validation data is emphasized and its effects on the analysis are examined the method is illustrated with simulated data 1997 by john wiley sons ltd

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

a bayesian semiparametric model for case control studies with errors in variables summary we develop a model and a numerical estimation scheme for a bayesian approach to inference in case control studies with errors in covariables the model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data the observed covariates and the proxy this nonparametric distribution defines the measurement error component of the model which relates the missing covariates x with a proxy w the oxymoron nonparametric bayes refers to a class of flexible mixture distributions for the likelihood of disease given covariates we choose a logistic regression model by using a parametric disease model and nonparametric exposure model we obtain robust interpretable results quantifying the effect of exposure

evolution of reaction diffusion patterns in infinite and bounded domains abstract we introduce a semi analytical method to study the evolution of spatial structures in reaction diffusion systems it consists in writing an integral equation for the relevant densities from the propagator of the linear part of the evolution operator in order to test the method we perform an exhaustive study of a one dimensional reaction diffusion model associated to an electrical device the ballast resistor we consider the evolution of step and bubble shaped initial density profiles in free space as well as in a semi infinite domain with dirichlet and neumann boundary conditions the piecewise linear form of the reaction term which preserves the basic ingredients of more complex nonlinear models makes it possible to obtain exact wave front solutions in free space and stationary solutions in the bounded domain short and long time behaviour can also be analytically studied whereas the evolution at intermediate times is analyzed by numerical techniques we paid particular attention to the features introduced in the evolution by boundary conditions

a bayesian approach to logistic regression models having measurement error following a mixture distribution to estimate the parameters in a logistic regression model when the predictors are subject to random or systematic measurement error we take a bayesian approach and average the true logistic probability over the conditional posterior distribution of the true value of the predictor given its observed value we allow this posterior distribution to consist of a mixture when the measurement error distribution changes form with observed exposure we apply the method to study the risk of alcohol consumption on breast cancer using the nurses health study data we estimate measurement error from a small subsample where we compare true with reported consumption some of the self reported non drinkers truly do not drink the resulting risk estimates differ sharply from those computed by standard logistic regression that ignores measurement error

algorithmic decomposition of shuffle on words we investigate shuffle decomposability into two words we give an algorithm which takes as input a dfa m under certain conditions and determines the unique candidate decomposition into words u and v such that l m uv if m is shuffle decomposable in time o u v even though this algorithm does not determine whether or not the dfa is shuffle decomposable the sublinear time complexity of only determining the two words under the assumption of decomposability is surprising given the complexity of shuffle and demonstrates an interesting property of the operation we also show that for given words u and v and a dfa m we can determine whether uv l m in polynomial time

shuffle factorization is unique we prove that given a finite set of words s there exists at most one normalized multiset p such that s is the shuffle of the words in p the multiset p is effectively computable

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

bayesian inference for the stereotype regression model application to a case control study of prostate cancer the stereotype regression model for categorical outcomes proposed by anderson j roy statist soc b 1984 46 1 30 is nested between the baseline category logits and adjacent category logits model with proportional odds structure the stereotype model is more parsimonious than the ordinary baseline category or multinomial logistic model due to a product representation of the log odds ratios in terms of a common parameter corresponding to each predictor and category specific scores the model could be used for both ordered and unordered outcomes for ordered outcomes the stereotype model allows more flexibility than the popular proportional odds model in capturing highly subjective ordinal scaling which does not result from categorization of a single latent variable but are inherently multi dimensional in nature as pointed out by greenland statist med 1994 13 1665 1677 an additional advantage of the stereotype model is that it provides unbiased and valid inference under outcome stratified sampling as in case control studies in addition for matched case control studies the stereotype model is amenable to classical conditional likelihood principle whereas there is no reduction due to sufficiency under the proportional odds model in spite of these attractive features the model has been applied less as there are issues with maximum likelihood estimation and likelihood based testing approaches due to non linearity and lack of identifiability of the parameters we present comprehensive bayesian inference and model comparison procedure for this class of models as an alternative to the classical frequentist approach we illustrate our methodology by analyzing data from the flint men s health study a case control study of prostate cancer in african american men aged 40 79 years we use clinical staging of prostate cancer in terms of tumors nodes and metastasis as the categorical response of interest

bayesian analysis of case control studies with categorical covariates in a case control study the appropriate likelihood is the retrospective likelihood i e the likelihood of exposure given disease for the classical frequentist analysis the prospective likelihood i e the likelihood of disease given exposure and the retrospective likelihood produce the same odds ratio estimators for exposure and so logistic regression may be used for both the bayesian analysis is not so simple but the bayesian framework for case control studies offers flexible possibilities for the hierarchical modelling that is needed in many contexts we review the bayesian approaches to the analysis of case control studies developed so far show how to extend these approaches to the situation of a study with any number of categorical or discretised continuous exposure variables and identifying suitable priors we then show how the resulting models may be fitted using markov chain monte carlo methods and provide an illustration based on genotype data

missing exposure data in stereotype regression model application to matched case control study with disease subclassification with advances in modern medicine and clinical diagnosis case control data with characterization of finer subtypes of cases are often available in matched case control studies missingness in exposure values often leads to deletion of entire stratum and thus entails a significant loss in information when subtypes of cases are treated as categorical outcomes the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category specific odds ratio parameters especially using the multinomial logit model the stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model the use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters we illustrate how to handle missing data in matched case control studies with finer disease subclassification within the cases under a stereotype regression model we present both monte carlo based full bayesian approach and expectation conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism we illustrate our methods by using data from an ongoing matched case control study of colorectal cancer simulation results are presented under various missing data mechanisms and departures from modeling assumptions

conditional independence models for epidemiological studies with covariate measurement error we construct a unifying representation of the structure of measurement error problems with particular reference to situations commonly encountered in epidemiological studies and outline how estimation of the parameters of interest can be carried out in a bayesian framework using gibbs sampling we show how this approach can be implemented for designs involving continuous measurement errors assessed through a validation substudy and discuss our results on simulated data

bayesian analysis of misclassified binary data from a matched case control study with a validation sub study bayesian methods are proposed for analysing matched case control studies in which a binary exposure variable is sometimes measured with error but whose correct values have been validated for a random sample of the matched case control sets three models are considered model 1 makes few assumptions other than randomness and independence between matched sets while models 2 and 3 are logistic models with model 3 making additional distributional assumptions about the variation between matched sets with models 1 and 2 the data are examined in two stages the first stage analyses data from the validation sample and is easy to perform the second stage analyses the main body of data and requires mcmc methods all relevant information is transferred between the stages by using the posterior distributions from the first stage as the prior distributions for the second stage with model 3 a hierarchical structure is used to model the relationship between the exposure probabilities of the matched sets which gives the potential to extract more information from the data all the methods that are proposed are generalized to studies in which there is more than one control for each case the bayesian methods and a maximum likelihood method are applied to a data set for which the exposure of every patient was measured using both an imperfect measure that is subject to misclassification and a much better measure whose classifications may be treated as correct to test methods the latter information was suppressed for all but a random sample of matched sets

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

wave block in excitable media due to regions of depressed excitability we study propagation failure using the one dimensional scalar bistable equation with a passive gap region by applying comparison principles for this type of equation the problem of finding conditions for block is reduced to finding conditions for the existence of steady state solutions we present a geometrical method that allows one to easily compute the critical gap length above which a steady state solution and thus block first occurs the method also helps to uncover the general bifurcation structure of the problem including the stability of the steady state solutions in obtaining these results we characterize the relationship between the properties of the system and propagation failure the method can easily be extended to other gap dynamics we use it to show that block associated with any local inhomogeneity must be associated with a limit point bifurcation

adjusting for errors in classification and measurement in the analysis of partly and purely categorical data abstract this article examines a method of adjusting subgroup means when there are errors both in the allocation of elements to the subgroups and in the measurement of the response the advantages with the method are that it is simple it is also applicable when there are many subgroups and it requires no distributional assumptions for the response variable the method is compared to the maximum likelihood method for a dichotomous response and an example from the swedish level of living survey is given

square free shuffles of words let u v denote the set of all shuffles of the words u and v it is shown that for each integer n 3 there exists a square free ternary word u of length n such that u u contains a square free word this property is then shown to also hold for infinite words i e there exists an infinite square free word u on three letters such that u can be shuffled with itself to produce an infinite square free word w u u

a likelihood approach to meta analysis with random effects in a meta analysis of a set of clinical trials a crucial but problematic component is providing an estimate and confidence interval for the overall treatment effect theta since in the presence of heterogeneity a fixed effect approach yields an artificially narrow confidence interval for theta the random effects method of dersimonian and laird which incorporates a moment estimator of the between trial components of variance sigma b2 has been advocated with the additional distributional assumptions of normality a confidence interval for theta may be obtained however this method does not provide a confidence interval for sigma b2 nor a confidence interval for theta which takes account of the fact that sigma b2 has to be estimated from the data we show how a likelihood based method can be used to overcome these problems and use profile likelihoods to construct likelihood based confidence intervals this approach yields an appropriately widened confidence interval compared with the standard random effects method examples of application to a published meta analysis and a multicentre clinical trial are discussed it is concluded that likelihood based methods are preferred to the standard method in undertaking random effects meta analysis when the value of sigma b2 has an important effect on the overall estimated treatment effect

front dynamics in heterogeneous diffusive media abstract we herein consider two component reaction diffusion systems with a specific bistable and odd symmetric nonlinearity which have the bifurcation structure of pitchfork type traveling front solutions with opposite velocities we introduce a spatial heterogeneity for example a heaviside like abrupt change at the origin in the space into diffusion coefficients numerically the responses of traveling fronts via the heterogeneity can be classified into four types of behavior depending on the strength of the heterogeneity which in the present paper is represented by the height of the jump passage stoppage and two types of reflection the goal of the present paper is to reduce the pde dynamics to finite dimensional ode systems on a center manifold and show the mathematical mechanism for producing the four types of response in the pde systems using finite dimensional ode systems the reduced ode systems include the terms referred to as heterogeneous perturbations originating from the interaction between traveling front solutions and the heterogeneity which is very important for determining the dynamics of the ode systems in the present paper we succeed in calculating these heterogeneous perturbations exactly and explicitly

wave blocking phenomena in bistable reaction diffusion systems the following bistable reaction variable diffusion systems including a parameter sigma is considered u 1 d x u x x frac 1 sigma f u v u 1 d x u x x sigma g u v traveling wave blocking problems are the motivation for studying the dependency of the heterogeneity of d x on the existence of stationary solutions which play the role of variers of traveling front or back waves

on the uniqueness of shuffle on words and finite languages we investigate a special variant of the shuffle decomposition problem for regular languages namely when the given regular language is the shuffle of finite languages the shuffle decomposition into finite languages is in general not unique that is there are l 1 l 2 l 3 l 4 with but l 1 l 2 l 3 l 4 however if all four languages are singletons with at least two combined letters it follows by a result of berstel and boasson j berstel l boasson shuffle factorization is unique theoretical computer science 273 2002 47 67 that the solution is unique that is l 1 l 2 l 3 l 4 we further show that if l 1 and l 2 are arbitrary finite sets and l 3 and l 4 are singletons with at least two letters in each the solution is unique therefore shuffle decomposition of words is unique not only over words but over arbitrary sets this is strong as we cannot let all four be arbitrary finite sets hopefully the obtained results will help to better understand the very nature of the shuffle operation

on the computational complexity of 2 interval pattern matching problems the focus of this paper is on the computational complexity of pattern matching problems over set of 2 intervals these problems occur in the context of molecular biology when a structured pattern i e a rna secondary structure given in the form of a 2 interval pattern has to be found in a sequence database we show that finding a 2 interval pattern in a set of 2 intervals is a np complete problem even if no 2 interval of the pattern precedes the other but can be solved in polynomial time for several interesting special cases in particular it is shown that the pseudo knot free rna secondary structure case is polynomial time solvable in our 2 interval formalism also we investigate the computational complexity of finding the longest 2 interval pattern in a set of 2 intervals and prove several np completeness results as well as polynomial time solvable special cases

likelihood calculations for matched case control studies and survival studies with tied death times summary a recursion is presented which permits rapid computation of a conditional likelihood function which arises in matched case control studies and survival studies with tied death times an example with seven parameters and ten large strata the largest of which contains 29 cases and 52 controls illustrates the feasibility of the conditional maximum likelihood solution these methods may be specialized to permit rapid calculation of the conditional maximum likelihood estimate of the common odds ratio for several 2 x 2 tables

variance estimation for epidemiologic effect estimates under misclassification this paper presents basic methods for construction of variance estimators for epidemiologic effect estimates when adjusting for misclassification methods are described for differential and non differential misclassification and for external and internal estimates of classification rates the methods take account of sampling variability in both the observed data and the estimated classification rates the methods are illustrated in a case control analysis of the association of antibiotic use during pregnancy with sudden infant death syndrome

on recognising words that are squares for the shuffle product abstract the shuffle of two words u and v of a is the language u v consisting of all words u 1 v 1 u 2 v 2 u k v k where k 0 and the u i and v i are words of a such that u u 1 u 2 u k and v v 1 v 2 v k in other words u v is the finite set of all words obtainable from merging the words u and v from left to right but choosing the next symbol arbitrarily from u or v a word u a is a square for the shuffle product if it is the shuffle of two identical words i e u v v for some v a whereas it can be decided in polynomial time whether or not u v 1 v 2 for given words u v 1 and v 2 j c spehner 1986 19 we show in this paper that it is np complete to determine whether or not a word u is a square for the shuffle product the novelty in our approach lies in representing words as linear graphs in which deciding whether or not a given word is a square for the shuffle product reduces to computing some inclusion free perfect matching finally we prove that it is np complete to determine whether or not an input word is in the shuffle of a word with its reverse

bayesian analysis of errors in variables regression models summary use of errors in variables models is appropriate in many practical experimental problems however inference based on such models is by no means straightforward in previous analyses simplifying assumptions have been made in order to ease this intractability but assumptions of this nature are unfortunate and restrictive in this paper we analyse errors in variables models in full generality under a bayesian formulation in order to compute the necessary posterior distributions we utilize various computational techniques two specific non linear errors in variables regression examples are considered the first is a re analysed berkson type model and the second is a classical errors in variables model our analyses are compared and contrasted with those presented elsewhere in the literature

equivalence between conditional and mixture approaches to the rasch model and matched case control studies with applications analyses of data using rasch models including the special case of matched case control studies are common applications of conditional likelihood in which the usual inferential procedures are applied only after conditioning on an approximately ancillary statistic another common approach to the analysis of rasch models is to integrate the nuisance parameters over a mixing distribution using the marginal likelihood obtained as the basis for inference we show that the full conditional likelihood can always be obtained exactly via the marginal approach given a particular choice of mixing distribution and derive necessary and sufficient conditions for the two approaches to agree previous work has shown that with sufficient flexibility in the mixing distribution the maxima of the marginal and conditional likelihoods will be equivalent under concordance criteria our argument requires no such criteria and for any dataset guarantees the equivalence of the whole of the two likelihoods not just their maxi

directly modelling matched case control data matching in case control studies is a situation in which one wishes to make inferences about a parameter of interest in the presence of nuisance parameters the usual approach is to apply a conditional likelihood a bivariate latent class log linear model for binomial responses is shown to yield a standard likelihood identical to the usual conditional one this extension of the rasch model for binary responses gives consistent estimates and a suitable likelihood function for cases matched with any fixed number of controls

generalized residuals for general models for contingency tables with application to item response theory generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error they have typically been applied to log linear models and to latent class models a general approach to generalized residuals is developed for a very general class of models for contingency tables to illustrate their use generalized residuals are applied to models based on item response theory irt models such models are commonly applied to analysis of standardized achievement or aptitude tests to obtain a realistic perspective on application of generalized residuals actual testing data are employed

on correcting for misclassification in twin studies and other matched pair studies in twin studies and other matched pair studies of the effect of a k level risk factor on disease risk one must estimate the proportion of pairs in each of k2 possible pair categories of which k k 1 categories represent discordant pairs in particular for a binary factor one must estimate proportions within two discordant pair categories and the variances of functions of these estimates this paper shows how to do so when misclassification is present and stable estimates of the classification rates are available unlike methods that estimate only the discordance ratio one can use the methods presented here to improve estimates of epidemiologic effects

global bifurcation phenomena of traveling wave solutions for some bistable reaction diffusion systems on considere le systeme bistable e u t e 2 u xx f u v v t v xx g u v ou e est petit on etudie les solutions onde de propagation qui tendent vers deux etats stables quand x

a simple bayesian analysis of misclassified binary data with a validation substudy summary a two stage bayesian method is presented for analyzing case control studies in which a binary variable is sometimes measured with error but the correct values of the variable are known for a random subset of the study group the first stage of the method is analytically tractable and mcmc methods are used for the second stage the posterior distribution from the first stage becomes the prior distribution for the second stage thus transferring all relevant information between the stages the method makes few distributional assumptions and requires no asymptotic approximations it is computationally fast and can be run using standard software it is applied to two data sets that have been analyzed by other methods and results are compared

nerve impulse propagation in a branching nerve system a simple model abstract local spatial changes of nerve axon geometry such as diameter increase and branching may cause that action potential waves approaching a region of geometric change fail to propagate beyond it in this paper this effect will be examined for a special kind of nonuniformity within the framework of a simple model an initial value problem for a single nonlinear diffusion equation on an unbounded domain

some comments on misspecification of priors in bayesian modelling of measurement error problems in this paper we discuss some aspects of misspecification of prior distributions in the context of bayesian modelling of measurement error problems a bayesian approach to the treatment of common measurement error situations encountered in epidemiology has been recently proposed its implementation involves first the structural specification through conditional independence relationships of three submodels a measurement model an exposure model and a disease model and secondly the choice of functional forms for the distributions involved in the submodels we present some results indicating how the estimation of the regression parameters of interest which is carried out using gibbs sampling can be influenced by a misspecification of the parametric shape of the prior distribution of exposure 1997 by john wiley sons ltd

effects of exposure misclassification on regression analyses of epidemiologic follow up study data in epidemiologic studies subjects are often misclassified as to their level of exposure ignoring this misclassification error in the analysis introduces bias in the estimates of certain parameters and invalidates many hypothesis tests for situations in which there is misclassification of exposure in a follow up study with categorical data we have developed a model that permits consideration of any number of exposure categories and any number of multiple category covariates when used with logistic and poisson regression procedures this model helps assess the potential for bias when misclassification is ignored when reliable ancillary information is available the model can be used to correct for misclassification bias in the estimates produced by these regression procedures

on the complexity and decidability of some problems involving shuffle abstract the complexity and decidability of various decision problems involving the shuffle operation denoted by are studied the following three problems are all shown to be np complete given a nondeterministic finite automaton nfa m and two words u and v is l m u v is u v l m and is l m u v it is also shown that there is a polynomial time algorithm to determine for nfa s m 1 m 2 and a deterministic pushdown automaton m 3 whether l m 1 l m 2 l m 3 the same is true when m 1 m 2 m 3 are one way nondeterministic l reversal bounded k counter machines with m 3 being deterministic other decidability and complexity results are presented for testing whether given languages l 1 l 2 and r from various languages families satisfy l 1 l 2 r and r l 1 l 2 several closure results on shuffle are also shown

computational tools for exact conditional logistic regression logistic regression analyses are often challenged by the inability of unconditional likelihood based approximations to yield consistent valid estimates and p values for model parameters this can be due to sparseness or separability in the data conditional logistic regression though useful in such situations can also be computationally unfeasible when the sample size or number of explanatory covariates is large we review recent developments that allow efficient approximate conditional inference including monte carlo sampling and saddlepoint approximations we demonstrate through real examples that these methods enable the analysis of significantly larger and more complex data sets we find in this investigation that for these moderately large data sets monte carlo seems a better alternative as it provides unbiased estimates of the exact results and can be executed in less cpu time than can the single saddlepoint approximation moreover the double saddlepoint approximation while computationally the easiest to obtain offers little practical advantage it produces unreliable results and cannot be computed when a maximum likelihood solution does not exist

the utility of mixed form likelihoods summary we highlight a feature of likelihood based methods that provides flexibility in model formulation and inference in particular overall likelihoods that consist of likelihood contributions with different forms are considered the particular forms may be predetermined by design criteria or may be selected based on features of the data inferences based on such mixed form likelihoods are valid provided standard regularity conditions hold and the parameters of interest have the same interpretation in the various forms the advantages of constructing overall likelihoods in this way are illustrated by applications involving the analysis of 2 2 k tables and left censored water quality data

models of unidirectional propagation in heterogeneous excitable media two differential equation models of excitable media threshold and recovery kinetics with solutions that exhibit unidirectional propagation are presented it is shown that unidirectional propagation in heterogeneous excitable media with non oscillatory kinetics can be initiated from homogeneous initial data simulations on a reaction diffusion model with fitzhugh nagumo kinetics and spatially heterogeneous parameters yields a rotating wave on a one dimensional circular spatial domain an ordinary differential equation model with four semi coupled excitable cells and heterogeneous parameters is analyzed to determine a critical parameter region over which unidirectional propagation may occur

recognizing binary shuffle squares is np hard abstract a shuffle of two words is formed by interleaving the characters into a new word keeping the characters of each word in order a word is a shuffle square if it is a shuffle of two identical words deciding whether a word is a shuffle square has been proved to be np complete independently by buss and soltys 5 and rizzi and vialette 20 the former proving the result for alphabets as small as 9 letters we prove in this paper that deciding whether a binary word is a shuffle square is np complete

consistent estimation in the rasch model based on nonparametric margins consider the class of two parameter marginal logistic rasch models for a test ofm true false items where the latent ability is assumed to be bounded using results of karlin and studen we show that this class of nonparametric marginal logistic nml models is equivalent to the class of marginal logistic models where the latent ability assumes at most m 2 2 values this equivalence has two implications first estimation for the nml model is accomplished by estimating the parameters of a discrete marginal logistic model second consistency for the maximum likelihood estimates of the nml model can be shown whenm is odd using the results of kiefer and wolfowitz an example is presented which demonstrates the estimation strategy and contrasts the nml model with a normal marginal logistic model