on the use of concordant pairs in matched case control studies a new estimator of the common odds ratio in one to one matched case control studies is proposed the connection between this estimator and the james stein estimating procedure is highlighted through the argument of estimating functions comparisons are made between this estimator the conditional maximum likelihood estimator and the estimator ignoring the matching in terms of finite sample bias mean squared error coverage probability and length of confidence interval in many situations the new estimator is found to be more efficient than the conditional maximum likelihood estimator without being as biased as the estimator that ignores matching the extension to multiple risk factors is also outlined

on essential components of the solution set of generalized games in this paper we prove that for any generalized game there exists at least one essential connected component of the set of it s equilibrium points

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

the stability of the set of kkm points abstract let m be the collection of all kkm mappings g and denote by f g the set of all kkm points of g in this paper we prove that there exists a dense residual subset q of m such that for each g q g is stable and there exists at least one essential component of f g for each g m

a logistic bivariate normal model for overdispersed two state markov processes we describe a logistic bivariate normal mixture model for a two state markov chain in which each individual makes transitions between states according to a subject specific transition probability matrix the use of the bivariate normal mixing distribution facilitates inferences regarding the correlation of the random effects and hence provides insight as to the nature of the subject to subject variability in the transition probabilities tests regarding the correlation can be based on likelihood ratio score or wald statistics estimates of the transition intensities of a latent continuous time conditionally markov process may also be computed we illustrate this methodology by application to a parasitic infection field study and contrast our findings with those previously published on this data set

euclidean path integral formalism in deformed space with minimum measurable length we study time evolution at the quantum level by developing the euclidean path integral approach for the general case where there exists a minimum measurable length we derive an expression for the momentum space propagator which turns out to be consistent with recently developed canonical transformation we also construct the propagator for maximal localization which corresponds to the amplitude that a state which is maximally localized at location propagates to a state which is maximally localized at location in a given time our expression for the momentum space propagator and the propagator for maximal localization is valid for any form of time independent hamiltonian the nonrelativistic free particle particle in a linear potential and the harmonic oscillator are discussed as examples

reducing mean squared error in the analysis of pair matched case control studies the standard estimator of the common odds ratio for pair matched case control studies the stratified estimate is consistent but it ignores all information from the concordant pairs at the other extreme the pooled estimator is more efficient as it uses all the data but is not consistent in order to trade between bias and precision liang and zeger 1988 biometrics 44 1145 1156 proposed an estimator that is a compromise between the stratified and pooled estimates in the current paper the possibility of optimizing the trade off is explored specifically the family of weighted averages of the stratified and pooled estimates is considered and the weight that minimizes an asymptotic approximation of mean squared error is derived in practice the optimal weight must be estimated from the data so that the estimator is only approximately optimal small sample properties are evaluated via simulations

a hausdorff metric inequality with applications to the existence of essential components abstract this paper gives a lemma about a hausdorff metric inequality between two nonempty compact subsets in metric spaces as applications some existence theorems for essential components of solutions for some nonlinear problems such as kkm points solutions in ky fan s lemma as well as nash equilibrium points are deduced

on testing departure from the binomial and multinomial assumptions this paper is concerned with testing the multinomial binomial assumption against the dirichlet multinomial beta binomial alternatives in particular we discuss the distribution of the asymptotic likelihood ratio lr test and obtain the c alpha goodness of fit test statistic the inadequacy of the regular chi square approximation to the lr test is supported by some monte carlo experiments the c alpha test is recommended based on empirical significance level and power and also computational simplicity two examples are given

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

generalized score test of homogeneity for mixed effects models many important problems in psychology and biomedical studies require testing for overdispersion correlation and heterogeneity in mixed effects and latent variable models and score tests are particularly useful for this purpose but the existing testing procedures depend on restrictive assumptions in this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero under some mild conditions not only do we derive asymptotic distributions of the test statistics but also propose a resampling procedure for approximating their asymptotic distributions conditional on the observed data to overcome the technical challenge we establish an invariance principle for random quadratic forms indexed by a parameter a simulation study is conducted to investigate the empirical performance of the test statistics a real data set is analyzed to illustrate the application of our theoretical results

tests of homogeneity for the relative risk in multiply matched case control studies summary we examine several tests of homogeneity of the odds ratio in the analysis of 2 x 2 tables arising from epidemiologic 1 r matched case control studies the t4 and t5 statistics proposed by liang and self 1985 biometrika 72 353 358 are unable to detect obvious inhomogeneity in two numerical examples and in simulation studies the null hypothesis is rejected by the chi square statistic of ejigou and mchugh 1984 bioinetrika 71 408 411 and by a new proposed method whose significance level must be simulated

a statistical distribution with an unbounded hazard function and its application to a theory from demography we introduce a statistical distribution with hazard function mu t proportional to psi t beta 1 for 0 less than or equal to t less than psi and shape parameter beta satisfying 0 less than beta less than 1 this hazard function is suggested by a theory of aging in demography we discuss properties of this distribution and maximum likelihood estimates of its parameters mixture distributions are considered to account for pooling across dissimilar populations this model is compared with the gompertz and generalized pareto distributions and used to estimate a finite limit on human lifespan based on the survival of a group of female centenarians

stability of solutions for ky fan s section theorem with some applications abstract in this paper we prove that most of problems in ky fan s section theorem in the sense of baire category are essential and that for any problem in ky fan s section theorem there exists at least one essential component of its solution set as applications we deduce both the existence of essential components of the set of ky fan s points based on ky fan s minimax inequality theorem and the existence of essential components of the set of nash equilibrium points for general n person non cooperative games with non concave payoffs

simex variance component tests in generalized linear mixed measurement error models in the analysis of clustered data with covariates measured with error a problem of common interest is to test for correlation within clusters and heterogeneity across clusters we examined this problem in the framework of generalized linear mixed measurement error models we propose using the simex method to construct a score test for the null hypothesis that all variance components are zero a key feature of this simex score test is that no assumptions need to be made regarding the distributions of the random eects and the unobserved covariates we illustrate this test by analyzing framingham heart disease data and evaluate its performance by simulation we also propose individual simex score tests for testing the variance components separately both tests can be easily implemented using existing statistical software

a locally most powerful test for homogeneity with many strata summary a locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting the test is based on the difference between the square of the score and the observed information about the nuisance parameters all evaluated at the null hypothesis several examples including constant normal mean with possibly different variances and matched case control studies are presented in detail the relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated two data sets on matched case control studies are used for illustration

conditional score functions some optimality results summary the conditional score function has previously been shown to generate the optimal estimating equation for a parameter of interest when the conditioning statistic is complete and sufficient for the nuisance parameters godambe 1976 the present paper generalizes these results to partial likelihood factorizations and then examines the nature of the problem when the appropriate conditioning statistics depend on the parameter of interest in this case globally optimal estimating functions are impossible a weaker criterion of optimal weighting leads to a class of estimated conditional score functions which satisfy an information equality the purpose of this paper is to develop and justify an approach based on conditional likelihood to estimation in the presence of nuisance parameters the arguments focus on the case when there is a complete and sufficient statistic s 0 for the nuisance parameters when the parameter of interest 0 is fixed an extended notion of completeness will be presented in the context of partial likelihoods the problem takes on two separate natures depending on whether the statistic s 0 truly depends on 0 or not if s s 0 is free of 0 then the conditional likelihood of the data given s has been shown to generate optimal inferential procedures giving a best estimating equation godambe 1976 and a best asymptotically normal estimator in a mixture setting lindsay 1980 if s 0 depends on 0 then it will be shown that the best estimating equation also a conditional likelihood score will generally be only locally optimal leaving no single best strategy consideration of an optimal weighting strategy yields estimators which have second order properties similar to the conditional likelihoods of the first type

generalized score test of homogeneity based on correlated random effects models summary we present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing in these models each subject has a particular random effect but the random effects between subjects are correlated we derive the general form of the score statistic for testing that the random effects have a variance equal to 0 we apply this result to both parametric and semiparametric models in both cases we show that under certain conditions the score statistic has an asymptotic normal distribution we consider several applications of this theory including overdispersion heterogeneity between groups spatial correlations and genetic linkage

test of homogeneity of binary data with explanatory variables summary apparent heterogeneity of the risk of a disease in different groups may be explained by subjectspecific risk factors unequally distributed in these groups we propose a score test of homogeneity that allows adjustment for known risk factors of the disease the test is based oni a random effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method the score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3 318 subjects scattered in 75 parishes it is shown that an apparent heterogeneity disappears when taking into account subject specific risk factors this test may also be useful for studying familial aggregation of a disease testing homogeneity of the distribution of binary traits in different groups has long been recognized as an important problem particularly in conventional genetics smith 1951 and in genetic epidemiology where it may be used to investigate the familial aggregation of a disease the presence of familial aggregation suggests a genetic determinant testing homogeneity of geographical units is also of interest the presence of heterogeneity suggests the presence of an unmeasured environmental factor another application occurs if the possible correlation of the data is treated as a nuisance it is useful to test whether the groups are homogeneous before performing ordinary regression models liang 1987 chi squared tests are used for testing homogeneity when the number of groups is small however the chi squared test is not applicable when the sizes of the groups are not large haldane 1940 and when the number of groups is large in such cases random effect models are preferred the probability of disease within a group have a common distribution thus the null hypothesis is specified by a null variance of the random effect and alternative hypotheses are specified by a unique parameter the variance of the random effect whatever the number of groups see potthoff and whittinghill 1966 wisniewsky 1968 and tarone 1979 in epidemiologic studies however we often need to test for homogeneity while adjusting for other risk factors of the disease indeed risk factors if differently distributed in the different groups may play the role of confounding factors relative to the group effect it is of paramount importance in genetic studies to investigate whether an apparent familial aggregation may be explained by nongenetic factors such as educational level or nutritional habits which may also segregate in families similarly geographical clusters may be explained by nonenvironmental factors unequally distributed in the geographical units based on a random effect logistic regression model we derive a score test of homogeneity that allows adjustment on explanatory variables the score statistic is the same as that proposed by hamerle 1990 in the context of repeated measurements but the variance proposed in the present paper is different simulations show that it leads to a more powerful test we use this test to investigate the possible geographical heterogeneity of cognitive impairment as measured by the mini mental state score in 3 318 subjects scattered in 75 parishes in southwestern france

score tests for zero covariances in recursive linear models for grouped or censored data abstract the score test statistic for testing whether an error covariance is zero is derived for a normal linear recursive model for fully observed censored or grouped data the test which is obtained by regarding non zero error covariances as arising from correlated random parameter variation is shown to be closely related to the information matrix test it turns out that the statistic which is asymptotically n 0 1 under the null examines the sample covariance of appropriately defined residuals

path integral and noncommutative poisson brackets we find that in presence of noncommutative poisson brackets the relation between lagrangian and hamiltonian is modified we discuss this property by using the path integral formalism for non relativistic systems we apply this procedure to the harmonic oscillator with a minimal length

unified approach to existence and stability of essential components abstract we give a unified approach to essential components for some nonlinear problems such as fixed points ky fan s points and nash equilibrium points etc

testing goodness of fit in regression a general approach for specified alternatives when fitting generalized linear models or the cox proportional hazards model it is important to have tools to test for lack of fit because lack of fit comes in all shapes and sizes distinguishing among different types of lack of fit is of practical importance we argue that an adequate diagnosis of lack of fit requires a specified alternative model such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis we know the direction of the departure from the model the goodness of fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases connections with penalized likelihood and random effects are discussed and the application of the proposed approach is illustrated with medical examples tailored functions for goodness of fit testing have been implemented in the r package globaltest copyright 2012 john wiley sons ltd

group testing regression models with fixed and random effects group testing where subjects are tested in pools rather than individually has a long history of successful application in infectious disease screening in this article we develop group testing regression models to include covariate effects that are best regarded as random we present approaches to fit mixed effects models using maximum likelihood investigate likelihood ratio and score tests for variance components and evaluate small sample performance using simulation we illustrate our methods using chlamydia and gonorrhea data collected by the state of nebraska as part of the infertility prevention project

score test for familial aggregation in probands studies application to alzheimer s disease when studying familial aggregation of a disease the following two stage design is often used first select index subjects cases and controls then record data on their relatives the likelihood corresponding to this design is derived and a score test of homogeneity is proposed for testing the hypothesis of no aggregation this test takes into account the selection procedure and allows adjustment to be made for explanatory variables it appears as the sum of three terms a pure test of homogeneity a test of comparison of observed minus expected cases in the two groups and a term which adjusts for the possible unequal probabilities of disease of the index subjects asymptotic efficiency and a simulation study show that the proposed test is superior to either the pure homogeneity test or tests based on the comparison of numbers of affected in the two groups the test statistic which has an asymptotically standard normal distribution is applied to a study of familial aggregation of early onset alzheimer s disease for which a highly significant value 9 46 is obtained this is the highest value among the three tests compared in agreement with the simulation study a logistic normal model is fitted to the data taking account of the selection procedure it allows to estimate the regression parameters and the variance of the random effect the likelihood ratio test for familial aggregation seems less powerful than the score test

tests for variation over groups in survival data abstract when survival data can be divided into natural groups such as in a clinical trial with patients from a number of different institutions the question arises whether effects are different for the different groups for situations where one is concerned with a random pattern of variation over groups this article proposes testing the null hypothesis of no variation using statistics based on the sums of martingale residuals over subjects within groups these tests are closely related to the locally most powerful tests of liang for testing for variation across a large number of strata the tests are applied to data from a lung cancer trial conducted by the eastern cooperative oncology group

the intraclass correlation coefficient distribution free definition and test a definition of the intraclass correlation coefficient is given on the basis of a general class of random effect model the conventional intraclass correlation coefficient and the intracluster correlation coefficient for binary data are both particular cases of the generalized coefficient we derive the score test for the hypothesis of null intraclass correlation in the exponential family the statistic does not depend on the particular distribution in this family and is related to the pairwise correlation coefficient the test can be adjusted for explanatory variables