regression models for longitudinal binary responses with informative drop outs this paper reviews both likelihood based and non likelihood generalized estimating equations regression models for longitudinal binary responses when there are drop outs throughout it is assumed that the regression parameters for the marginal expectations of the binary responses are of primary scientific interest the association or time dependence between the responses is largely regarded as a nuisance characteristic of the data the performance of the methods is compared in terms of asymptotic bias under mis specification of the association between the responses and the missing data mechanism or drop out process

the karamata integration theorem on time scales and its applications in dynamic and difference equations abstract we derive a time scale version of the well known result from the theory of regular variation namely the karamata integration theorem we show an application of this theorem in asymptotic analysis of linear second order dynamic equations we obtain a classification and asymptotic formulae for all positive solutions which unify extend and improve the existing results in addition we utilize these results in combination with a transformation between equations on different time scales to study the critical double root case in linear difference equations this leads to solving open problems posed in the literature

doubly robust estimates for binary longitudinal data analysis with missing response and missing covariates longitudinal studies often feature incomplete response and covariate data likelihood based methods such as the expectation maximization algorithm give consistent estimators for model parameters when data are missing at random mar provided that the response model and the missing covariate model are correctly specified however we do not need to specify the missing data mechanism an alternative method is the weighted estimating equation which gives consistent estimators if the missing data and response models are correctly specified however we do not need to specify the distribution of the covariates that have missing values in this article we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are mar this method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified simulation studies demonstrate that this method performs well in a variety of situations

sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures robins introduced marginal structural models msms and inverse probability of treatment weighted iptw estimators for the causal effect of a time varying treatment on the mean of repeated measures we investigate the sensitivity of iptw estimators to unmeasured confounding we examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user specified function we present augmented iptw estimators of msm parameters and prove their consistency for the causal effect of an msm assuming a correct confounding bias function for unmeasured confounding we apply the methods to assess sensitivity of the analysis of hernan et al who used an msm to estimate the causal effect of zidovudine therapy on repeated cd4 counts among hiv infected men in the multicenter aids cohort study under the assumption of no unmeasured confounders a 95 per cent confidence interval for the treatment effect includes zero we show that under the assumption of a moderate amount of unmeasured confounding a 95 per cent confidence interval for the treatment effect no longer includes zero thus the analysis of hernan et al is somewhat sensitive to unmeasured confounding we hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications

model checking techniques based on cumulative residuals depuis longtemps on utilise les residus pour apprecier graphiquement et muneriquement l adequation de modeles de regression l analyse conventionnelle des residus fondee sur les graphes des residus bruts ou des courbes lissees est eminemment subjective tandis que la plupart des tests numeriques d ajustement informent peu sur la nature de l inadequation nous developpons des techniques d examen d un modele objectives et informatives qui reposent soit sur les sommes des residus cumulees selon certaines coordonnees comme une covariable on le predicteur lineaire soit sur des regroupements partiels sommes ou moyennes mobiles selon ces coordonnees pour une grande variete de modeles statistiques et de structures des observations dont les modeles lineaires generalises sur observations independantes ou correlees les distributions de ces processus stochastiques sous le modele postule peuvent etre approchees par des processus gaussiens centres faciles a simuler on pent done comparer graphiquement et numeriquement chaque processus observe a une serie de realisations du ment chaque processus observe a une serie de realisations du processus gaussien ces comparaisons permettent d evaluer objectivement dans quelle mesure une tendance observee sur un graphique serait attribuable a une mauvaise specification du modele plutot qu aux fluctuations d echantillonnage ces techniques sont particulierement utiles pour l examen de la fonction de lien ou de la forme fonctionnelle d une covariable plusieurs exemples medicaux illustrent cette approche

a note about models for selectivity bias on decrit une representation tabulaire simplifiee qui fait ressortir une hypothese structurale implicite importante dans des modeles de selection bases sur la censure

brill noether theory of curves on enriques surfaces i the positive cone and gonality we study the existence of linear series on curves lying on an enriques surface and general in their complete linear system using a method that works also below the bogomolov reider range we compute in all cases the gonality of such curves we also give a new result about the positive cone of line bundles on an enriques surface and we show how this relates to the gonality

akaike s information criterion in generalized estimating equations correlated response data are common in biomedical studies regression analysis based on the generalized estimating equations gee is an increasingly important method for such data however there seem to be few model selection criteria available in gee the well known akaike information criterion aic cannot be directly applied since aic is based on maximum likelihood estimation while gee is nonlikelihood based we propose a modification to aic where the likelihood is replaced by the quasi likelihood and a proper adjustment is made for the penalty term its performance is investigated through simulation studies for illustration the method is applied to a real data set

modelling progression of cd4 lymphocyte count and its relationship to survival time the purpose of this article is to model the progression of cd4 lymphocyte count and the relationship between different features of this progression and survival time the complicating factors in this analysis are that the cd4 lymphocyte count is observed only at certain fixed times and with a high degree of measurement error and that the length of the vector of observations is determined in part by the length of survival if probability of death depends on the true unobserved cd4 lymphocyte count then the survival process must be modelled wu and carroll 1988 biometrics 44 175 188 proposed a random effects model for two sample longitudinal data in the presence of informative censoring in which the individual effects included only slopes and intercepts we propose methods for fitting a broad class of models of this type in which both the repeated cd4 lymphocyte counts and the survival time are modelled using random effects these methods permit us to estimate parameters describing the progression of cd4 lymphocyte count as well as the effect of differences in the cd4 trajectory on survival we apply these methods to results of aids clinical trials

a note on nikulin surfaces and their moduli spaces we study a number of natural linear systems carried by any polarized nikulin surface of genus g determine their positivity and establish their brill noether theory as an application we compute the classes of some natural effective divisors on the moduli space of nikulin surfaces relying upon recent work of farkas and rimanyi

dependent competing risks and summary survival curves summary in many contexts where there is interest in inferring the marginal distribution of a survival time t subject to censoring embodied in a latent waiting time c the times t and c may not be independent this paper presents a new class of nonparametric assumptions on the conditional distribution of t given c and shows how they lead to consistent generalizations of the kaplan meier 1958 survival curve estimator the new survival curve estimators are used under weak assumptions to construct bounds on the marginal survival which can be much narrower than those of peterson 1976 in stratified populations where t and c are independent only within strata examples indicate that the kaplan meier estimator is often approximately consistent

the generic green lazarsfeld secant conjecture using lattice theory on special k3 surfaces calculations on moduli stacks of pointed curves and voisin s proof of green s conjecture on syzygies of canonical curves we prove the prym green conjecture on the naturality of the resolution of a general prym canonical curve of odd genus as well as many cases of the green lazarsfeld secant conjecture on syzygies of non special line bundles on general curves

adjusting for nonignorable drop out using semiparametric nonresponse models abstract consider a study whose design calls for the study subjects to be followed from enrollment time t 0 to time t t at which point a primary endpoint of interest y is to be measured the design of the study also calls for measurements on a vector v t of covariates to be made at one or more times t during the interval 0 t we are interested in making inferences about the marginal mean 0 of y when some subjects drop out of the study at random times q prior to the common fixed end of follow up time t the purpose of this article is to show how to make inferences about 0 when the continuous drop out time q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables in particular we consider two models for the conditional hazard of drop out given v t y where v t denotes the history of the process v t through time t t 0 t in the first model we assume that q t v t y exp 0 y where 0 is a scalar paramet

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

multivariate logistic models for incomplete binary responses abstract in this article we describe a likelihood based regression model appropriate for analyzing incomplete multivariate binary responses we focus on marginal models that is models where the marginal mean or expectation of the binary response is related to a set of covariates the association between the binary responses is modeled in terms of conditional log odds ratios when the nonresponse mechanism is ignorable it is not necessary to specify a nonresponse model and valid inferences can be obtained provided that the likelihood for the responses has been correctly specified but when the nonresponse mechanism is nonignorable valid inferences can only be obtained by incorporating a model for nonresponse an unresolved issue with nonignorable models concerns the identifiability of the parameters so far no general and practically useful necessary and sufficient conditions for identifiability are available here we suggest some simple procedures for examining the identifiability status of nonign

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

normal generation and clifford index on algebraic curves for a smooth curve c it is known that a very ample line bundle mathcal l on c is normally generated if cliff mathcal l cliff c and there exist extremal line bundles mathcal l non normally generated very ample line bundle with cliff mathcal l cliff c with h 1 mathcal l le 1 however it has been unknown whether there exists an extremal line bundle mathcal l with h 1 mathcal l ge 2 in this paper we prove that for any positive integers g c with g 2c 5 and c equiv 0 mod 2 there exists a smooth curve of genus g and clifford index c carrying an extremal line bundle mathcal l with h 1 mathcal l 2 in fact a smooth quadric hypersurface section c of a general projective k3 surface always has an extremal line bundle mathcal l with h 1 mathcal l 2 more generally if c has a line bundle mathcal m computing the clifford index c of c with 3c 2 3 deg mathcal m leq g 1 then c has such an extremal line bundle mathcal l

a hyper kahler compactification of the intermediate jacobian fibration associated with a cubic 4 fold let x be a general cubic fourfold it was observed by donagi and markman that the relative intermediate jacobian fibration j u with u p5 x associated to the smooth hyperplane sections of x carries a natural holomorphic symplectic form making the fibration lagrangian in this paper we obtain a smooth projective compactification j of j with the property that the holomorphic symplectic form on j extends to a holomorphic symplectic form on j in particular j is a 10 dimensional compact hyper kahler manifold which we show to be deformation equivalent to the exceptional example of o grady this proves a conjecture by markushevich

the role of the propensity score in estimating dose response functions summary estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large standard covariance adjustment methods are often inadequate rosenbaum rubin 1983 propose an alternative method for adjusting for pre treatment variables for the binary treatment case based on the so called propensity score here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi valued treatments estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large and their distribution varies substantially with treatment status standard adjustment methods such as covari ance adjustment are often inadequate rosenbaum rubin 1983 1984 propose an alternative method for adjusting for pre treatment variables based on the propensity score the conditional probability of receiving the treatment given pre treatment variables they demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre treatment variables the rosenbaum rubin proposals deal exclusively with binary valued treat ments in many cases of interest however treatments take on more than two values here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi valued treatments the key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid as the propensity score does it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated

linear systems on k3 sections on etudie la presence d un g d r special sur une section d hyperplan donnee c d une surface k 3 et les consequences sur l existence d un tel g d r sur toute courbe non singuliere c e c

goodness of fit processes for logistic regression simulation results in this paper we use simulations to compare the performance of new goodness of fit tests based on weighted statistical processes to three currently available tests the hosmer lemeshow decile of risk test the pearson chi square and the unweighted sum of squares tests the simulations demonstrate that all tests have the correct size the power for all tests to detect lack of fit due to an omitted quadratic term with a sample of size 100 is close to or exceeds 50 per cent to detect moderate departures from linearity and is over 90 per cent for these same alternatives for sample size 500 all tests have low power with sample size 100 to detect lack of fit due to an omitted interaction between a dichotomous and continuous covariate while the power exceeds 80 per cent to detect extreme interaction with a sample size of 500 the power is low to detect any alternative link function with sample size 100 and for most alternative links for sample size 500 only in the case of sample size 500 and an extremely asymmetric link function is the power over 80 per cent the results from these simulations show that no single test new or current performs best in detecting lack of fit due to an omitted covariate or incorrect link function however one of the new weighted tests has power comparable to other tests in all settings simulated and had the highest power in the difficult case of an omitted interaction term we illustrate the tests within the context of a model for factors associated with abstinence from drug use in a randomized trial of residential treatment programmes we conclude the paper with a summary and specific recommendations for practice

estimates of marginal survival for dependent competing risks based on an assumed copula summary when time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product limit estimators which assume independent censoring if no assumption about the relationship between the two times is made the marginal survival functions are not identifiable a natural function that defines the association between the two random variables is the copula we show that if this function is known then the competing risks data are sufficient to identify the marginal survival functions and construct a suitable estimator this estimator is consistent and reduces to the kaplan meier estimator when death and censoring times are independent this statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks

improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data considerable recent interest has focused on doubly robust estimators for a population mean response in the presence of incomplete data which involve models for both the propensity score and the regression of outcome on covariates the usual doubly robust estimator may yield severely biased inferences if neither of these models is correctly specified and can exhibit nonnegligible bias if the estimated propensity score is close to zero for some observations we propose alternative doubly robust estimators that achieve comparable or improved performance relative to existing methods even with some estimated propensity scores close to zero

generalized lazarsfeld mukai bundles and a conjecture of donagi and morrison abstract let s be a k3 surface and assume for simplicity that it does not contain any 2 curve using coherent systems we express every non simple lazarsfeld mukai bundle on s as an extension of two sheaves of some special type that we refer to as generalized lazarsfeld mukai bundles this has interesting consequences concerning the brill noether theory of curves c lying on s from now on let g denote the genus of c and a be a complete linear series of type g d r on c such that d g 1 and the corresponding brill noether number is negative first we focus on the cases where a computes the clifford index if r 1 and with only some completely classified exceptions we show that a coincides with the restriction to c of a line bundle on s this is a refinement of green and lazarsfeld s result on the constancy of the clifford index of curves moving in the same linear system then we study a conjecture of donagi and morrison predicting that under no hypothesis on its clifford index a is contained in a g e s which is cut out from a line bundle on s and satisfies e g 1 we provide counterexamples to the last inequality already for r 2 a slight modification of the conjecture which holds for r 1 2 is proved under some hypotheses on the pair c a and its deformations we show that the result is optimal in the sense that our hypotheses cannot be avoided by exhibiting in appendix a some counterexamples obtained jointly with andreas leopold knutsen

a lack of fit test for the mean function in a generalized linear model abstract a supremum type statistic based on partial sums of residuals is proposed to test the validity of the mean function of the response variable in a generalized linear model the proposed test does not need a partition of the space of covariates to handle the case of nonreplication the new test is consistent against the alternative under which the deterministic part of the model is not the one specified in the null hypothesis the asymptotic null distribution of the test statistic can be approximated through simulations this approximation is valid even if the variance of the response variable is misspecified in the model for practical sample sizes the adequacy of this large sample approximation to the null distribution of the test statistic is carefully examined power comparisons with other lack of fit tests are also performed to show the advantage of the test in particular we find that the new procedure is rather sensitive to detect a misspecified mean function if the assumed mean functio

asymptotic behavior of increasing solutions to a system of n nonlinear differential equations abstract we consider the system x i a i t x i 1 i sgn x i 1 i 1 n n 2 where a i i 1 n are positive continuous functions on a i 0 i 1 n with 1 n 1 and x n 1 means x 1 we analyze the asymptotic behavior of the solutions to this system whose components are eventually positive increasing in particular we derive exact asymptotic formulas for the extreme case where all the solution components tend to infinity the so called strongly increasing solutions we offer two approaches one is based on the asymptotic equivalence theorem and the other utilizes the theory of regular variation the above mentioned system includes as special cases two term nonlinear scalar differential equations of arbitrary order n and systems of n 2 second order nonlinear equations provided n is even which are related to elliptic partial differential systems applications to these objects are presented and a comparison with existing results is made it turns out that some of our results yield new information even in the simplest case a second order emden fowler differential equation

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

semiparametric efficiency in multivariate regression models with missing data abstract we consider the efficiency bound for the estimation of the parameters of semiparametric models defined solely by restrictions on the means of a vector of correlated outcomes y when the data on y are missing at random we show that the semiparametric variance bound is the asymptotic variance of the optimal estimator in a class of inverse probability of censoring weighted estimators and that this bound is unchanged if the data are missing completely at random for this case we study the asymptotic performance of the generalized estimating equations gee estimators of mean parameters and show that the optimal gee estimator is inefficient except for special cases the optimal weighted estimator depends on unknown population quantities but for monotone missing data we propose an adaptive estimator whose asymptotic variance can achieve the bound

minimal resolutions chow forms and ulrich bundles on k3 surfaces the minimal resolution conjecture mrc for points on a projective varietyx p predicts that the minimal graded free resolution of a general set x of points is as simple as the geometry of x allows originally the most studied case has been that when x p see epsw the general form of the mrc for subvarieties x p was formulated in mus and fmp the betti diagram of a large enough set x consisting of general points is obtained from the betti diagram of x by adding two rows indexed by u 1 and u where u is an integer depending on all differences bi 1 u 1 bi u are known and depend on the hilbert polynomial px and i u and see fmp the minimal resolution conjecture for general points on x predicts that

test the reliability of doubly robust estimation with missing response data in statistical inference one has to make sure that the underlying regression model is correctly specified otherwise the resulting estimation may be biased model checking is an important method to detect any departure of the regression model from the true one missing data is a ubiquitous problem in social and medical studies if the underlying regression model is correctly specified recent researches show great popularity of the doubly robust estimates method for handling missing data because of its robustness to the misspecification of either the missing data model or the conditional mean model i e the model for the conditional expectation of true regression model conditioning on the observed quantities however little work has been devoted to the goodness of fit test for doubly robust estimates method in this paper we propose a testing method to assess the reliability of the estimator derived from the doubly robust estimating equation with possibly missing response and always observed auxiliary variables numerical studies demonstrate that the proposed test can control type i errors well furthermore the proposed method can detect departures from model assumptions in the marginal mean model of interest powerfully a real dementia data set is used to illustrate the method for the diagnosis of model misspecification in the problem of missing response with an always observed auxiliary variable for cross sectional data

how biased is the apparent error rate of a prediction rule abstract a regression model is fitted to an observed set of data how accurate is the model for predicting future observations the apparent error rate tends to underestimate the true error rate because the data have been used twice both to fit the model and to check its accuracy we provide simple estimates for the downward bias of the apparent error rate the theory applies to general exponential family linear models and general measures of prediction error special attention is given to the case of logistic regression on binary data with error rates measured by the proportion of misclassified cases several connected ideas are compared mallows s cp cross validation generalized cross validation the bootstrap and akaike s information criterion

analysis of semi parametric regression models with non ignorable non response in this article we consider the problem of making inferences about the parameter 0 indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables outcome or covariates are missing for some study subjects and the probability of non response depends upon both observed and unobserved data values that is non response is non ignorable we propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal can for estimating 0 when the non response probabilities can be parametrically modelled and a can estimator exists the proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration we show that the asymptotic variance of the optimal estimator in our class attains the semi parametric variance bound for the model in some models no can estimator of 0 exists we provide a general algorithm for determining when can estimators of 0 exist our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular asymptotically linear estimators in an arbitrary semi parametric model with non ignorable non response in which the probability of observing complete data is bounded away from zero and the non response probabilities can be parametrically modelled 1997 by john wiley sons ltd

a paradox concerning nuisance parameters and projected estimating functions summary this paper is concerned with a paradox associated with parameter estimation in the presence of nuisance parameters in a statistical model with unknown nuisance parameters the efficiency of an estimator of a parameter usually increases when the nuisance para meters are known however the opposite phenomenon can sometimes occur in this paper we elucidate the occurrence of this paradox by examining estimating functions in particular we focus on the projected estimating function which is defined by the projection of the score function on to a given estimating function a sufficient condition for the paradox to occur is the orthogonality of the two components of the projected estimating functions corresponding to parameters of interest and nuisance parameters in addition a numerical assessment is conducted in the context of a simple model to investigate the improvement of the asymptotic efficiency of estimators

pattern mixture models for multivariate incomplete data consider a random sample on variables x1 xv with some values of xv missing selection models specify the distribution of x1 xv over respondents and nonrespondents to xv and the conditional distribution that xv is missing given x1 xv in contrast pattern mixture models specify the conditional distribution of x 1 xv given that xv is observed or missing respectively and the marginal distribution of the binary indicator for whether or not xv is missing for multivariate data with a general pattern of missing values the literature has tended to adopt the selection modeling approach see for example little and rubin here pattern mixture models are proposed for this more general problem pattern mixture models are chronically underidentified in particular for the case of univariate nonresponse mentioned above there are no data on the distribution of xv given x1 xv 1 in the stratum with xv missing thus the models require restrictions or prior information to identify the paramet

q regular variation and q difference equations we introduce the concept of q regularly varying functions and establish basic properties of such functions among other things it is shown that considering regular variation in q calculus is somehow natural and leads to interesting observations and simplifications compared with classical continuous and discrete theories the obtained theory is applied to an investigation of asymptotic behavior of solutions to linear second order q difference equations

an asymptotic analysis of nonoscillatory solutions of q difference equations via q regular variation abstract we do a thorough asymptotic analysis of nonoscillatory solutions of the q difference equation d q r t d q y t p t y q t 0 considered on the lattice q k k n 0 q 1 we classify the solutions according to various aspects that take into account their asymptotic behavior we show relations among the asymptotic classes for every positive solution we establish asymptotic formulae several discrepancies are revealed when comparing the results with their existing differential equations or difference equations counterparts however it should be noted that many of our observations in the q case have not their continuous or discrete analogies yet important roles in our considerations are played by the theory of q regular variation and various transformations the results are illustrated by examples

conditional akaike information for mixed effects models summary this paper focuses on the akaike information criterion aic for linear mixed effects models in the analysis of clustered data we make the distinction between questions regarding the population and questions regarding the particular clusters in the data we show that the aic in current use is not appropriate for the focus on clusters and we propose instead the conditional akaike information and its corresponding criterion the conditional aic caic the penalty term in caic is related to the effective degrees of freedom p for a linear mixed model proposed by hodges sargent 2001 p reflects an intermediate level of complexity between a fixed effects model with no cluster effect and a corresponding model with fixed cluster effects the caic is defined for both maximum likelihood and residual maximum likelihood estimation a pharmacokinetics data appli cation is used to illuminate the distinction between the two inference settings and to illustrate the use of the conditional aic in model selection

exotic g_2 g2 manifolds we exhibit the first examples of closed 7 dimensional riemannian manifolds with holonomy g 2 that are homeomorphic but not diffeomorphic these are also the first examples of closed ricci flat manifolds that are homeomorphic but not diffeomorphic the examples are generated by applying the twisted connected sum construction to fano 3 folds of picard rank 1 and 2 the smooth structures are distinguished by the generalised eells kuiper invariant introduced by the authors in a previous paper

embedding pointed curves in k3 surfaces we analyze morphisms from pointed curves to k3 surfaces with a distinguished rational curve such that the marked points are taken to the rational curve perhaps with specified cross ratios this builds on work of mukai and others characterizing embeddings of curves into k3 surfaces via non abelian brill noether theory our study leads naturally to enumerative problems which we solve in several specific cases these have applications to the existence of sections of del pezzo fibrations with prescribed invariants

estimating equations for association structures this paper investigates generalized estimating equations for association parameters which are frequently of interest in family studies with emphasis on covariance estimation separate link functions are used to connect the mean the scale and the correlation to linear predictors involving possibly different sets of covariates and separate estimating equations are proposed for the three sets of parameters simulations show that the robust sandwich variance estimator and the jackknife variance estimator for the correlation parameters are generally close to the empirical variance for the sample size of 50 clusters the results contradict ziegler et al and kastner and ziegler where the sandwich estimator obtained from the software mareg was shown to be unsuitable for practical usage the problem appears to arise because the mareg variance estimator does not account for variability in estimation of the scale parameters but may be valid with fixed scale we also find that the formula for the approximate jackknife variance estimator in ziegler et al is deficient resulting in systematic deviations from the fully iterated jackknife variance estimator a general jackknife formula is provided and performs well in numerical studies data from a study on the genetics of alcoholism is used to illustrate the importance of reliable variance estimation in biomedical applications

comments on an information criterion for marginal structural models by r w platt m a brookhart s r cole d westreich and e f schisterman

a c_p criterion for semiparametric causal inference for marginal structural models which recently play an important role in causal inference we consider a model selection problem in the framework of a semiparametric approach using inverse probability weighted estimation or doubly robust estimation in this framework the modeling target is a potential outcome which may be a missing value and so we cannot apply the aic nor its extended version to this problem in other words there is no analytical information criterion obtained according to its classical derivation for this problem hence we define a mean squared error appropriate for treating the potential outcome and then we derive its asymptotic unbiased estimator as a c p criterion from an asymptotics for the semiparametric approach and using an ignorable treatment assignment condition in simulation study it is shown that the proposed criterion exceeds a conventionally derived existing criterion in the squared error and model selection frequency specifically in all simulation settings the proposed criterion provides clearly smaller squared errors and higher frequencies selecting the true or nearly true model moreover in real data analysis we check that there is a clear difference between the selections by the two criteria

methods for dealing with time dependent confounding longitudinal studies where data are repeatedly collected on subjects over a period are common in medical research when estimating the effect of a time varying treatment or exposure on an outcome of interest measured at a later time standard methods fail to give consistent estimators in the presence of time varying confounders if those confounders are themselves affected by the treatment robins and colleagues have proposed several alternative methods that provided certain assumptions hold avoid the problems associated with standard approaches they include the g computation formula inverse probability weighted estimation of marginal structural models and g estimation of structural nested models in this tutorial we give a description of each of these methods exploring the links and differences between them and the reasons for choosing one over the others in different settings

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

goodness of fit methods for generalized linear mixed models we develop graphical and numerical methods for checking the adequacy of generalized linear mixed models glmms these methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable under the assumed model the asymptotic distributions of these stochastic processes can be approximated by certain zero mean gaussian processes whose realizations can be generated through monte carlo simulation each observed process can then be compared both visually and analytically to a number of realizations simulated from the null distribution these comparisons enable one to assess objectively whether the observed residual patterns reflect model misspecification or random variation the proposed methods are particularly useful for checking the functional form of a covariate or the link function extensive simulation studies show that the proposed goodness of fit tests have proper sizes and are sensitive to model misspecification applications to two medical studies lead to improved models

moduli of theta characteristics via nikulin surfaces we study moduli spaces of k3 surfaces endowed with a nikulin involution and their image in the moduli space r g of prym curves of genus g we observe a striking analogy with mukai s well known work on ordinary k3 surfaces many of mukai s results have a very precise prym nikulin analogue for instance a general prym curve from r g is a section of a nikulin surface if and only if g 7 and g 6 furthermore r 7 has the structure of a fibre space over the corresponding moduli space of polarized nikulin surfaces we then use these results to study the geometry of the moduli space s g of even spin curves with special emphasis on the transition case of s 8 which is a 21 dimensional calabi yau variety

the mercat conjecture for stable rank 2 vector bundles on generic curves we prove the mercat conjecture for rank 2 vector bundles on generic curves of every genus for odd genus we identify the effective divisor in mg where the mercat conjecture fails and compute its slope the clifford index of a smooth curve c defined as the non negative quantity cliff c min deg l 2r l l pic c h c l 2 deg l g 1 stratifies the moduli space mg of curves of genus g with the smallest stratum being that consisting of hyperelliptic curves which have clifford index zero while the definition is obviously inspired by the classical clifford theorem the notion came to real prominence in the works of green lazarsfeld g gl voisin v2 and many others in the context of syzygies of canonical curves for a general curve c of genus g one has cliff c bg 1 2 c the locus of curves c mg with cliff c bg 1 2 c is a subvariety of codimension 1 respectively 2 when g is odd respectively even much studied by harris and mumford hm it has been a long standing problem to find an adequate definition of the clifford index for higher rank vector bundles on curves a higher rank clifford index should not only capture the behavior of the generic curve from the point of view of special higher rank vector bundles but also provide a geometrically meaningful stratification ofmg an interesting definition has been put forward by lange and newstead ln1 for a semistable vector bundle e of rank 2 and slope e on a curve c of genus g one defines its clifford index as cliff e e h c e 2 0 the rank 2 clifford index of c is then defined as the quantity cliff2 c min cliff e e uc 2 d d 2g 2 h c e 4 observe that if l is a line bundle on c with deg l 2h0 c l 2 cliff c that is l computes the clifford index of c then cliff l l cliff c in particular the inequality cliff2 c cliff c holds for every curve c of genus g the main achievement of this paper is the proof of the following result theorem 1 for a general curve c of genus g the following equality holds cliff2 c cliff c g 1 2 equivalently if e is a semistable rank 2 vector bundle on c contributing to cliff2 c then h c e e 2 cliff c mercat me conjectured the equality cliff2 c cliff c for every smooth curve c mg counterexamples to this expectation have been found using noether lefschetz special k3 surfaces in fo1 fo2 and ln2 however these examples are special in moduli and theorem 1 proves mercat s conjecture for generic curves of every genus

brill noether loci and the gonality stratification of m g for an irreducible smooth projective complex curve c of genus g the gonality defined as gon c min d z 1 there exists a gd on c is perhaps the second most natural invariant it gives an indication of how far c is from being rational in a way different from what the genus does for g 3 we consider the stratification of the moduli space mg of smooth curves of genus g given by gonality mg 2 m 1 g 3 m 1 g k mg

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

moduli of curves on enriques surfaces abstract we compute the number of moduli of all irreducible components of the moduli space of smooth curves on enriques surfaces in most cases the moduli maps to the moduli space of prym curves are generically injective or dominant exceptional behavior is related to existence of enriques fano threefolds and to curves with nodal prym canonical model

on the splitting of lazarsfeld mukai bundles on k3 surfaces abstract let x be a k3 surface let c be a smooth curve on x and let z be a base point free pencil on c then the lazarsfeld mukai bundle e c z of rank 2 associated with c and z is given by an extension of the torsion free sheaf j z o x c by o x where j z is the ideal sheaf of z in x we can see that if c is very ample as a divisor on x e c z is an acm bundle with respect to o x c in this paper by using this fact we will characterize a necessary condition for e c z to be given by an extension of two line bundles on x by acm line bundles with respect to o x c

a cautionary note concerning the use of stabilized weights in marginal structural models marginal structural models are commonly used to estimate the causal effect of a time varying treatment in presence of time dependent confounding when fitting an msm to data the analyst must specify both the structural model for the outcome and the treatment models for the inverse probability of treatment weights the use of stabilized weights is recommended because they are generally less variable than the standard weights in this paper we are concerned with the use of the common stabilized weights when the structural model is specified to only consider partial treatment history such as the current or most recent treatments we present various examples of settings where these stabilized weights yield biased inferences while the standard weights do not these issues are first investigated on the basis of simulated data and subsequently exemplified using data from the honolulu heart program unlike common stabilized weights we find that basic stabilized weights offer some protection against bias in structural models designed to estimate current or most recent treatment effects copyright 2014 john wiley sons ltd

estimation with missing data beyond double robustness summary we propose an estimator that is more robust than doubly robust estimators based on weighting completecasesusingweightsotherthaninverseprobabilitywhenestimatingthepopulationmean of a response variable subject to ignorable missingness we allow multiple models for both the propensity score and the outcome regression our estimator is consistent if any of the multiple models is correctly specified such multiple robustness against model misspecification is a significant improvement over double robustness which allows only one propensity score model and one outcome regression model our estimator attains the semiparametric efficiency bound when one propensity score model and one outcome regression model are correctly specified without requiring knowledge of which models are correct

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

doubly robust estimation in missing data and causal inference models the goal of this article is to construct doubly robust dr estimators in ignorable missing data and causal inference models in a missing data model an estimator is dr if it remains consistent when either but not necessarily both a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified because with observational data one can never be sure that either a missingness model or a complete data model is correct perhaps the best that can be hoped for is to find a dr estimator dr estimators in contrast to standard likelihood based or nonaugmented inverse probability weighted estimators give the analyst two chances instead of only one to make a valid inference in a causal inference model an estimator is dr if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct inference based on dr estimators should improve upon previous approaches indeed we present the results of simulation studies which demonstrate that the finite sample performance of dr estimators is as impressive as theory would predict the proposed method is applied to a cardiovascular clinical trial

application of empirical bayes inference to estimation of rate of change in the presence of informative right censoring we apply parametric empirical bayes inference of morris7 to the estimation of rate of change from incomplete longitudinal studies where the right censoring process is considered informative that is the length of time the subjects participate in the study is associated with level of the study variable ignoring such an association can result in a biased estimate of rate of change the proposed method provides estimates of rate of change for individual subjects as well as for the entire group adjusted for informative right censoring the method is considered more robust than those based on a specific parametric model for the censoring distribution under non informative right censoring these estimators of slopes are equivalent to the bayes estimators derived by fearn 11 we illustrate the method with an example involving renal transplant data we evaluate the method s performance through a simulation study

the focused information criterion a variety of model selection criteria have been developed of general and specific types most of these aim at selecting a single model with good overall properties for example formulated via average prediction quality or shortest estimated overall distance to the true model the akaike the bayesian and the deviance information criteria along with many suitable variations are examples of such methods these methods are not concerned however with the actual use of the selected model which varies with context and application the present article takes the view that the model selector should instead focus on the parameter singled out for interest in particular a model that gives good precision for one estimand may be worse when used for inference for another estimand we develop a method that for a given focus parameter estimates the precision of any submodel based estimator the framework is that of large sample likelihood inference using an unbiased estimate of limiting risk we propose a foc

analysis of longitudinal binary data from multiphase sampling the efficient use of surrogate or auxiliary information has been investigated within both model based and design based approaches to data analysis particularly in the context of missing data here we consider the use of such data in epidemiological studies of disease incidence in which surrogate measures of disease status are available for all subjects at two time points but definitive diagnoses are available only in stratified subsamples we briefly review methods for the analysis of two phase studies of disease prevalence at a single time point and we discuss the extension of four of these methods to the analysis of incidence studies their performance is compared with special reference to a study of the incidence of senile dementia

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimating the causal effect of zidovudine on cd4 count with a marginal structural model for repeated measures even in the absence of unmeasured confounding factors or model misspecification standard methods for estimating the causal effect of a time varying treatment on the mean of a repeated measures outcome for example gee regression may be biased when there are time dependent variables that are simultaneously confounders of the effect of interest and are predicted by previous treatment in contrast the recently developed marginal structural models msms can provide consistent estimates of causal effects when unmeasured confounding and model misspecification are absent we describe an msm for repeated measures that parameterizes the marginal means of counterfactual outcomes corresponding to prespecified treatment regimes the parameters of msms are estimated using a new class of estimators inverse probability of treatment weighted estimators we used an msm to estimate the effect of zidovudine therapy on mean cd4 count among hiv infected men in the multicenter aids cohort study we estimated a potential expected increase of 5 4 95 per cent confidence interval 1 8 12 7 cd4 lymphocytes l per additional study visit while on zidovudine therapy we also explain the theory and implementation of msms for repeated measures data and draw upon a simple example to illustrate the basic ideas

regular variation on measure chains ukazujeme souvislosti mezi nedavno zavedenou definici regularni variace pomoci delta derivace a definici karamatova typu je dokazana v ta o vno eni a reprezentaci je ukazano e pro rozumnou teorii je pot eba dodatecneho p edpokladu na zrnitost jsou odvozeny r zne vlastnosti regularn se m nicich funkci teorie je aplikovana p i popisu asymptotick ch vlastnosti eseni dynamick ch rovnic druheho adu