marginalized transition models for longitudinal binary data with ignorable and non ignorable drop out we extend the marginalized transition model of heagerty to accommodate non ignorable monotone drop out using a selection model weakly identified drop out parameters are held constant and their effects evaluated through sensitivity analysis for data missing at random mar efficiency of inverse probability of censoring weighted generalized estimating equations ipcw gee is as low as 40 per cent compared to a likelihood based marginalized transition model mtm with comparable modelling burden mtm and ipcw gee regression parameters both display misspecification bias for mar and non ignorable missing data and both reduce bias noticeably by improving model fit

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

estimation and comparison of changes in the presence of information right censoring by modeling the censoring process abstract in estimating and comparing the rates of change of a continuous variable between two groups the unweighted averages of individual simple least squares estimates from each group are often used under a linear random effects model when all individuals have completed observations at identical time points these statistics are maximum likelihood estimates for the expected rates of change however with censored of missing data these estimates are no longer efficient when compared to generalized least squares estimates when in addition the right censoring process is dependent upon the individual rates of change i e informative right censoring the generalized least squares estimates will be biased likelihood ratio test for informativeness of the censoring process and maximum likelihood estimates for the expected rates of change and the parameters of the right censoring process are developed under a linear random effect models with a probit model for the right censoring process in realistic situations we illustrate that the bias in estimating group rate of change and the reduction of power in comparing group difference could be substantial when strong dependency of the right censoring process on individual rates of change is ignored author

estimation of regression models for the mean of repeated outcomes under nonignorable nonmonotone nonresponse we propose a new class of models for making inference about the mean of a vector of repeated outcomes when the outcome vector is incompletely observed in some study units and missingness is nonmonotone each model in our class is indexed by a set of unidentified selection bias functions which quantify the residual association of the outcome at each occasion t and the probability that this outcome is missing after adjusting for variables observed prior to time t and for the past nonresponse pattern in particular selection bias functions equal to zero encode the investigator s a priori belief that nonresponse of the next outcome does not depend on that outcome after adjusting for the observed past we call this assumption sequential explainability since each model in our class is nonparametric it fits the data perfectly well as such our models are ideal for conducting sensitivity analyses aimed at evaluating the impact that different degrees of departure from sequential explainability have on inference about the marginal means of interest although the marginal means are identified under each of our models their estimation is not feasible in practice because it requires the auxiliary estimation of conditional expectations and probabilities given high dimensional variables we henceforth discuss the estimation of the marginal means under each model in our class assuming additionally that at each occasion either one of the following two models holds a parametric model for the conditional probability of nonresponse given current outcomes and past recorded data or a parametric model for the conditional mean of the outcome on the nonrespondents given the past recorded data we call the resulting procedure 2 t multiply robust as it protects at each of the t time points against misspecification of one of these two working models although not against simultaneous misspecification of both we extend our proposed class of models and estimators to incorporate data configurations which include baseline covariates and a parametric model for the conditional mean of the vector of repeated outcomes given the baseline covariates

semiparametric modeling of repeated measurements under outcome dependent follow up in regression analysis of repeated measurements that are taken at subject specific times the availability of the outcome data may be related to the past outcome and to other measured variables that are not in the intended regression model in this paper we propose a natural extension of the semiparametric regression procedure of lin and ying j am stat assoc 2001 96 103 126 by building a class of inverse intensity rate ratio weighted estimators that accommodate such outcome dependent follow up the estimators have a closed form are radicaln consistent asymptotically normal and do not require estimation of any infinite dimensional parameters we give several simulations to demonstrate the estimator s performance and show a sensitivity study under follow up with various degrees of dependence on outcome related variables we illustrate our approach using data from a randomized health services research study with noncompliance to scheduled visits

missing data methods for generalized linear models a comparative review missing data is a major issue in many applied problems especially in the biomedical sciences we review four common approaches for inference in generalized linear models glms with missing covariate data maximum likelihood ml multiple imputation mi fully bayesian fb and weighted estimating equations wees there is considerable interest in how these four methodologies are related the properties of each approach the advantages and disadvantages of each methodology and computational implementation we examine data that are missing at random and nonignorable missing for ml we focus on techniques using the em algorithm and in particular discuss the em by the method of weights and related procedures as discussed by ibrahim for mi we examine the techniques developed by rubin for fb we review approaches considered by ibrahim et al for wee we focus on the techniques developed by robins et al we use a real dataset and a detailed simulation study to compare the four methods

information and asymptotic efficiency in parametric nonparametric models asymptotic lower bounds for estimation of the parameters of models with both parametric and nonparametric components are given in the form of representation theorems for regular estimates and asymptotic minimax bounds the methods used involve i the notion of a hellinger differentiable root density where part of the differentiation is with respect to the nonparametric part of the model to obtain appropriate scores and ii calculation of the effective score for the real or vector finite dimensional parameter of interest as that component of the score function orthogonal to all nuisance parameter scores perhaps infinite dimensional the resulting asymptotic information for estimation of the parametric component of the model is just 4 times the squared l 2 norm of the effective score a corollary of these results is a simple necessary condition for adaptive estimation adaptation is possible only if the scores for the parameter of interest are orthogonal to the scores for the nuisance function or nonparametric part of the model examples considered include the one sample location model with and without symmetry mixture models the two sample shift model and cox s proportional hazards model

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

on dynamic random graphs with degree homogenization via anti preferential attachment probabilities abstract we analyze a dynamic random undirected graph in which newly added vertices are connected to those already present in the graph either using with probability p an anti preferential attachment mechanism or with probability 1 p a preferential attachment mechanism we derive the asymptotic degree distribution in the general case and study the asymptotic behavior of the expected degree process in the general and that of the degree process in the pure anti preferential attachment case degree homogenization mainly affects convergence rates for the former case and also the limiting degree distribution in the latter lastly we perform a simulative study of a variation of the introduced model allowing for anti preferential attachment probabilities given in terms of the current maximum degree of the graph

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

bounds on net survival probabilities for dependent competing risks bounds on the marginal survival function based on data from a competing risks experiment are obtained these bounds require an investigator to specify a range of possible concordances for the times to occurrences of the competing risks these bounds are tighter than those of peterson 1976 proceedings of the national academy of sciences 73 11 13

estimation of the causal effect of a time varying exposure on the marginal mean of a repeated binary outcome abstract we provide sufficient conditions for estimating from longitudinal data the causal effect of a time dependent exposure or treatment on the marginal probability of response for a dichotomous outcome we then show how one can estimate this effect under these conditions using the g computation algorithm of robins we also derive the conditions under which some current approaches to the analysis of longitudinal data such as the generalized estimating equations gee approach of zeger and liang the feedback model techniques of liang and zeger and within subject conditional methods can provide valid tests and estimates of causal effects we use our methods to estimate the causal effect of maternal stress on the marginal probability of a child s illness from the mothers stress and children s morbidity data and compare our results with those previously obtained by zeger and liang using a gee approach

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

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

regression analysis for categorical variables with outcome subject to nonignorable nonresponse abstract we develop a log linear model for categorical response subject to nonignorable nonresponse the paper differs from fay 1986 in its focus on estimation and hypothesis testing in a regression setting as opposed to imputation in a multivariate setting we present several new results concerning the existence of solutions on the boundary of the parameter space and the construction of confidence intervals for estimates we illustrate the method by estimating the proportion of voters preferring truman in a 1948 preelection poll mosteller hyman mccarthy marks and truman 1949 results may depend strongly on the model assumed for nonresponse goodness of fit tests are available for comparing alternative models

marginal analyses of longitudinal data with an informative pattern of observations we consider solutions to generalized estimating equations with singular working correlation matrices of which the estimator of diggle et al 2007 is a special case we give explicit conditions for consistent estimation when the pattern of observations may be informative in such cases simulations reveal reduced bias and reduced mean squared error compared with existing alternatives a study of peritoneal dialysis is used to illustrate the methodology

expected estimating equations to accommodate covariate measurement error estimating equations which are not necessarily likelihood based score equations are becoming increasingly popular for estimating regression model parameters this paper is concerned with estimation based on general estimating equations when true covariate data are missing for all the study subjects but surrogate or mismeasured covariates are available instead the method is motivated by the covariate measurement error problem in marginal or partly conditional regression of longitudinal data we propose to base estimation on the expectation of the complete data estimating equation conditioned on available data the regression parameters and other nuisance parameters are estimated simultaneously by solving the resulting estimating equations the expected estimating equation eee estimator is equal to the maximum likelihood estimator if the complete data scores are likelihood scores and conditioning is with respect to all the available data a pseudo eee estimator which requires less computation is also investigated asymptotic distribution theory is derived small sample simulations are conducted when the error process is an order 1 autoregressive model regression calibration is extended to this setting and compared with the eee approach we demonstrate the methods on data from a longitudinal study of the relationship between childhood growth and adult obesity

global sensitivity analysis for repeated measures studies with informative drop out a semi parametric approach in practice both testable and untestable assumptions are generally required to draw inference about the mean outcome measured at the final scheduled visit in a repeated measures study with drop out scharfstein et al 2014 proposed a sensitivity analysis methodology to determine the robustness of conclusions within a class of untestable assumptions in their approach the untestable and testable assumptions were guaranteed to be compatible their testable assumptions were based on a fully parametric model for the distribution of the observable data while convenient these parametric assumptions have proven especially restrictive in empirical research here we relax their distributional assumptions and provide a more flexible semi parametric approach we illustrate our proposal in the context of a randomized trial for evaluating a treatment of schizoaffective disorder

analysis of change in the presence of informative censoring application to a longitudinal clinical trial of progressive renal disease the rate of change in a continuous variable measured serially over time is often used as an outcome in longitudinal studies or clinical trials when patients terminate the study before the scheduled end of the study there is a potential for bias in estimation of rate of change using standard methods which ignore the missing data mechanism these methods include the use of unweighted generalized estimating equations methods and likelihood based methods assuming an ignorable missing data mechanism we present a model for analysis of informatively censored data based on an extension of the two stage linear random effects model where each subject s random intercept and slope are allowed to be associated with an underlying time to event the joint distribution of the continuous responses and the time to event variable are then estimated via maximum likelihood using the em algorithm and using the bootstrap to calculate standard errors we illustrate this methodology and compare it to simpler approaches and usual maximum likelihood using data from a multi centre study of the effects of diet and blood pressure control on progression of renal disease the modification of diet in renal disease mdrd study sensitivity analyses and simulations are used to evaluate the performance of this methodology in the context of the mdrd data under various scenarios where the drop out mechanism is ignorable as well as non ignorable

diameters in preferential attachment models in this paper we investigate the diameter in preferential attachment pa models thus quantifying the statement that these models are small worlds the models studied here are such that edges are attached to older vertices proportional to the degree plus a constant i e we consider affine pa models there is a substantial amount of literature proving that quite generally pa graphs possess power law degree sequences with a power law exponent 2

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

semiparametric and nonparametric regression analysis of longitudinal data this article deals with the regression analysis of repeated measurements taken at irregular and possibly subject specific time points the proposed semiparametric and nonparametric models postulate that the marginal distribution for the repeatedly measured response variable y at time t is related to the vector of possibly time varying covariates x through the equations e y t x t 0 t 0x t and e y t x t 0 t 0 t x t where 0 t is an arbitrary function of t 0 is a vector of constant regression coefficients and 0 t is a vector of time varying regression coefficients the stochastic structure of the process y is completely unspecified we develop a class of least squares type estimators for 0 which is proven to be n consistent and asymptotically normal with simple variance estimators furthermore we develop a closed form estimator for a cumulative function of 0 t which is shown to be n consistent and on proper normalization converges weakly to a zero mean gaussian pr

closed form estimates for missing counts in two way contingency tables one method for analyzing contingency tables with missing observations is to model the missing data mechanism using log linear models previous methods for obtaining estimates of missing counts and parameters have required an iterative algorithm in many cases however one can obtain estimates by use of a simple algebraic formula we illustrate the method with data on smoking and birth weight

log linear models for survey data with non ignorable non response we demonstrate the feasibility of constructing interpreting and fitting computable log linear models to categorical survey data with arbitrary non nested patterns of non ignorable non response under our approach the non response probability for each cell of the classification defined by the categories of interest is modelled separately from the classification probability itself and we adopt a model formulation which allows the non response model to depend on scores discrete covariates continuous covariates or a mixture of types of covariate

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

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

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

inference from nonrandomly missing categorical data an example from a genetic study on turner s syndrome abstract the process leading to partial classification with categorical data is sometimes nonrandom a particular model accounting for incomplete data which allows the probability of uncertain classification to depend on category identity is utilized for an analysis of data obtained from a genetic study on turner s syndrome estimates of population proportions are obtained from maximum likelihood a method for handling nonrandomly missing data arrayed in contingency tables is discussed sensitivity analyses incorporating parameters related to the missing data mechanism are recommended for estimation and testing

semiparametric efficient estimation for incomplete longitudinal binary data with application to smoking trends incomplete longitudinal data often are analyzed with estimating equations for inference on a parameter from a marginal mean regression model generalized estimating equations although commonly used for incomplete longitudinal data are invalid for data that are not missing completely at random there exists a class of inverse probability weighted estimating equations that are valid under dropouts missing at random including an easy to implement but inefficient member a relatively computationally complex semiparametric efficient estimator in this class has been applied to continuous data a specific form of this estimator is developed for binary data and used as a benchmark for assessing the efficiency of the simpler estimator in a simulation study both are applied in the estimation of 15 year cigarette smoking trends in the united states from a cohort of 5077 young adults the results suggest that declines in smoking from previous reports have been exaggerated

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

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

bivariate binary data analysis with nonignorably missing outcomes one of the objectives in the northern manhattan stroke study is to investigate the impact of stroke subtype on the functional status 2 years after the first ischemic stroke a challenge in this analysis is that the functional status at 2 years after stroke is not completely observed in this paper we propose a method to handle nonignorably missing binary functional status when the baseline value and the covariates are completely observed the proposed method consists of fitting four separate binary regression models for the baseline outcome the outcome 2 years after the stroke the product of the previous two and finally the missingness indicator we then conduct a sensitivity analysis by varying the assumptions about the third and the fourth binary regression models our method belongs to an imputation paradigm and can be an alternative to the weighting method of rotnitzky and robins 1997 statistics in medicine 16 81 102 a jackknife variance estimate is proposed for the variance of the resulting estimate the proposed analysis can be implemented using statistical software such as sas

doubly robust estimation of the area under the receiver operating characteristic curve in the presence of verification bias the area under the receiver operating characteristic curve auc is a popular summary measure of the efficacy of a medical diagnostic test to discriminate between healthy and diseased subjects a frequently encountered problem in studies that evaluate a new diagnostic test is that not all patients undergo disease verification because the verification test is expensive invasive or both furthermore the decision to send patients to verification often depends on the new test and on other predictors of true disease status in such cases usual estimators of the auc based on verified patients only are biased in this article we develop estimators of the auc of markers measured on any scale that adjust for selection to verification these estimators adjust for measured patient covariates and diagnostic test results and also for an assumed degree of residual selection bias they can then be used in a sensitivity analysis to examine how the auc estimates change when different plausible degrees of residual asso

estimation and comparison of changes in the presence of informative right censoring conditional linear model a general linear regression model for the usual least squares estimated rate of change slope on censoring time is described as an approximation to account for informative right censoring in estimating and comparing changes of a continuous variable in two groups two noniterative estimators for the group slope means the linear minimum variance unbiased lmvub estimator and the linear minimum mean squared error lmmse estimator are proposed under this conditional model in realistic situations we illustrate that the lmvub and lmmse estimators derived under a simple linear regression model are quite competitive compared to the pseudo maximum likelihood estimator pmle derived by modeling the censoring probabilities generalizations to polynomial response curves and general linear models are also described

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

a class of pattern mixture models for normal incomplete data summary likelihood based methods are developed for analyzing a random sample on two continuous variables when values of one of the variables are missing normal maximum likelihood estimates when values are missing completely at random were derived by anderson 1957 they are also maximum likelihood providing the missing data mechanism is ignorable in rubin s 1976 sense that the mechanism depends only on observed data a new class of pattern mixture models little 1993 is described for the situation where missingness is assumed to depend on an arbitrary unspecified function of a linear combination of the two variables maximum likelihood for models in this class is straightforward and yields the estimates of anderson 1957 when missingness depends solely on the completely observed variable and the estimates of brown 1990 when missingness depends solely on the incompletely observed variable another choice of linear combination yields estimates from complete case analysis large sample and bayesian methods are described for this model the data do not supply information about the ratio of the coefficients of the linear combination that controls missingness if this ratio is not welldetermined based on prior knowledge a prior distribution can be specified and bayesian inference is then readily accomplished alternatively sensitivity of inferences can be displayed for a variety of choices of the ratio

nonparametric analysis of randomized experiments with missing covariate and outcome data abstract analysis of randomized experiments with missing covariate and outcome data is problematic because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data this article shows how population parameters can be bounded without making untestable distributional assumptions bounds are also derived under the assumption that covariate data are missing completely at random in each case the bounds are sharp they exhaust all of the information available given the data and the maintained assumptions the bounds are illustrated with applications to data obtained from a clinical trial and data relating family structure to the probability that a youth graduates from high school

weighted generalized estimating functions for longitudinal response and covariate data that are missing at random longitudinal studies often feature incomplete response and covariate data it is well known that biases can arise from naive analyses of available data but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing data indicators various factors may influence the availability of response and covariate data at scheduled assessment times and at any given assessment time the response may be missing covariate data may be missing or both response and covariate data may be missing here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models inverse probability weighted generalized estimating equations offer an appealing approach for doing this here we develop these equations for a particular model generating intermittently missing at random data empirical studies demonstrate that the consistent e

handling estimating equation with nonignorably missing data based on sir algorithm abstract in this paper the estimation of parameters in estimating equation with nonignorably missing data is considered based on a logistic regression model for the response mechanism and an assumed parametric model for the distribution of respondents we propose to use the sampling importance resampling sir algorithm to calculate the conditional expectation for non respondents the proposed method can avoid the difficulty of high dimensional kernel smoothing on calculating the conditional expectation under nonignorably missing data based on the sir algorithm we derive a modified estimating equation to facilitate comparison we apply the empirical likelihood method to derive the parameters estimator some numerical simulation results based on linear and nonlinear models show that the proposed method is robust and performs the best among the compared existing methods so we extend the estimation method of e g y using sir algorithm with nonignorably missing response to the estimation of parameters in generalized estimating equation and obtain a new and more robust estimation method

singular continuous floquet operator for systems with increasing gaps abstract consider the floquet operator of a time independent quantum system periodically perturbed by a rank one kick acting on a separable hilbert space e ih0te i t where t and are the period and the coupling constant respectively assume the spectrum of the self adjoint operator h0 is pure point simple bounded from below and the gaps between the eigenvalues n grow like n 1 n cnd with d 2 under some hypotheses on the arithmetical nature of the eigenvalues and the vector cyclic for h0 we prove the floquet operator of the perturbed system has purely singular continuous spectrum

random networks with sublinear preferential attachment the giant component we study a dynamical random network model in which at every construction step a new vertex is introduced and attached to every existing vertex independently with a probability proportional to a concave function f of its current degree we give a criterion for the existence of a giant component which is both necessary and sufficient and which becomes explicit when f is linear otherwise it allows the derivation of explicit necessary and sufficient conditions which are often fairly close we give an explicit criterion to decide whether the giant component is robust under random removal of edges we also determine asymptotically the size of the giant component and the empirical distribution of component sizes in terms of the survival probability and size distribution of a multitype branching random walk associated with f

the evolutionary game of pressure or interference resistance and collaboration in this paper we extend the framework of the evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions to address the pressure executed by the major player or principal on the large group of small players who can resist this pressure or collaborate with the major player we prove rigorous results on the convergence of various markov decision models of interacting small agents including evolutionary growth i e pairwise in groups and by coalition formation to a deterministic evolution on the distributions of the state spaces of small players paying main attention to situations with an infinite state space of small players we supply precise rates of convergence the theoretical results of the paper are applied to the analysis of the processes of inspection corruption cyber security counter terrorism banks and firms merging strategically enhanced preferential attachment and many other

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

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

semiparametric regression models for repeated measures of mortal cohorts with non monotone missing outcomes and time dependent covariates we propose a semiparametric marginal modeling approach for longitudinal analysis of cohorts with data missing due to death and non response to estimate regression parameters interpreted as conditioned on being alive our proposed method accommodates outcomes and time dependent covariates that are missing not at random with non monotone missingness patterns via inverse probability weighting missing covariates are replaced by consistent estimates derived from a simultaneously solved inverse probability weighted estimating equation thus we utilize data points with the observed outcomes and missing covariates beyond the estimated weights while avoiding numerical methods to integrate over missing covariates the approach is applied to a cohort of elderly female hip fracture patients to estimate the prevalence of walking disability over time as a function of body composition inflammation and age

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

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

estimation of the time dependent accelerated failure time model in the presence of confounding factors summary cox oakes 1984 p 66 introduced the strong version of the accelerated failure time model with time dependent exposures we provide conditions under which this model could be used to estimate from observational data the causal effect of a time varying exposure or treatment on time to an event of interest in the presence of time dependent confounding variables we propose a class of semiparametric tests and estimators for the model parameters this class contains an estimator that is semipara metric efficient in the sense of begun et al 1983 the purpose of this paper is first to provide conditions under which it would be possible to estimate from observational data the causal effect of a time dependent treatment or exposure on time to an event of interest in the presence of time dependent confounding covariates and then to construct estimators for the treatment effect under these condi tions our approach will be based on the semiparametric estimation of the parameters of the strong version of the accelerated failure time model with time dependent exposures or treatments introduced by cox oakes 1984 p 66 the usual approach to the estimation of the effect of a time varying treatment on survival is to model the hazard of failure at t as a function of past treatment history using a time dependent proportional hazards model we show that the usual approach may be biased whether or not one further adjusts for past confounder history in the analysis when a there exists a time dependent risk factor for or predictor of the event of interest that also predicts subsequent treatment and b past treatment history predicts subsequent risk factor level the following four examples demonstrate conditions a and b will often be true in an observational study in which there is treatment by indication the drug zidovudine formerly azt used in the treatment of the acquired immunodeficiency syndrome is a direct red blood cell toxin that is contra indicated in anaemic subjects i e subjects with depressed red cell counts since the toxic effects of zidovudine can worsen the anaemia further anaemic patients are at increased risk of death thus in an observational study of the effect of zidovudine on survival of patients with the acquired immunodeficiency syndrome anaemia is both a risk factor for death

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

parameterization and bayesian modeling progress in statistical computation often leads to advances in statistical modeling for example it is surprisingly common that an existing model is reparameterized solely for computational purposes but then this new configuration motivates a new family of models that is useful in applied statistics one reason why this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood in a bayesian framework however a transformation of parameters typically suggests a new family of prior distributions we discuss examples in censored and truncated data mixture modeling multivariate imputation stochastic processes and multilevel models

inference in randomized studies with informative censoring and discrete time to event endpoints summary in this article we present a method for estimating and comparing the treatment specific distributions of a discrete time to event variable from right censored data our method allows for 1 adjustment for informative censoring due to measured prognostic factors for time to event and censoring and 2 quantification of the sensitivity of the inference to residual dependence between time to event and censoring due to unmeasured factors we develop our approach in the context of a randomized trial for the treatment of chronic schizophrenia we perform a simulation study to assess the practical performance of our methodology