the control of confounding by intermediate variables in epidemiologic studies of the effect of an exposure on disease the crude association of exposure with disease may fail to reflect a causal association due to confounding by one or more covariates most previous discussions of confounding in the epidemiologic literature have considered only point exposure studies that is studies that measure exposure and covariate status only once at start of follow up in this paper we offer definitions of confounding suitable for longitudinal studies that obtain data on exposure covariate and vital status at several points in time an important difference between longitudinal studies and point exposure studies is that in longitudinal studies a time dependent covariate can be simultaneously a confounder and an intermediate variable on the causal pathway from exposure to disease in this paper i propose an estimator the extended standardized risk difference that provides control for confounding by a covariate that is simultaneously a confounder and an intermediate variable

root n consistent semiparametric regression on considere une variable aleatoire x z dans 7b r p 7b r q on construit un estimateur generalisant l estimateur des moindres carres ordinaires en inserant des estimateurs non parametriques de la regression dans la projection orthogonale non lineaire sur z

the foundations of confounding in epidemiology abstract a statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented confounding by a covariate c in the presence of data on c is distinguished from confounding in the absence of data on c a covariate c is defined to be a nonconfounder in the absence of data on c if the population parameter of interest can be unbiasedly estimated asymptotically absent data on c under this definition c may be a confounder for some parameters of interest and a nonconfounder for others if c is a confounder for a parameter of interest that has a causal interpretation we call c a causal confounder when data on c are available c is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through c bayesians frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render c a non confounder in particular c will in general be a nonconfounder precisely when the crude data ignoring c are s sufficient for the parameter of interest the intuitive view held by many practicing epidemiologists that confounding by c represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori

burgers equation and the sticky particles model under general assumptions on the initial data we show that the entropy solution x t u x t of the one dimensional inviscid burgers equation is the velocity function of a sticky particles model whose initial mass distribution is lebesgue measure precisely the particles trajectories x t x0 t x are given by a forward flow x s t r r r x0 s t x xs tx0 s x and txs t u xs t s t e u s xs t u x t e u 0 x0 t x

conditional permutation tests and the propensity score in observational studies abstract in observational studies the distribution of treatment assignments is unknown and therefore randomization tests are not generally applicable however permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies provided treatment assignment is strongly ignorable these tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score several tests that are commonly used in observational studies are particular instances of this general procedure moreover conditional permutation tests and covariance adjustment are closely related in the sense that the conditional permutation distribution of the covariance adjusted difference leads to the same inferences as the conditional permutation distribution of the unadjusted difference of sample means a backtrack algorithm is developed to permit efficient calculation of the exact conditional si

bounded efficient and multiply robust estimation of average treatment effects using instrumental variables instrumental variables ivs are widely used for estimating causal effects in the presence of unmeasured confounding under the standard iv model however the average treatment effect ate is only partially identifiable to address this we propose novel assumptions that allow for identification of the ate our identification assumptions are clearly separated from model assumptions needed for estimation so that researchers are not required to commit to a specific observed data model in establishing identification we then construct multiple estimators that are consistent under three different observed data models and multiply robust estimators that are consistent in the union of these observed data models we pay special attention to the case of binary outcomes for which we obtain bounded estimators of the ate that are guaranteed to lie between 1 and 1 our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings

global structure of riemann solutions to a system of two dimensional hyperbolic conservation laws abstract the riemann problem for a two dimensional nonstrictly hyperbolic system of conservation laws is considered without the restriction that each jump of the initial data projects one planar elementary wave ten topologically distinct solutions are obtained by applying the method of generalized characteristic analysis some of these solutions involve the nonclassical waves i e the delta shock wave and the delta contact discontinuity for which we explicitly give the expressions of their strengths locations and propagation speeds moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one dimensional cauchy problem which provides a verification that our construction produces the correct unique global solutions

euler poisson systems as action minimizing paths in the wasserstein space this paper uses a variational approach to establish existence of solutions t vt for the 1 d euler poisson system by minimizing an action we assume that the initial and terminal points 0 t are prescribed in mathcal p 2 mathbb r the set of borel probability measures on the real line of finite second order moments we show existence of a unique minimizer of the action when the time interval 0 t satisfies t these solutions conserve the hamiltonian and they yield a path t t in mathcal p 2 mathbb r when t y t is a dirac mass the euler poisson system reduces to ddot y y 0 the kinetic version of the euler poisson that is the vlasov poisson system was studied in ambrosio and gangbo comm pure appl math to appear as a hamiltonian system

radon measure solutions for steady compressible euler equations of hypersonic limit conical flows and newton s sine squared law abstract we formulate a mathematical problem on hypersonic limit of three dimensional steady uniform non isentropic compressible euler flows of polytropic gases passing a straight cone with arbitrary cross section and attacking angle which is to study radon measure solutions of a nonlinear hyperbolic system of conservation laws on the unit 2 sphere the construction of a measure solution with density containing dirac measures supported on the surface of the cone is reduced to find a regular periodic solution of highly nonlinear and singular ordinary differential equations ode for a circular cone with zero attacking angle we then proved the newton s sine squared law by obtaining such a measure solution this provides a mathematical foundation for the newton s theory of pressure distribution on three dimensional bodies in hypersonic flows

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

well posedness for pressureless euler system with a flocking dissipation in wasserstein space abstract we prove the well posedness of nonhomogeneous pressureless euler system in 2 wasserstein space with the initial mass and energy being finite our method is based on a main observation pioneered by brenier and grenier that we can recover the solution of the pressureless system from a conservation law with its flux function being determined by the initial density and velocity

existence and uniqueness of discontinuous solutions for a hyperbolic system in this paper we prove the global existence and uniqueness of solutions to the cauchy problem of a hyperbolic system which probably contains so called waves

multiply robust causal inference with double negative control adjustment for categorical unmeasured confounding unmeasured confounding is a threat to causal inference in observational studies in recent years the use of negative controls to mitigate unmeasured confounding has gained increasing recognition and popularity negative controls have a long standing tradition in laboratory sciences and epidemiology to rule out non causal explanations although they have been used primarily for bias detection recently miao and colleagues have described sufficient conditions under which a pair of negative control exposure and outcome variables can be used to identify non parametrically the average treatment effect ate from observational data subject to uncontrolled confounding we establish non parametric identification of the ate under weaker conditions in the case of categorical unmeasured confounding and negative control variables we also provide a general semiparametric framework for obtaining inferences about the ate while leveraging information about a possibly large number of measured covariates in particular we derive the semiparametric efficiency bound in the non parametric model and we propose multiply robust and locally efficient estimators when non parametric estimation may not be feasible we assess the finite sample performance of our methods in extensive simulation studies finally we illustrate our methods with an application to the post licensure surveillance of vaccine safety among children

conditional generalized estimating equations for the analysis of clustered and longitudinal data a common and important problem in clustered sampling designs is that the effect of within cluster exposures i e exposures that vary within clusters on outcome may be confounded by both measured and unmeasured cluster level factors i e measurements that do not vary within clusters when some of these are ill not accounted for estimation of this effect through population averaged models or random effects models may introduce bias we accommodate this by developing a general theory for the analysis of clustered data which enables consistent and asymptotically normal estimation of the effects of within cluster exposures in the presence of cluster level confounders semiparametric efficient estimators are obtained by solving so called conditional generalized estimating equations we compare this approach with a popular proposal by neuhaus and kalbfleisch 1998 biometrics 54 638 645 who separate the exposure effect into a within and a between cluster component within a random intercept model we find that the latter approach yields consistent and efficient estimators when the model is linear but is less flexible in terms of model specification under nonlinear models this approach may yield inconsistent and inefficient estimators though with little bias in most practical settings

gmm redundancy results for general missing data problems we consider questions of efficiency and redundancy in the gmm estimation problem in which we have two sets of moment conditions where two sets of parameters enter into one set of moment conditions while only one set of parameters enters into the other we then apply these results to a selectivity problem in which the first set of moment conditions is for the model of interest and the second set of moment conditions is for the selection process we use these results to explain the counterintuitive result in the literature that under an ignorability assumption that justifies gmm with weighted moment conditions weighting using estimated probabilities of selection is better than weighting using the true probabilities we also consider estimation under an exogeneity of selection assumption such that both the unweighted and the weighted moment conditions are valid and we show that when weighting is not needed for consistency it is also not useful for efficiency

existence of global entropy solutions to general system of keyfitz kranzer type abstract in this paper we apply the div curl lemma in the compensated compactness theory tartar 1979 38 murat 1978 34 to the special pair of functions c w i e x t to obtain a very short proof of the existence of global entropy solutions for quite general system 1 1 of keyfitz kranzer type keyfitz and kranzer 1980 24 where c is a constant and w i e x t are variants in 1 1 this work extends in some sense the previous work by the author lu 2011 32 for a special system of keyfitz kranzer or aw rascle type as a by product a simple proof of the existence and stability of entropy solutions is also obtained for the hyperbolic system of isentropic gas dynamics in eulerian coordinates under the compactness assumption of u x e x t or x e x t in w loc 1 r r 1 2 where u e x t e x t are viscosity velocity and density

increasing the power of the mann whitney test in randomized experiments through flexible covariate adjustment the mann whitney u test is frequently used to evaluate treatment effects in randomized experiments with skewed outcome distributions or small sample sizes it may lack power however because it ignores the auxiliary baseline covariate information that is routinely collected wald and score tests in so called probabilistic index models generalize the mann whitney u test to enable adjustment for covariates but these may lack robustness by demanding correct model specification and do not lend themselves to small sample inference using semiparametric efficiency theory we here propose an alternative extension of the mann whitney u test which increases its power by exploiting covariate information in an objective way and which lends itself to permutation inference simulation studies and an application to an hiv clinical trial show that the proposed permutation test attains the nominal type i error rate and can be drastically more powerful than the classical mann whitney u test copyright 2014 john wiley sons ltd

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

interactions of delta shock waves for the transport equations with split delta functions this paper is concerned with the interactions of shock waves and the vacuum states between the two contact discontinuities for the transport equations the solutions are obtained constructively when the initial data are three piecewise constant states the global structure and large time asymptotic behaviors of the solutions are analyzed case by case moreover it can be found that the riemann solutions are stable for such small perturbations with initial data by studying the limits of the solutions when the perturbed parameter e tends to zero

non selfsimilar solutions for a hyperbolic system of conservation laws in two space dimensions the non selfsimilar riemann problem for a two dimensional nonstrictly hyperbolic system of conservation laws is considered where the initial data are two constant states separated by a smooth curve without dimension reduction or coordinate transformation the two dimensional global solutions are constructed for six cases according to the normal velocities on both sides of the initial discontinuity moreover the interactions of non selfsimilar elementary waves are discussed by respectively taking the initial discontinuity as a parabola and a circle which enable us to provide the global structures of the entropy solutions explicitly c 2012 elsevier inc all rights reserved

existence of global bounded weak solutions to nonsymmetric systems of keyfitz kranzer type in this paper we study the global l solutions for the cauchy problem of nonsymmetric system 1 1 of keyfitz kranzer type when n 1 1 1 is the aw rascle traffic flow model first we introduce a new flux approximation to obtain a lower bound e 0 for the parabolic system generated by adding artificial viscosity to the aw rascle system then using the compensated compactness method with the help of l1 estimate of we t x we prove the pointwise convergence of the viscosity solutions under the general conditions on the function p which includes prototype function p 1 a where 1 0 0 a is a constant second by means of bv estimates on the riemann invariants and the compensated compactness method we prove the global existence of bounded entropy weak solutions for the cauchy problem of general nonsymmetric systems 1 1

non standard shocks in the buckley leverett equation abstract it is shown how delta shock waves which consist of dirac delta distributions and classical shocks can be used to construct non monotone solutions of the buckley leverett equation these solutions are interpreted using a recent variational definition of delta shock waves in which the rankine hugoniot deficit is explicitly accounted for 6 the delta shock waves are also limits of approximate solutions constructed using a recent extension of the weak asymptotic method to complex valued approximations 15 finally it is shown how these non standard shocks can be fitted together to construct similarity and traveling wave solutions which are non monotone but still admissible in the sense that characteristics either enter or are parallel to the shock trajectories

variance component tests of multivariate mediation effects under composite null hypotheses mediation effects of multiple mediators are determined by two associations one between an exposure and mediators s m and the other between the mediators and an outcome conditional on the exposure m y the test for mediation effects is conducted under a composite null hypothesis that is either one of the s m and m y associations is zero or both are zeros without accounting for the composite null the type 1 error rate within a study containing a large number of multimediator tests may be much less than the expected we propose a novel test to address the issue for each mediation test j j 1 j we examine the s m and m y associations using two separate variance component tests assuming a zero mean working distribution with a common variance for the element wise s m and m y associations score tests for the variance components are constructed we transform the test statistics into two normally distributed statistics under the null using a recently developed result we conduct j hypothesis tests accounting for the composite null hypothesis by adjusting for the variances of the normally distributed statistics for the s m and m y associations advantages of the proposed test over other methods are illustrated in simulation studies and a data application where we analyze lung cancer data from the cancer genome atlas to investigate the smoking effect on gene expression through dna methylation in 15 114 genes

efficient estimation of average treatment effects using the estimated propensity score we are interested in estimating the average effect of a binary treatment on a scalar outcome if assignment to the treatment is exogenous or unconfounded that is independent of the potential outcomes given covariates biases associated with simple treatmentcontrol average comparisons can be removed by adjusting for differences in the covariates rosenbaum and rubin 1983 show that adjusting solely for differences between treated and control units in the propensity score removes all biases associated with differences in covariates although adjusting for differences in the propensity score removes all the bias this can come at the expense of efficiency as shown by hahn 1998 heckman ichimura and todd 1998 and robins mark and newey 1992 we show that weighting by the inverse of a nonparametric estimate of the propensity score rather than the true propensity score leads to an efficient estimate of the average treatment effect we provide intuition for this result by showing that this estimator can be interpreted as an empirical likelihood estimator that efficiently incorporates the information about the propensity score

the performance of estimators based on the propensity score we investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required like inverse probability weighting kernel and other variants of matching as well as different parametric models the simulation design used is based on real data usually employed for the evaluation of labour market programmes in germany we vary several dimensions of the design that are of practical importance like sample size the type of the outcome variable and aspects of the selection process we find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators a conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property

sharp sensitivity bounds for mediation under unmeasured mediator outcome confounding it is often of interest to decompose the total effect of an exposure into a component that acts on the outcome through some mediator and a component that acts independently through other pathways said another way we are interested in the direct and indirect effects of the exposure on the outcome even if the exposure is randomly assigned it is often infeasible to randomize the mediator leaving the mediator outcome confounding not fully controlled we develop a sensitivity analysis technique that can bound the direct and indirect effects without parametric assumptions about the unmeasured mediator outcome confounding

sticky particles and scalar conservation laws one dimensional scalar conservation laws with nondecreasing initial conditions and general fluxes are shown to be the appropriate equations to describe large systems of free particles on the real line which stick under collision with conservation of mass and momentum

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

estimation of the failure time distribution in the presence of informative censoring we present a method for estimating the survival curve of a continuous failure time random variable from right censored data our method allows adjustment for informative censoring due to measured prognostic factors for time to event and censoring while simultaneously quantifying the sensitivity of the inference to residual dependence between failure and censoring due to unmeasured factors we present the results of a simulation study and illustrate our approach using data from the aids clinical trial group 175 study

a framework for bayesian nonparametric inference for causal effects of mediation we propose a bayesian non parametric bnp framework for estimating causal effects of mediation the natural direct and indirect effects the strategy is to do this in two parts part 1 is a flexible model using bnp for the observed data distribution part 2 is a set of uncheckable assumptions with sensitivity parameters that in conjunction with part 1 allows identification and estimation of the causal parameters and allows for uncertainty about these assumptions via priors on the sensitivity parameters for part 1 we specify a dirichlet process mixture of multivariate normals as a prior on the joint distribution of the outcome mediator and covariates this approach allows us to obtain a simple closed form of each marginal distribution for part 2 we consider two sets of assumptions a the standard sequential ignorability imai et al 2010 and b weakened set of the conditional independence type assumptions introduced in daniels et al 2012 and propose sensitivity analyses for both we use this approach to assess mediation in a physical activity promotion trial

concentration and cavitation in the vanishing pressure limit of solutions to the euler equations for nonisentropic fluids numerical simulations 2 d riemann problem in gas dynamics and formation of spiral in nonlinear problems in engineering and science numerical and analytical approach beijing 1991 science press beijing 1992 pp 167 179 discrete contin dyn syst 1 1995 555 584 6 2000 419 430 for the euler equations for gas dynamics in the regime of small pressure showed that for one case the particles seem to be more sticky and tend to concentrate near some shock locations and for the other case in the region of rarefaction waves the particles seem to be far apart and tend to form cavitation in the region in this paper we identify and analyze the phenomena of concentration and cavitation by studying the vanishing pressure limit of solutions of the full euler equations for nonisentropic compressible fluids with a scaled pressure it is rigorously shown that any riemann solution containing two shocks and possibly one contact discontinuity to the euler equations for nonisentropic fluids tends to a shock solution to the corresponding transport equations and the intermediate densities between the two shocks tend to a weighted measure that along with the two shocks and possibly contact discontinuity forms the shock as the pressure vanishes by contrast it is also shown that any riemann solution containing two rarefaction waves and possibly one contact discontinuity to the euler equations for nonisentropic fluids tends to a two contact discontinuity solution to the transport equations and the nonvacuum intermediate states between the two rarefaction waves tend to a vacuum state as the pressure vanishes some numerical results exhibiting the processes of concentration and cavitation are presented as the pressure decreases 2003 elsevier b v all rights reserved msc 35l65 35b30 76e19 35q35 35l67 35b25 65m06

a global unique solvability of entropic weak solution to the one dimensional pressureless euler system with a flocking dissipation abstract we present a unique global solvability and flocking estimate of an entropic weak solution to the one dimensional pressureless euler system with a flocking dissipation in all to all coupling setting this model appears naturally as a quasi equilibrium model for hydrodynamic description of cucker smale flocking for the unique global solvability we adopt the variation approach from ding and huang s work 19 on the inhomogeneous pressureless gas dynamic model when initial mass and velocity are locally integrable and bounded measurable functions respectively we give explicit representations for the global entropic weak solutions our results do not require any smallness of initial data except that initial mass density is almost everywhere positive

identification and efficient estimation of the natural direct effect among the untreated the natural direct effect nde or the effect of an exposure on an outcome if an intermediate variable was set to the level it would have been in the absence of the exposure is often of interest to investigators in general the statistical parameter associated with the nde is difficult to estimate in the non parametric model particularly when the intermediate variable is continuous or high dimensional in this paper we introduce a new causal parameter called the natural direct effect among the untreated discus identifiability assumptions propose a sensitivity analysis for some of the assumptions and show that this new parameter is equivalent to the nde in a randomized controlled trial we also present a targeted minimum loss estimator tmle a locally efficient double robust substitution estimator for the statistical parameter associated with this causal parameter the tmle can be applied to problems with continuous and high dimensional intermediate variables and can be used to estimate the nde in a randomized controlled trial with such data additionally we define and discuss the estimation of three related causal parameters the natural direct effect among the treated the indirect effect among the untreated and the indirect effect among the treated

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

on semiparametric estimation of a path specific effect in the presence of mediator outcome confounding path specific effects constitute a broad class of mediated effects from an exposure to an outcome via one or more causal pathways along a set of intermediate variables most of the literature concerning estimation of mediated effects has focused on parametric models with stringent assumptions regarding unmeasured confounding we consider semiparametric inference of a path specific effect when these assumptions are relaxed in particular we develop a suite of semiparametric estimators for the effect along a pathway through a mediator but not through an exposure induced confounder of that mediator these estimators have different robustness properties as each depends on different parts of the likelihood of the observed data one estimator is locally semiparametric efficient and multiply robust the latter property implies that machine learning can be used to estimate nuisance functions we demonstrate these properties as well as finite sample properties of all the estimators in a simulation study we apply our method to an hiv study in which we estimate the effect comparing two drug treatments on a patient s average log cd4 count mediated by the patient s level of adherence but not by previous experience of toxicity which is clearly affected by which treatment the patient is assigned to and may confound the effect of the patient s level of adherence on their virologic outcome

on bayesian estimation of marginal structural models summary the purpose of inverse probability of treatment ipt weighting in estimation of marginal treatment effects is to construct a pseudo population without imbalances in measured covariates thus removing the effects of confounding and informative censoring when performing inference in this article we formalize the notion of such a pseudo population as a data generating mechanism with particular characteristics and show that this leads to a natural bayesian interpretation of ipt weighted estimation using this interpretation we are able to propose the first fully bayesian procedure for estimating parameters of marginal structural models using an ipt weighting our approach suggests that the weights should be derived from the posterior predictive treatment assignment and censoring probabilities answering the question of whether and how the uncertainty in the estimation of the weights should be incorporated in bayesian inference of marginal treatment effects the proposed approach is compared to existing methods in simulated data and applied to an analysis of the canadian co infection cohort

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

radially symmetric shadow wave solutions to the system of pressureless gas dynamics in arbitrary dimensions abstract radially symmetric shadow wave solutions to the system of multidimensional pressureless gas dynamics are introduced which allow one to capture concentration of mass the transformation to a one dimensional system with source terms is performed and physically meaningful boundary conditions at the origin are determined entropy conditions are derived and applied to single out physical nonnegative mass and dissipative entropic solutions a complete solution to the pseudo riemann problem with initial data exhibiting a single delta shock on a sphere is obtained

high mach number limit of one dimensional piston problem for non isentropic compressible euler equations polytropic gas we study the high mach number limit of the one dimensional piston problem for the full compressible euler equations of polytropic gas for both cases that the piston rushes into or recedes from the uniform still gas at a constant speed there are two different situations and one needs to consider measure solutions of the euler equations to deal with the concentration of mass on the piston or formation of vacuum we formulate the piston problem in the framework of radon measure solutions and show its consistency by proving that the integral weak solutions of the piston problems converge weakly in the sense of measures to singular measure solutions of the limiting problems as the mach number of the piston increases to infinity we study the high mach number limit of the one dimensional piston problem for the full compressible euler equations of polytropic gas for both cases that the piston rushes into or recedes from the uniform still gas at a constant speed there are two different situations and one needs to consider measure solutions of the euler equations to deal with the concentration of mass on the piston or formation of vacuum we formulate the piston problem in the framework of radon measure solutions and show its consistency by proving that the integral weak solutions of the piston problems converge weakly in the sense of measures to singular measure solutions of the limiting problems as the mach number of the piston increases to infinity

covariate adjustment using propensity scores for dependent censoring problems in the accelerated failure time model in many medical studies estimation of the association between treatment and outcome of interest is often of primary scientific interest standard methods for its evaluation in survival analysis typically require the assumption of independent censoring this assumption might be invalid in many medical studies where the presence of dependent censoring leads to difficulties in analyzing covariate effects on disease outcomes this data structure is called semicompeting risks data for which many authors have proposed an artificial censoring technique however confounders with large variability may lead to excessive artificial censoring which subsequently results in numerically unstable estimation in this paper we propose a strategy for weighted estimation of the associations in the accelerated failure time model weights are based on propensity score modeling of the treatment conditional on confounder variables this novel application of propensity scores avoids excess artificial censoring caused by the confounders and simplifies computation monte carlo simulation studies and application to aids and cancer research are used to illustrate the methodology

multiple robustness in factorized likelihood models we consider inference under a nonparametric or semiparametric model with likelihood that factorizes as the product of two or more variation independent factors we are interested in a finite dimensional parameter that depends on only one of the likelihood factors and whose estimation requires the auxiliary estimation of one or several nuisance functions we investigate general structures conducive to the construction of so called multiply robust estimating functions whose computation requires postulating several dimension reducing models but which have mean zero at the true parameter value provided one of these models is correct

estimation of a semiparametric natural direct effect model incorporating baseline covariates establishing cause effect relationships is a standard goal of empirical science once the presence of a causal relationship is established the precise causal mechanism involved becomes a topic of interest a particularly popular type of mechanism analysis concerns questions of mediation that is to what extent an effect is direct and to what extent it is mediated by a third variable a semiparametric theory has recently been proposed which allows multiply robust estimation of direct and mediated marginal effect functionals in observational studies tchetgen tchetgen shpitser 2012 in this paper we extend the new theory to handle parametric models of natural direct and indirect effects within levels of pre exposure variables with an identity or log link function where the model for the observed data likelihood is otherwise unrestricted we show that estimation is generally not feasible in this model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations given high dimensional covariates thus we consider multiply robust estimation and propose a more general model which assumes that a subset but not all of several working models holds

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

eulerian droplet model delta shock waves and solution of the riemann problem abstract we study an eulerian droplet model which can be seen as the pressureless gas system with a source term a subsystem of this model and the inviscid burgers equation with source term the condition for loss of regularity of a solution to burgers equation with source term is established the same condition applies to the eulerian droplet model and its subsystem the riemann problem for the eulerian droplet model is constructively solved by going through the solution of the riemann problems for the inviscid burgers equation with a source term and the subsystem respectively under suitable generalized rankine hugoniot relations and entropy condition the existence of delta shock solution is established the existence of a solution to the generalized rankine hugoniot conditions is proven some numerical illustrations are presented

estimation in partially linear models with missing covariates the partially linear model y xt z has been studied extensively when data are completely observed in this article we consider the case where the covariate x is sometimes missing with missingness probability depending on y z new methods are developed for estimating and our methods are shown to outperform asymptotically methods based only on the complete data asymptotic efficiency is discussed and the semiparametric efficient score function is derived justification of the use of the nonparametric bootstrap in this context is sketched the proposed estimators are extended to a working independence analysis of longitudinal clustered data and applied to analyze an aids clinical trial dataset the results of a simulation experiment are also given to illustrate our approach

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

inverse odds ratio weighted estimation for causal mediation analysis an important scientific goal of studies in the health and social sciences is increasingly to determine to what extent the total effect of a point exposure is mediated by an intermediate variable on the causal pathway between the exposure and the outcome a causal framework has recently been proposed for mediation analysis which gives rise to new definitions formal identification results and novel estimators of direct and indirect effects in the present paper the author describes a new inverse odds ratio weighted iorw approach to estimate so called natural direct and indirect effects the approach which uses as a weight the inverse of an estimate of the odds ratio function relating the exposure and the mediator is universal in that it can be used to decompose total effects in a number of regression models commonly used in practice specifically the approach may be used for effect decomposition in generalized linear models with a nonlinear link function and in a number of other commonly used models such as the cox proportional hazards regression for a survival outcome the approach is simple and can be implemented in standard software provided a weight can be specified for each observation an additional advantage of the method is that it easily incorporates multiple mediators of a categorical discrete or continuous nature

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

method for solving eigenvalue problems of the helmholtz equation with a circular outer and a number of eccentric circular inner boundaries the eigenvalue problem of the helmholtz equation is of importance because various physical phenomena are governed by this equation this article presents a method for solving the boundary value problem governed by the helmholtz equation with a circular outer boundary and a number of eccentric circular inner boundaries in this problem it is difficult to satisfy the multiconnected boundary conditions the present analysis uses the point matching approach for treating the inner boundary conditions and presents the expression for finding the eigenvalues numerical calculations have been carried out for the system having one two or four eccentric circular inner boundaries

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

the riemann problem admitting δ δ shocks and vacuum states the vanishing viscosity approach in this paper using the vanishing viscosity method we construct a solution of the riemann problem for the system of conservation laws ut u2 x 0 vt 2 uv x 0 wt 2 v2 uw x 0 with the initial data u x 0 v x 0 w x 0 u v w x 0 this problem admits shock wave type solutions and vacuum states shock is a new type of singular solutions to systems of conservation laws first introduced in e yu panov v m shelkovich shock waves as a new type of solutions to systems of conservation laws j differential equations 228 2006 49 86 it is a distributional solution of the riemann problem such that for t 0 its second component v may contain dirac measures the third component w may contain a linear combination of dirac measures and their derivatives while the first component u has bounded variation using the above mentioned results we also solve the shock cauchy problem for the first two equations of the above system since shocks can be constructed by the vanishing viscosity method they are natural solutions to systems of conservation laws we describe the formation of the shocks and the vacuum states from smooth solutions of the parabolic problem the results of this paper as well as those of the above mentioned paper show that solutions of systems of conservation laws can develop not only dirac measures as in the case of shocks but their derivatives as well

sensitivity analysis for unobserved confounding of direct and indirect effects using uncertainty intervals to estimate direct and indirect effects of an exposure on an outcome from observed data strong assumptions about unconfoundedness are required since these assumptions cannot be tested using the o

contagion shocks in one dimension we consider an agent based model of emotional contagion coupled with motion in one dimension that has recently been studied in the computer science community the model involves movement with a speed proportional to a fear variable that undergoes a temporal consensus averaging based on distance to other agents we study the effect of riemann initial data for this problem leading to shock dynamics that are studied both within the agent based model as well as in a continuum limit we examine the behavior of the model under distinguished limits as the characteristic contagion interaction distance and the interaction timescale both approach zero the limiting behavior is related to a classical model for pressureless gas dynamics with sticky particles in comparison we observe a threshold for the interaction distance vs interaction timescale that produce qualitatively different behavior for the system in one case particle paths do not cross and there is a natural eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit

generalized variational principles global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics we study systems of conservation laws arising in two models of adhesion particle dynamics the first is the system of free particles which stick under collision the second is a system of gravitationally interacting particles which also stick under collision in both cases mass and momentum are conserved at the collisions so the dynamics is described by 2 2 systems of conservations laws we show that for these systems global weak solutions can be constructed explicitly using the initial data by a procedure analogous to the lax oleinik variational principle for scalar conservation laws however this weak solution is not unique among weak solutions satisfying the standard entropy condition we also study a modified gravitational model in which instead of momentum some other weighted velocity is conserved at collisions for this model we prove both existence and uniqueness of global weak solutions we then study the qualitative behavior of the solutions with random initial data we show that for continuous but nowhere differentiable random initial velocities all masses immediately concentrate on points even though they were continuously distributed initially and the set of shock locations is dense

free vibration analysis of circular plates with multiple circular holes using indirect biems in this paper a semi analytical approach is proposed to solve natural frequencies and natural modes for circular plates with multiple circular holes by using the indirect formulation in conjunction with degenerate kernels and fourier series all the kernels in the indirect formulation are expanded into degenerate form by uniformly collocating points on the boundary a linear algebraic system can be constructed the direct searching approach is adopted to determine the natural frequency through singular value decomposition svd after determining the unknown fourier coefficients the corresponding mode shape is obtained by using the indirect boundary integral formulations the results of the annular plate as a special case are compared with the analytical solution to verify the validity of the present method for the cases of circular plates with multiple circular holes the results are also compared with those of finite element method fem using abaqus besides the effect of eccentricity of the hole on the natural frequencies is also considered good accuracy high rate of convergence and computational efficiency are the main features of the present method due to the semianalytical procedure r 2007 elsevier ltd all rights reserved

estimation of controlled direct effects when regression models adjust for mediators on the causal path from exposure to outcome the regression coefficient of exposure is commonly viewed as a measure of the direct exposure effect this interpretation can be misleading even with a randomly assigned exposure this is because adjustment for post exposure measurements introduces bias whenever their association with the outcome is confounded by more than just the exposure by the same token adjustment for such confounders stays problematic when these are themselves affected by the exposure robins accommodated this by introducing linear structural nested direct effect models with direct effect parameters that can be estimated by using inverse probability weighting by a conditional distribution of the mediator the resulting estimators are consistent but inefficient and can be extremely unstable when the mediator is absolutely continuous we develop direct effect estimators which are not only more efficient but also consistent under a less demanding model for a conditional expectation of the outcome we find that the one estimator which avoids inverse probability weighting altogether performs best this estimator is intuitive computationally straightforward and as demonstrated by simulation competes extremely well with ordinary least squares estimators in settings where standard regression is valid

semiparametric efficiency in gmm models with auxiliary data we study semiparametric efficiency bounds and efficient estimation of parameters defined through general moment restrictions with missing data identification relies on auxiliary data containing information about the distribution of the missing variables conditional on proxy variables that are observed in both the primary and the auxiliary database when such distribution is common to the two data sets the auxiliary sample can be independent of the primary sample or can be a subset of it for both cases we derive bounds when the probability of missing data given the proxy variables is unknown or known or belongs to a correctly specified parametric family we find that the conditional probability is not ancillary when the two samples are independent for all cases we discuss efficient semiparametric estimators an estimator based on a conditional expectation projection is shown to require milder regularity conditions than one based on inverse probability weighting

generalized causal mediation analysis the goal of mediation analysis is to assess direct and indirect effects of a treatment or exposure on an outcome more generally we may be interested in the context of a causal model as characterized by a directed acyclic graph dag where mediation via a specific path from exposure to outcome may involve an arbitrary number of links or stages methods for estimating mediation or pathway effects are available for a continuous outcome and a continuous mediator related via a linear model while for a categorical outcome or categorical mediator methods are usually limited to two stage mediation we present a method applicable to multiple stages of mediation and mixed variable types using generalized linear models we define pathway effects using a potential outcomes framework and present a general formula that provides the effect of exposure through any specified pathway some pathway effects are nonidentifiable and their estimation requires an assumption regarding the correlation between counterfactuals we provide a sensitivity analysis to assess the impact of this assumption confidence intervals for pathway effect estimates are obtained via a bootstrap method the method is applied to a cohort study of dental caries in very low birth weight adolescents a simulation study demonstrates low bias of pathway effect estimators and close to nominal coverage rates of confidence intervals we also find low sensitivity to the counterfactual correlation in most scenarios

two step estimation in ratio of mediator probability weighted causal mediation analysis this study investigates appropriate estimation of estimator variability in the context of causal mediation analysis that employs propensity score based weighting such an analysis decomposes the total effect of a treatment on the outcome into an indirect effect transmitted through a focal mediator and a direct effect bypassing the mediator ratio of mediator probability weighting estimates these causal effects by adjusting for the confounding impact of a large number of pretreatment covariates through propensity score based weighting in step 1 a propensity score model is estimated in step 2 the causal effects of interest are estimated using weights derived from the prior step s regression coefficient estimates statistical inferences obtained from this 2 step estimation procedure are potentially problematic if the estimated standard errors of the causal effect estimates do not reflect the sampling uncertainty in the estimation of the weights this study extends to ratio of mediator probability weighting analysis a solution to the 2 step estimation problem by stacking the score functions from both steps we derive the asymptotic variance covariance matrix for the indirect effect and direct effect 2 step estimators provide simulation results and illustrate with an application study our simulation results indicate that the sampling uncertainty in the estimated weights should not be ignored the standard error estimation using the stacking procedure offers a viable alternative to bootstrap standard error estimation we discuss broad implications of this approach for causal analysis involving propensity score based weighting

mediation analysis with time varying exposures and mediators in this paper we consider causal mediation analysis when exposures and mediators vary over time we give non parametric identification results discuss parametric implementation and also provide a weighting approach to direct and indirect effects based on combining the results of two marginal structural models we also discuss how our results give rise to a causal interpretation of the effect estimates produced from longitudinal structural equation models when there are time varying confounders affected by prior exposure and mediator natural direct and indirect effects are not identified however we define a randomized interventional analogue of natural direct and indirect effects that are identified in this setting the formula that identifies these effects we refer to as the mediational g formula when there is no mediation the mediational g formula reduces to robins regular g formula for longitudinal data when there are no time varying confounders affected by prior exposure and mediator values then the mediational g formula reduces to a longitudinal version of pearl s mediation formula however the mediational g formula itself can accommodate both mediation and time varying confounders and constitutes a general approach to mediation analysis with time varying exposures and mediators

the riemann problem for pressureless fluid dynamics with distribution solutions in colombeau s sense the riemann problem for the equations of pressureless fluid dynamics was considered solutions of this problem were constructed by employing the viscosity vanishing approach for some initial data solutions showed high singularity around the shock waves a new mathematical theory of generalized functions initiated by j f colombeau was applied to dealing with the multiplication of singular distributions as a byproduct the entropy condition was obtained for singular distribution solutions

stability of the riemann solutions for a nonstrictly hyperbolic system of conservation laws abstract we prove that the riemann solutions are stable for a nonstrictly hyperbolic system of conservation laws under local small perturbations of the riemann initial data the proof is based on the detailed analysis of the interactions of delta shock waves with shock waves and rarefaction waves during the interaction process of the delta shock wave with the rarefaction wave a new kind of nonclassical wave namely a delta contact discontinuity is discovered here which is a dirac delta function supported on a contact discontinuity and has already appeared in the interaction process for the magnetohydrodynamics equations m nedeljkov and m oberguggenberger interactions of delta shock waves in a strictly hyperbolic system of conservation laws j math anal appl 344 2008 1143 1157 moreover the global structures and large time asymptotic behaviors of the solutions are constructed and analyzed case by case

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

causal mediation analysis with multiple mediators in diverse fields of empirical research including many in the biological sciences attempts are made to decompose the effect of an exposure on an outcome into its effects via a number of different pathways for example we may wish to separate the effect of heavy alcohol consumption on systolic blood pressure sbp into effects via body mass index bmi via gamma glutamyl transpeptidase ggt and via other pathways much progress has been made mainly due to contributions from the field of causal inference in understanding the precise nature of statistical estimands that capture such intuitive effects the assumptions under which they can be identified and statistical methods for doing so these contributions have focused almost entirely on settings with a single mediator or a set of mediators considered en bloc in many applications however researchers attempt a much more ambitious decomposition into numerous path specific effects through many mediators in this article we give counterfactual definitions of such path specific estimands in settings with multiple mediators when earlier mediators may affect later ones showing that there are many ways in which decomposition can be done we discuss the strong assumptions under which the effects are identified suggesting a sensitivity analysis approach when a particular subset of the assumptions cannot be justified these ideas are illustrated using data on alcohol consumption sbp bmi and ggt from the izhevsk family study we aim to bridge the gap from single mediator theory to multiple mediator practice highlighting the ambitious nature of this endeavor and giving practical suggestions on how to proceed

bias reduced doubly robust estimation over the past decade doubly robust estimators have been proposed for a variety of target parameters in causal inference and missing data models these are asymptotically unbiased when at least one of two nuisance working models is correctly specified regardless of which while their asymptotic distribution is not affected by the choice of root n consistent estimators of the nuisance parameters indexing these working models when all working models are correctly specified this choice of estimators can have a dramatic impact under misspecification of at least one working model in this article we will therefore propose a simple and generic estimation principle for the nuisance parameters indexing each of the working models which is designed to improve the performance of the doubly robust estimator of interest relative to the default use of maximum likelihood estimators for the nuisance parameters the proposed approach locally minimizes the squared first order asymptotic bias of the doubly robust estim

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

robust inference on population indirect causal effects the generalized front door criterion standard methods for inference about direct and indirect effects require stringent no unmeasured confounding assumptions which often fail to hold in practice particularly in observational studies the goal of the paper is to introduce a new form of indirect effect the population intervention indirect effect that can be non parametrically identified in the presence of an unmeasured common cause of exposure and outcome this new type of indirect effect captures the extent to which the effect of exposure is mediated by an intermediate variable under an intervention that holds the component of exposure directly influencing the outcome at its observed value the population intervention indirect effect is in fact the indirect component of the population intervention effect introduced by hubbard and van der laan interestingly our identification criterion generalizes judea pearl s front door criterion as it does not require no direct effect of exposure not mediated by the intermediate variable for inference we develop both parametric and semiparametric methods including a novel doubly robust semiparametric locally efficient estimator that perform very well in simulation studies finally the methods proposed are used to measure the effectiveness of monetary saving recommendations among women enrolled in a maternal health programme in tanzania

well posedness for pressureless flow we study the uniqueness problem for pressureless gases previous results on this topic are only known for the case when the initial data is assumed to be a bounded measurable function this assumption is unnatural because the solution is in general a radon measure in this paper the uniqueness of the weak solution is proved for the case when the initial data is a radon measure we show that besides the oleinik entropy condition it is also important to require the energy to be weakly continuous initially our uniqueness result is obtained in the same functional space as the existence theorem

semiparametric theory for causal mediation analysis efficiency bounds multiple robustness and sensitivity analysis whilst estimation of the marginal total causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences in recent years investigators have also become increasingly interested in mediation analysis specifically upon evaluating the total effect of the exposure investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure not through or through a mediator variable that occurs subsequently to the exposure and prior to the outcome although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect similar methods for mediation analysis are currently lacking thus this paper develops a general semiparametric framework for obtaining inferences about so called marginal natural direct and indirect causal effects while appropriately accounting for a large number of pre exposure confounding factors for the exposure and the mediator variables our analytic framework is particularly appealing because it gives new insights on issues of efficiency and robustness in the context of mediation analysis in particular we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable

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

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

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

a higher order asymptotic approximation for the fundamental frequency of a multiply connected membrane abstract the fundamental frequency of a fixed membrane is the square root of the lowest eigenvalue of negative laplace operator with dirichlet boundary conditions a multiply connected membrane with inner cores of vanishing maximal dimensions 2 c j is considered in the present article the modified perturbation method developed for a doubly connected membrane is extended to provide a general formula for the fundamental frequency of the multiply connected membrane a higher order asymptotic approximation as c j 0 for the fundamental frequency of a membrane with inner circular cores of radius c j is specified it is an excellent extension of the results in the literature moreover a second order asymptotic approximation as c 0 for the fundamental frequency of a circular membrane of radius 1 with finitely many inner circular cores of small radius c is found and computed explicitly the effects of the positions of the inner cores on the second order asymptotic approximation are investigated the accuracy of the second order asymptotic approximation is also shown by the comparisons among the asymptotic approximations and the numerical values computed by other investigators