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

functions analytic on the half plane as quantum mechanical states a transform between the state space of one dimensional quantum mechanical systems and a direct sum of two spaces of square integrable functions analytic on the open upper half plane is constructed it gives a representation of usual quantum mechanics on which the free evolution is trivial and the representation of canonical transformation very simple generalizations to higher dimensions are also discussed

using information on realized effects to determine prospective causal effects the potential outcomes approach to causal inference postulates that each individual has a number of possibly latent outcomes each of which would be observed under a different treatment for any individual some of these outcomes will be unobservable or counterfactual information about post treatment characteristics sometimes allows statements about what would have happened if an individual or group with these characteristics had received a different treatment these are statements about the realized effects of the treatment determining the likely effect of an intervention before making a decision involves inference about effects in populations defined only by characteristics observed before decisions about treatment are made information on realized effects can tighten bounds on these prospectively defined measures of the intervention effect we derive formulae for the bounds and their sampling variances and illustrate these points with data from a hypothetical study of the efficacy of screening mammography

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

causal inference in paired two arm experimental studies under noncompliance with application to prognosis of myocardial infarction motivated by a study about prompt coronary angiography in myocardial infarction we propose a method to estimate the causal effect of a treatment in two arm experimental studies with possible noncompliance in both treatment and control arms we base the method on a causal model for repeated binary outcomes before and after the treatment which includes individual covariates and latent variables for the unobserved heterogeneity between subjects moreover given the type of noncompliance the model assumes the existence of three subpopulations of subjects compliers never takers and always takers we estimate the model using a two step estimator at the first step we estimate the probability that a subject belongs to one of the three subpopulations on the basis of the available covariates at the second step we estimate the causal effects through a conditional logistic method the implementation of which depends on the results from the first step the estimator is approximately consistent and under certain circumstances exactly consistent we provide evidence that the bias is negligible in relevant situations we compute standard errors on the basis of a sandwich formula the application shows that prompt coronary angiography in patients with myocardial infarction may significantly decrease the risk of other events within the next 2 years with a log odds of about 2 given that noncompliance is significant for patients being given the treatment because of high risk conditions classical estimators fail to detect or at least underestimate this effect copyright 2013 john wiley sons ltd

estimation of controlled direct effects on a dichotomous outcome using logistic structural direct effect models we consider the problem of assessing whether an exposure affects a dichotomous outcome other than by modifying a given mediator the standard approach logistic regression adjusting for both exposure and the mediator is known to be biased in the presence of confounders for the mediator outcome relationship because additional regression adjustment for such confounders is only justified when they are not affected by the exposure inverse probability weighting has been advocated but is not ideally tailored to mediators that are continuous or have strong measured predictors we overcome this limitation by developing inference for a novel class of causal models that are closely related to robins logistic structural direct effect models but do not inherit their difficulties of estimation we study identification and efficient estimation under the assumption that all confounders for the exposure outcome and mediator outcome relationships have been measured and find adequate performance in simulation studies we discuss extensions to case control studies and relevant implications for the generic problem of adjustment for time varying confounding

instrumental variable estimators for binary outcomes instrumental variables ivs can be used to construct estimators of exposure effects on the outcomes of studies affected by nonignorable selection of the exposure estimators that fail to adjust for the effects of nonignorable selection will be biased and inconsistent such situations commonly arise in observational studies but are also a problem for randomized experiments affected by nonignorable noncompliance in this article we review iv estimators for studies in which the outcome is binary and consider the links between different approaches developed in the statistics and econometrics literatures the implicit assumptions made by each method are highlighted and compared within our framework we illustrate our findings through the reanalysis of a randomized placebo controlled trial and highlight important directions for future work in this area

predicting extreme avalanches in self organized critical sandpiles in a finite size abelian sandpile model extreme avalanches are repelling each other taking a time series of the avalanche size and using a decision variable derived from that we predict the occurrence of a particularly large avalanche in the next time step the larger the magnitude of these target avalanches the better is their predictability the predictability which is based on a finite size effect is discussed as a function of the system size

influence of the event magnitude on the predictability of an extreme event we investigate the predictability of extreme events in time series the focus of this work is to understand under which circumstances large events are better predictable than smaller events therefore we use a simple prediction algorithm based on precursory structures which are identified using the maximum likelihood principle using the receiver operator characteristic curve as a measure for the quality of predictions we find that the dependence on the event size is closely linked to the probability distribution function of the underlying stochastic process we evaluate this dependence on the probability distribution function analytically and numerically if we assume that the optimal precursory structures are used to make the predictions we find that large increments are better predictable if the underlying stochastic process has a gaussian probability distribution function whereas larger increments are harder to predict if the underlying probability distribution function has a power law tail in the case of an exponential distribution function we find no significant dependence on the event size furthermore we compare these results with predictions of increments in correlated data namely velocity increments of a free jet flow the velocity increments in the free jet flow are in dependence on the time scale either asymptotically gaussian or asymptotically exponential distributed the numerical results for predictions within free jet data are in good agreement with the previous analytical considerations for random numbers

structural nested mean models for assessing time varying effect moderation this article considers the problem of assessing causal effect moderation in longitudinal settings in which treatment or exposure is time varying and so are the covariates said to moderate its effect intermediate causal effects that describe time varying causal effects of treatment conditional on past covariate history are introduced and considered as part of robins structural nested mean model two estimators of the intermediate causal effects and their standard errors are presented and discussed the first is a proposed two stage regression estimator the second is robins g estimator the results of a small simulation study that begins to shed light on the small versus large sample performance of the estimators and on the bias variance trade off between the two estimators are presented the methodology is illustrated using longitudinal data from a depression study

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

semiparametric analysis of the additive risk model in contrast to the proportional hazards model the additive risk model specifies that the hazard function associated with a set of possibly time varying covariates is the sum of rather than the product of the baseline hazard function and the regression function of covariates this formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model and is more plausible than the latter for many applications in the present paper simple procedures with high efficiencies are developed for making inference about the regression parameters under the additive risk model with an unspecified baseline hazard function

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

the statistical analysis of failure time data preface 1 introduction 1 1 failure time data 1 2 failure time distributions 1 3 time origins censoring and truncation 1 4 estimation of the survivor function 1 5 comparison of survival curves 1 6 generalizations to accommodate delayed entry 1 7 counting process notation bibliographic notes exercises and complements 2 failure time models 2 1 introduction 2 2 some continuous parametric failure time models 2 3 regression models 2 4 discrete failure time models bibliographic notes exercises and complements 3 inference in parametric models and related topics 3 1 introduction 3 2 censoring mechanisms 3 3 censored samples from an exponential distribution 3 4 large sample likelihood theory 3 5 exponential regression 3 6 estimation in log linear regression models 3 7 illustrations in more complex data sets 3 8 discrimination among parametric models 3 9 inference with interval censoring 3 10 discussion bibliographic notes exercises and complements 4 relative risk cox regression models 4 1 introduction 4 2 estimation of beta 4 3 estimation of the baseline hazard or survivor function 4 4 inclusion of strata 4 5 illustrations 4 6 counting process formulas 4 7 related topics on the cox model 4 8 sampling from discrete models bibliographic notes exercises and complements 5 counting processes and asymptotic theory 5 1 introduction 5 2 counting processes and intensity functions 5 3 martingales 5 4 vector valued martingales 5 5 martingale central limit theorem 5 6 asymptotics associated with chapter 1 5 7 asymptotic results for the cox model 5 8 asymptotic results for parametric models 5 9 efficiency of the cox model estimator 5 10 partial likelihood filtration bibliographic notes exercises and complements 6 likelihood construction and further results 6 1 introduction 6 2 likelihood construction in parametric models 6 3 time dependent covariates and further remarks on likelihood construction 6 4 time dependence in the relative risk model 6 5 nonnested conditioning events 6 6 residuals and model checking for the cox model bibliographic notes exercises and complements 7 rank regression and the accelerated failure time model 7 1 introduction 7 2 linear rank tests 7 3 development and properties of linear rank tests 7 4 estimation in the accelerated failure time model 7 5 some related regression models bibliographic notes exercises and complements 8 competing risks and multistate models 8 1 introduction 8 2 competing risks 8 3 life history processes bibliographic notes exercises and complements 9 modeling and analysis of recurrent event data 9 1 introduction 9 2 intensity processes for recurrent events 9 3 overall intensity process modeling and estimation 9 4 mean process modeling and estimation 9 5 conditioning on aspects of the counting process history bibliographic notes exercises and complements 10 analysis of correlated failure time data 10 1 introduction 10 2 regression models for correlated failure time data 10 3 representation and estimation of the bivariate survivor function 10 4 pairwise dependency estimation 10 5 illustration australian twin data 10 6 approaches to nonparametric estimation of the bivariate survivor function 10 7 survivor function estimation in higher dimensions bibliographic notes exercises and complements 11 additional failure time data topics 11 1 introduction 11 2 stratified bivariate failure time analysis 11 3 fixed study period survival studies 11 4 cohort sampling and case control studies 11 5 missing covariate data 11 6 mismeasured covariate data 11 7 sequential testing with failure time endpoints 11 8 bayesian analysis of the proportional hazards model 11 9 some analyses of a particular data set bibliographic notes exercises and complements glossary of notation appendix a some sets of data appendix b supporting technical material bibliography author index subject index

analytic representations based on su 1 1 coherent states and their applications we consider two analytic representations of the su 1 1 lie group the representation in the unit disc based on the su 1 1 perelomov coherent states and the barut girardello representation based on the eigenstates of the su 1 1 lowering generator we show that these representations are related through a laplace transform a weak resolution of the identity in terms of the perelomov su 1 1 coherent states is presented which is valid even when the bargmann index k is smaller than various applications of these results in the context of the two photon realization of su 1 1 in quantum optics are also discussed

estimation of treatment effects in randomised trials with non compliance and a dichotomous outcome using structural mean models in this paper we consider the estimation of the effect of received treatment in randomised clinical trials with non compliance and a dichotomous outcome using structural mean models we allow both for the assigned and received treatments to be continuous categorical or ordinal and for the possibility that the assigned treatment has a direct effect on the outcome through pathways other than the received treatment we also consider the application of our results to observational studies the parameters f of a structural mean model measure on an appropriate scale how the effect of the received treatment on the treated population varies across levels of pre treatment covariates thus these models are useful for assessing whether or not the effect of received treatment is modified by baseline covariates robins 1989 1994 showed that when the randomisation probabilities are known both additive and multiplicative structural mean models that respectively impose a linear

two stage instrumental variable methods for estimating the causal odds ratio analysis of bias we present closed form expressions of asymptotic bias for the causal odds ratio from two estimation approaches of instrumental variable logistic regression i the two stage predictor substitution 2sps method and ii the two stage residual inclusion 2sri approach under the 2sps approach the first stage model yields the predicted value of treatment as a function of an instrument and covariates and in the second stage model for the outcome this predicted value replaces the observed value of treatment as a covariate under the 2sri approach the first stage is the same but the residual term of the first stage regression is included in the second stage regression retaining the observed treatment as a covariate our bias assessment is for a different context from that of terza j health econ 2008 27 3 531 543 who focused on the causal odds ratio conditional on the unmeasured confounder whereas we focus on the causal odds ratio among compliers under the principal stratification framework our closed form bias results show that the 2sps logistic regression generates asymptotically biased estimates of this causal odds ratio when there is no unmeasured confounding and that this bias increases with increasing unmeasured confounding the 2sri logistic regression is asymptotically unbiased when there is no unmeasured confounding but when there is unmeasured confounding there is bias and it increases with increasing unmeasured confounding the closed form bias results provide guidance for using these iv logistic regression methods our simulation results are consistent with our closed form analytic results under different combinations of parameter settings

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

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

the barut girardello coherent states it is shown that the completeness problem of the sl 2 r coherent states proposed by barut and girardello leads to a moment problem not a mellin transform this moment problem which also appears in the theory of para bose oscillators has been solved following the sharma mehta mukunda sudarshan solution of the problem the matrix element of finite transformation in the coherent state basis is shown to satisfy a quasiorthogonality condition analogous to the orthogonality condition of the matrix element in the canonical basis finally the barut girardello hilbert space of entire analytic functions of growth 1 1 turns out to be only a subspace of bargmann s well known hilbert space of analytic functions this subspace which has been called the reduced bargmann space in a previous paper is an invariant subspace of sl 2 r with this identification the generators of the group in this realization turn out to be the well known boson operators of holman and biedenharn

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

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

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

on the conditional logistic estimator in two arm experimental studies with non compliance and before after binary outcomes the behavior of the conditional logistic estimator is analyzed under a causal model for two arm experimental studies with possible non compliance in which the effect of the treatment is measured by a binary response variable we show that when non compliance may only be observed in the treatment arm the effect measured on the logit scale of the treatment on compliers and that of the control on non compliers can be identified and consistently estimated under mild conditions the same does not happen for the effect of the control on compliers a simple correction of the conditional logistic estimator is then proposed which allows us to considerably reduce the bias in estimating this quantity and the causal effect of the treatment over control on compliers a two step estimator results on the basis of which we can also set up a wald test for the hypothesis of absence of a causal effect of the treatment the asymptotic properties of the estimator are studied by exploiting the general theory on maximum likelihood estimation of misspecified models finite sample properties of the estimator and of the related wald test are studied by simulation the extension of the approach to the case of missing responses is also outlined the approach is illustrated by an application to a dataset deriving from a study on the efficacy of a training course on the breast self examination practice copyright 2010 john wiley sons ltd

data driven prediction of thresholded time series of rainfall and self organized criticality models we study the occurrence of events subject to threshold in a representative self organized criticality soc sandpile model and in high resolution rainfall data the predictability in both systems is analyzed by means of a decision variable sensitive to event clustering and the quality of the predictions is evaluated by the receiver operating characteristic roc method in the case of the soc sandpile model the scaling of quiet time distributions with increasing threshold leads to increased predictability of extreme events a scaling theory allows us to understand all the details of the prediction procedure and to extrapolate the shape of the roc curves for the most extreme events for rainfall data the quiet time distributions do not scale for high thresholds which means that the corresponding roc curves cannot be straightforwardly related to those for lower thresholds in this way roc curves are useful for highlighting differences in predictability of extreme events between toy models and real world phenomena

poincare contraction of su 1 1 fock bargmann structure some aspects of the contraction process so0 1 2 to poincare are studied the starting point is the choice of a suitable parametrization for the de sitterian phase space so0 1 2 so 2 approximately su 1 1 u 1 the authors show that the contraction to poincare must be realized by restricting the fock bargmann space to a specific subspace this constraint is necessary to make the divergent terms disappear in particular the classical result according to which the discrete series representation of su 1 1 contracts onto the wigner representation p m is described at a global level

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

analytic and contour representations in the unit disk based on su 1 1 coherent states a contour representation in the unit disk based on su 1 1 coherent states is introduced the scalar product is given by a contour integral the regions of convergence of the functions representing ket and bra states are studied an analytic representation in the unit disk is also considered where the scalar product is represented by an integral over the unit disk with the lobachevsky measure various relations which connect these analytic functions with other phase space quantities are derived

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

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

causal models for randomized trials with two active treatments and continuous compliance in many clinical trials compliance with assigned treatment could be measured on a continuous scale e g the proportion of assigned treatment actually taken in general inference about principal causal effects can be challenging particularly when there are two active treatments the problem is exacerbated for continuous measures of compliance we address this issue by first proposing a structural model for the principal effects we then specify compliance models within each arm of the study these marginal models are identifiable the joint distribution of the observed and counterfactual compliance variables is assumed to follow a gaussian copula model which links the two marginal models and includes a dependence parameter that cannot be identified this dependence parameter can be varied as part of a sensitivity analysis we illustrate the methodology with an analysis of data from a smoking cessation trial as part of the analysis we estimate causal effects at particular levels of the compliance variables and within subpopulations that have similar compliance behavior

representation and properties of para bose oscillator operators ii coherent states and the minimum uncertainty states the energy position and momentum eigenstates of a para bose oscillator system were considered in paper i here we consider the bargmann or the analytic function description of the para bose system this brings in in a natural way the coherent states z defined as the eigenstates of the annihilation operator the transformation functions relating this description to the energy position and momentum eigenstates are explicitly obtained possible resolution of the identity operator using coherent states is examined a particular resolution contains two integrals one containing the diagonal basis z z and the other containing the pseudodiagonal basis z z we briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations the problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible dependence of this minimum value is considered

severity of bias of a simple estimator of the causal odds ratio in mendelian randomization studies mendelian randomization studies estimate causal effects using genetic variants as instruments instrumental variable methods are straightforward for linear models but epidemiologists often use odds ratios to quantify effects also odds ratios are often the quantities reported in meta analyses many applications of mendelian randomization dichotomize genotype and estimate the population causal log odds ratio for unit increase in exposure by dividing the genotype disease log odds ratio by the difference in mean exposure between genotypes this wald type estimator is biased even in large samples but whether the magnitude of bias is of practical importance is unclear we study the large sample bias of this estimator in a simple model with a continuous normally distributed exposure a single unobserved confounder that is not an effect modifier and interpretable parameters we focus on parameter values that reflect scenarios in which we apply mendelian randomization including realistic values for the degree of confounding and strength of the causal effect we evaluate this estimator and the causal odds ratio using numerical integration and obtain approximate analytic expressions to check results and gain insight a small simulation study examines finite sample bias and mild violations of the normality assumption for our simple data generating model we find that the wald estimator is asymptotically biased with a bias of around 10 in fairly typical mendelian randomization scenarios but which can be larger in more extreme situations recently developed methods such as structural mean models require fewer untestable assumptions and we recommend their use when the individual level data they require are available the wald type estimator may retain a role as an approximate method for meta analysis based on summary data

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

marginal and nested structural models using instrumental variables the objective of many scientific studies is to evaluate the effect of a treatment on an outcome of interest ceteris paribus instrumental variables ivs serve as an experimental handle independent of potential outcomes and potential treatment status and affecting potential outcomes only through potential treatment status we propose marginal and nested structural models using ivs in the spirit of marginal and nested structural models under no unmeasured confounding a marginal structural iv model parameterizes the expectations of two potential outcomes under an active treatment and the null treatment respectively for those in a covariate specific subpopulation who would take the active treatment if the instrument were externally set to each specific level a nested structural iv model parameterizes the difference between the two expectations after transformed by a link function and hence the average treatment effect on the treated at each instrument level we develop iv outcome regression iv propensi

testing universality in critical exponents the case of rainfall one of the key clues to consider rainfall as a self organized critical phenomenon is the existence of power law distributions for rain event sizes we have studied the problem of universality in the exponents of these distributions by means of a suitable statistic whose distribution is inferred by several variations of a permutational test in contrast to more common approaches our procedure does not suffer from the difficulties of multiple testing and does not require the precise knowledge of the uncertainties associated to the power law exponents when applied to seven sites monitored by the atmospheric radiation measurement program the tests lead to the rejection of the universality hypothesis despite the fact that the exponents are rather close to each other we discuss the reasons of the rejection

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

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

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

causal inference with generalized structural mean models summary we estimate cause effect relationships in empirical research where exposures are not completely controlled as in observational studies or with patient non compliance and self selected treatment switches in randomized clinical trials additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log linear models when accommodating binary data we propose the generalized structural mean model to overcome these limitations this is a semiparametric two stage model which extends the structural mean model to handle non linear average exposure effects the first stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure free outcomes in exposed subsets of the population for identification of the structural parameters a second stage nuisance model is introduced this takes the form of a classical association model for expected outcomes given observed exposure under the model we derive estimating equations which yield consistent asymptotically normal and efficient estimators of the structural effects we examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect the double logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self selected non compliance

testing concordance of instrumental variable effects in generalized linear models with application to mendelian randomization instrumental variable regression is one way to overcome unmeasured confounding and estimate causal effect in observational studies built on structural mean models there has been considerable work recently developed for consistent estimation of causal relative risk and causal odds ratio such models can sometimes suffer from identification issues for weak instruments this hampered the applicability of mendelian randomization analysis in genetic epidemiology when there are multiple genetic variants available as instrumental variables and causal effect is defined in a generalized linear model in the presence of unmeasured confounders we propose to test concordance between instrumental variable effects on the intermediate exposure and instrumental variable effects on the disease outcome as a means to test the causal effect we show that a class of generalized least squares estimators provide valid and consistent tests of causality for causal effect of a continuous exposure on a dichotomous outcome in logistic models the proposed estimators are shown to be asymptotically conservative when the disease outcome is rare such estimators are consistent because of the log linear approximation of the logistic function optimality of such estimators relative to the well known two stage least squares estimator and the double logistic structural mean model is further discussed

factorization of analytic representations in the unit disc and number phase statistics of a quantum harmonic oscillator the inner outer part factorization of analytic representations in the unit disc is used for an effective characterization of the number phase statistical properties of a quantum harmonic oscillator it is shown that the factorization is intimately connected with the number phase weyl semigroup and its properties in the barut girardello analytic representation the factorization is implemented as a convolution several examples are given which demonstrate the physical significance of the factorization and its role for quantum statistics in particular we study the effect of phase space interference on the factorization properties of a superposition state

semiparametric instrumental variable estimation of treatment response models this article introduces a new class of instrumental variable iv estimators for linear and nonlinear treatment response models with covariates the rationale for focusing on nonlinear models is that if the dependent variable is binary or limited or if the effect of the treatment varies with covariates a nonlinear model is appropriate in the spirit of roehrig econometrica 56 1988 433 identification is attained nonparametrically and does not depend on the choice of the parametric specification for the response function of interest one virtue of this approach is that it allows the researcher to construct estimators that can be interpreted as the parameters of a well defined approximation to a treatment response function under functional form misspecification in contrast to some usual iv models heterogeneity of treatment effects is not restricted by the identification conditions the ideas and estimators in this article are illustrated using iv to estimate the effects of 401 k retirement programs on savings

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

time varying effect moderation using the structural nested mean model estimation using inverse weighted regression with residuals this article considers the problem of examining time varying causal effect moderation using observational longitudinal data in which treatment candidate moderators and possible confounders are time varying the structural nested mean model snmm is used to specify the moderated time varying causal effects of interest in a conditional mean model for a continuous response given time varying treatments and moderators we present an easy to use estimator of the snmm that combines an existing regression with residuals rr approach with an inverse probability of treatment weighting iptw strategy the rr approach has been shown to identify the moderated time varying causal effects if the time varying moderators are also the sole time varying confounders the proposed iptw rr approach provides estimators of the moderated time varying causal effects in the snmm in the presence of an additional auxiliary set of known and measured time varying confounders we use a small simulation experiment to compare iptw rr versus the traditional regression approach and to compare small and large sample properties of asymptotic versus bootstrap estimators of the standard errors for the iptw rr approach this article clarifies the distinction between time varying moderators and time varying confounders we illustrate the methodology in a case study to assess if time varying substance use moderates treatment effects on future substance use

instrumental variable analysis of multiplicative models with potentially invalid instruments instrumental variable iv methods have potential to consistently estimate the causal effect of an exposure on an outcome in the presence of unmeasured confounding however validity of iv methods relies on strong assumptions some of which cannot be conclusively verified from observational data one such assumption is that the effect of the proposed instrument on the outcome is completely mediated by the exposure we consider the situation where this assumption is violated but the remaining iv assumptions hold that is the proposed iv 1 is associated with the exposure and 2 has no unmeasured causes in common with the outcome we propose a method to estimate multiplicative structural mean models of binary outcomes in this scenario in the presence of unmeasured confounding we also extend the method to address multiple scenarios including mediation analysis the method adapts the asymptotically efficient g estimation approach that was previously proposed for additive structural mean models and it can be carried out using off the shelf software for generalized method of moments monte carlo simulation studies show that the method has low bias and accurate coverage we applied the method to a case study of circulating vitamin d and depressive symptoms using season of blood collection as a potentially invalid instrumental variable potential applications of the proposed method include randomized intervention studies as well as mendelian randomization studies with genetic variants that affect multiple phenotypes possibly including the outcome published 2016 this article is a u s government work and is in the public domain in the usa

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

the abelian sandpile and related models abstract the abelian sandpile model is the simplest analytically tractable model of self organized criticality this paper presents a brief review of known results about the model the abelian group structure of the algebra of operators allows an exact calculation of many of its properties in particular when there is a preferred direction one can calculate all the critical exponents characterizing the distribution of avalanche sizes in all dimensions for the undirected case the model is related to q 0 state potts model this enables exact calculation of some exponents in two dimensions and there are some conjectures about others we also discuss a generalization of the model to a network of communicating reactive processors this includes sandpile models with stochastic toppling rules as a special case we also consider a nondashabelian stochastic variant which lies in a different universality class related to directed percolation

efficiency bounds for semiparametric regression efficiency bounds for conditional moment restrictions with a nonparametric component are derived there is a given function of the data a random sample from a distribution f and a parameter the restriction is that a conditional expectation of this function is zero at some point in the parameter space the parameter has two parts a finite dimensional component and a general function evaluated at a subset of the conditioning variables an example is a regression function that is additive in parametric and nonparametric component as arises in sample selection models copyright 1992 by the econometric society

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

general theory for interactions in sufficient cause models with dichotomous exposures the sufficient component cause framework assumes the existence of sets of sufficient causes that bring about an event for a binary outcome and an arbitrary number of binary causes any set of potential outcomes can be replicated by positing a set of sufficient causes typically this representation is not unique a sufficient cause interaction is said to be present if within all representations there exists a sufficient cause in which two or more particular causes are all present a singular interaction is said to be present if for some subset of individuals there is a unique minimal sufficient cause empirical and counterfactual conditions are given for sufficient cause interactions and singular interactions between an arbitrary number of causes conditions are given for cases in which none some or all of a given set of causes affect the outcome monotonically the relations between these results interactions in linear statistical models and pearl s probability of causation are discussed

estimation of treatment effects in randomized trials with non compliance and a dichotomous outcome summary we propose a class of estimators of the treatment effect on a dichotomous outcome among the treated subjects within covariate and treatment arm strata in randomized trials with non compliance recent papers by vansteelandt and goetghebeur and robins and rotnitzky have presented consistent and asymptotically linear estimators of a causal odds ratio which rely beyond correct specification of a model for the causal odds ratio on a correctly specified model for a potentially high dimensional nuisance parameter in this paper we propose consistent asymptotically linear and locally efficient estimators of a causal relative risk and a new parameter called a switch causal relative risk which relies only on the correct specification of a model for the parameter of interest our estimators are always consistent and asymptotically linear at the null hypothesis of no treatment effect thereby providing valid testing procedures we examine the finite sample properties of these instrumental variable based estimators and the associated testing procedures in simulations and a data analysis of decaffeinated coffee consumption and miscarriage

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