the bias due to incomplete matching observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group in practice there is a trade off between the desires to find matches for all treated units and to obtain matched treated control pairs that are extremely similar to each other we derive expressions for the bias in the average matched pair difference due to the failure to match all treated units incomplete matching and the failure to obtain exact matches inexact matching a practical example shows that the bias due to incomplete matching can be severe and moreover can be avoided entirely by using an appropriate multivariate nearest available matching algorithm which in the example leaves only a small residual bias due to inexact matching

moving towards best practice when using inverse probability of treatment weighting iptw using the propensity score to estimate causal treatment effects in observational studies the propensity score is defined as a subject s probability of treatment selection conditional on observed baseline covariates weighting subjects by the inverse probability of treatment received creates a synthetic sample in which treatment assignment is independent of measured baseline covariates inverse probability of treatment weighting iptw using the propensity score allows one to obtain unbiased estimates of average treatment effects however these estimates are only valid if there are no residual systematic differences in observed baseline characteristics between treated and control subjects in the sample weighted by the estimated inverse probability of treatment we report on a systematic literature review in which we found that the use of iptw has increased rapidly in recent years but that in the most recent year a majority of studies did not formally examine whether weighting balanced measured covariates between treatment groups we then proceed to describe a suite of quantitative and qualitative methods that allow one to assess whether measured baseline covariates are balanced between treatment groups in the weighted sample the quantitative methods use the weighted standardized difference to compare means prevalences higher order moments and interactions the qualitative methods employ graphical methods to compare the distribution of continuous baseline covariates between treated and control subjects in the weighted sample finally we illustrate the application of these methods in an empirical case study we propose a formal set of balance diagnostics that contribute towards an evolving concept of best practice when using iptw to estimate causal treatment effects using observational data

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

poincare birkhoff witt property for bicovariant differential algebras on simple quantum groups we investigate the possibility of constructing bicovariant differential calculi on quantum groups soq n and spq n as a quantization of an underlying bicovariant bracket we show that in contrast to the gl n and sl n cases neither of the possible graded so and sp bicovariant brackets associated with a quasitriangular r matrices obey the jacobi identity when the differential forms are lie algebra valued the absence of a classical poisson structure gives an indication that differential algebras describing bicovariant differential calculi on quantum orthogonal and symplectic groups are not of poincare birkhoff witt type

classification of bicovariant differential calculi on quantum groups suppose thatq is not a root of unity we classify all bicovariant differential calculi of dimension greater than one on the quantum groupsgl q n o q n andsp q n for which the differentials du of the matrix entriesu generate the left module of first order forms our first classification theorem asserts that there are precisely two one parameter families of such calculi ongl q n forn 3 in the limitq 1 only two of these calculi give the ordinary differential calculus ongl n our second main theorem states that apart from finitely manyq there exist precisely two differential calculi with these properties ono q n andsp q n forn 4 this strengthens the corresponding result proved in our previous paper ss2 there are four such calculi ono q 3 we introduce two new 4 dimensional bicovariant differential calculi ono q 3

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

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

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

sample size formulae for two stage randomized trials with survival outcomes two stage randomized trials are growing in importance in developing adaptive treatment strategies i e treatment policies or dynamic treatment regimes usually the first stage involves randomization to one of the several initial treatments the second stage of treatment begins when an early nonresponse criterion or response criterion is met in the second stage nonresponding subjects are re randomized among second stage treatments sample size calculations for planning these two stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome we produce simple albeit conservative sample size formulae by using upper bounds on the variances the resulting formulae only require the working assumptions needed to size a standard single stage randomized trial and in common settings are only mildly conservative these sample size formulae are based on either a weighted kaplan meier estimator of survival probabilities at a fixed time point or a weighted version of the log rank test

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

inferential procedures for multifaceted coefficients of generalizability a two facet measurement model with broad application in the behavioral sciences is identified and its coefficient of generalizability cg is examined a normalizing transformation is proposed and an asymptotic variance expression is derived three other multifaceted measurement models and cgs are identified and variance expressions are presented next an empirical investigation of the procedures follows and it is shown that in most cases type i error control in inferential applications is precise and that the estimates are relatively efficient compared with the correlation coefficient implications for further research and for practice are noted in an appendix four additional models cgs and variance expressions are presented

non standard quantum 1 1 poincare group a t matrix approach the hopf algebra dual form for the non standard uniparametric deformation of the 1 1 poincare algebra iso 1 1 is deduced in this framework the quantum coordinates that generate funw iso 1 1 define an infinite dimensional lie algebra the t matrix formalism is used to derive a universal r matrix for both uwiso 1 1 and funw iso 1 1 it is also shown how these results can be generalized for the triangular deformations of 1 1 poincare and galilei algebras that include a spacetime dilation generator

duality for exotic bialgebras in the classification of hietarinta three triangular 4 4 r matrices lead via the frt formalism to matrix bialgebras which are not deformations of the trivial one in this paper we find the bialgebras which are in duality with these three exotic matrix bialgebras we note that the l t duality of frt is not sufficient for the construction of the bialgebras in duality we find also the quantum planes corresponding to these bialgebras both by the wess zumino r matrix method and by manin s method

extension of feldt s approach to testing homogeneity of coefficients of reliability limitations and extensions of feldt s approach to testing the equality of cronbach s alpha coefficients in independent and matched samples are discussed in particular this approach is used to test equality of intraclass correlation coefficients

identifiability stratification and minimum variance estimation of causal effects the weakest sufficient condition for the identifiability of causal effects is the weakly ignorable treatment assignment which implies that potential responses are independent of treatment assignment in each fine subpopulation stratified by a covariate in this paper we expand the independence that holds in fine subpopulations to the case that the independence may also hold in several coarse subpopulations each of which consists of several fine subpopulations and may have overlaps with other coarse subpopulations we first show that the identifiability of causal effects occurs if and only if the coarse subpopulations partition the whole population we then propose a principle called minimum variance principle which says that the estimator possessing the minimum variance is preferred in dealing with the stratification and the estimation of the causal effects the simulation results with the detail programming and a practical example demonstrate that it is a feasible and reasonable way to achieve our goals

classification of bicovariant differential calculi on the jordanian quantum groups and and quantum lie algebras assuming that the bicovariant bimodules are generated as left modules by the differentials of the quantum group generators we classify all four dimensional first order bicovariant calculi on the jordanian quantum group and all three dimensional first order bicovariant calculi on the jordanian quantum group it is found that there are three one parameter families of four dimensional bicovariant first order calculi on and that there is a single unique three dimensional bicovariant calculus on this three dimensional calculus may be obtained through a classical like reduction from any one of the three families of four dimensional calculi on details of the higher order calculi and also the quantum lie algebras are presented for all calculi the quantum lie algebra obtained from the bicovariant calculus on is shown to be isomorphic to the quantum lie algebra we obtain as an ad submodule within the jordanian universal enveloping algebra and also through a consideration of the decomposition of the tensor product of two copies of the deformed adjoint module we also obtain the quantum killing form for this quantum lie algebra

test theory and psychometrika the past twenty five years on the occasion ofpsychometrika s fiftieth anniversary the past twenty five years developments in mental test theory are reviewed with special emphasis on the topics receiving attention in the pages of this journal analogous reviews forpsychometrika s first quarter century were given by gulliksen and guilford in 1961 much of the recent progress in test theory and in other branches of psychometrics as well has been made by treating the problems in this field as being essentially ones of statistical inference it is concluded that a research in test theory is in a healthy state and b psychometrika is an important source of information about that research

differential calculus on compact matrix pseudogroups quantum groups the paper deals with non commutative differential geometry the general theory of differential calculus on quantum groups is developed bicovariant bimodules as objects analogous to tensor bundles over lie groups are studied tensor algebra and external algebra constructions are described it is shown that any bicovariant first order differential calculus admits a natural lifting to the external algebra so the external derivative of higher order differential forms is well defined and obeys the usual properties the proper form of the cartan maurer formula is found the vector space dual to the space of left invariant differential forms is endowed with a bilinear operation playing the role of the lie bracket commutator generalized antisymmetry relation and jacobi identity are proved

differential calculi on the quantum group glp q 2 the author presents a systematical study of left covariant differential calculus on the quantum group glp q 2 a two parameter deformation of the general linear group in particular the author explicitly constructs the most general bicovariant calculus it depends on a new parameter s the corresponding lie algebra of left coinvariant vector fields is a two parameter deformation of the classical lie algebra p and q appear only in the combination r pq in the limit p q to 1 one obtains non standard bicovariant differential calculi on the classical lie group

bicovariant differential calculi on glp q 2 and quantum subgroups in a previous paper all bicovariant differential calculi on the two parameter quantum group glp q 2 were determined in this work the authors elaborate some of their properties and discuss relations with work by other authors furthermore they show that there are two different ways in which bicovariant differential calculi on glq 2 where p q induce corresponding calculi on the quantum subgroup slq 2 it is shown that on slq 2 there are only two different bicovariant differential calculi from these one obtains the 4d or calculi on suq 2 the classical limit of the two differential calculi on slq 2 is investigated revealing a relation with recent work on deformed differential calculi on commutative function algebras

causal inference for mann whitney wilcoxon rank sum and other nonparametric statistics the nonparametric mann whitney wilcoxon mww rank sum test is widely used to test treatment effect by comparing the outcome distributions between two groups especially when there are outliers in the data however such statistics generally yield invalid conclusions when applied to nonrandomized studies particularly those in epidemiologic research although one may control for selection bias by using available approaches of covariates adjustment such as matching regression analysis propensity score matching and marginal structural models such analyses yield results that are not only subjective based on how the outliers are handled but also often difficult to interpret a popular alternative is a conditional permutation test based on randomization inference rosenbaum pr covariance adjustment in randomized experiments and observational studies statistical science 2002 17 3 286 327 because it requires strong and implausible assumptions that may not be met in most applications this approach has limited applications in practice in this paper we address this gap in the literature by extending mww and other nonparametric statistics to provide causal inference for nonrandomized study data by integrating the potential outcome paradigm with the functional response models frm frm is uniquely positioned to model dynamic relationships between subjects rather than attributes of a single subject as in most regression models such as the mww test within our context the proposed approach is illustrated with data from both real and simulated studies copyright 2013 john wiley sons ltd

from association to causation in observational studies the role of tests of strongly ignorable treatment assignment abstract if treatment assignment is strongly ignorable then adjustment for observed covariates is sufficient to produce consistent estimates of treatment effects in observational studies a general approach to testing this critical assumption is developed and applied to a study of the effects of nuclear fallout on the risk of childhood leukemia r a fisher s advice on the interpretation of observational studies was make your theories elaborate formally make causal theories sufficiently detailed that under the theory strongly ignorable assignment has testable consequences

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

braided lie algebras and bicovariant differential calculi over co quasitriangular hopf algebras we show that if g is the quantum tangent space or quantum lie algebra in the sense of woronowicz of a bicovariant first order differential calculus over a co quasitriangular hopf algebra a r then a certain extension of it is a braided lie algebra in the category of a comodules this is used to show that the woronowicz quantum universal enveloping algebra u g is a bialgebra in the braided category of a comodules we show that this algebra is quadratic when the calculus is inner examples with this unexpected property include finite groups and quantum groups with their standard differential calculi we also find a quantum lie functor for co quasitriangular hopf algebras which has properties analogous to the classical one this functor gives trivial results on standard quantum groups oq g but reasonable ones on examples closer to the classical case such as the cotriangular jordanian deformations in addition we show that split braided lie algebras define generalized lie algebras in a different sense of deforming the adjoint representation we construct these and their enveloping algebras for oq sl n recovering the witten algebra for n 2

quantum lie algebras their existence uniqueness and q antisymmetry quantum lie algebras are generalizations of lie algebras which have the quantum parameter h built into their structure they have been defined concretely as certain submodules of the quantized enveloping algebras on them the quantum lie product is given by the quantum adjoint action

adjusting treatment effect estimates by post stratification in randomized experiments summary experimenters often use post stratification to adjust estimates post stratification is akin to blocking except that the number of treated units in each stratum is a random variable because stratification occurs after treatment assignment we analyse both post stratification and blocking under the neyman rubin model and compare the efficiency of these designs we derive the variances for a post stratified estimator and a simple difference in means estimator under different randomization schemes post stratification is nearly as efficient as blocking the difference in their variances is of the order of 1 n2 with a constant depending on treatment proportion post stratification is therefore a reasonable alternative to blocking when blocking is not feasible however in finite samples post stratification can increase variance if the number of strata is large and the strata are poorly chosen to examine why the estimators variances are different we extend our results by conditioning on the observed number of treated units in each stratum conditioning also provides more accurate variance estimates because it takes into account how close or far a realized random sample is from a comparable blocked experiment we then show that the practical substance of our results remains under an infinite population sampling model finally we provide an analysis of an actual experiment to illustrate our analytical results

matrix element bialgebras determined by quadratic coordinate algebras abstract we develop the theory of manin s construction of quantum groups from finitely generated quadratic algebras in general this construction yields a bialgebra with matrix comultiplication we give formulae for the relations in the algebra and sufficient conditions for the existence of an antipode and for polynomiality of the algebra these are more systematic than the calculational approach of previous treatments

testing the equality of two dependent kappa statistics procedures are developed and compared for testing the equality of two dependent kappa statistics in the case of two raters and a dichotomous outcome variable such problems may arise when each of a sample of subjects are rated under two distinct settings and it is of interest to compare the observed levels of inter observer and intra observer agreement the procedures compared are extensions of previously developed procedures for comparing kappa statistics computed from independent samples the results of a monte carlo simulation show that adjusting for the dependency between samples tends to be worthwhile only if the between setting correlation is comparable in magnitude to the within setting correlations in this case a goodness of fit procedure that takes into account the dependency between samples is recommended

classification of bicovariant differential calculi on quantum groups of type a b c and d under the assumptions thatq is not a root of unity and that the differentialsduji of the matrix entries span the left module of first order forms we classify bicovariant differential calculi on quantum groupsan 1 bn cn anddn we prove that apart one dimensional differential calculi and from finitely many values ofq there are precisely2n such calculi on the quantum groupan 1 slq n forn 3 all these calculi have the dimensionn2 for the quantum groupsbn cn anddn we show that except for finitely manyq there exist precisely twon2 dimensional bicovariant calculi forn 3 wheren 2n 1 forbn andn 2n forcn dn the structure of these calculi is explicitly described and the corresponding ad invariant right ideals of ker e are determined in the limitq 1 two of the 2n calculi foran 1 and one of the two calculi forbn cn anddn contain the ordinary classical differential calculus on the corresponding lie group as a quotient

classification of left covariant differential calculi on the quantum group slq 2 abstract for transcendental values of q the quantum tangent spaces of all left covariant first order differential calculi of dimension less than four on the quantum group sl q 2 are given all such differential calculi are determined and investigated for which the left invariant differential one forms u 1 2 u 2 1 and u 1 1 u 2 2 generate as a bimodule and the universal higher order differential calculus has the same dimension as in the classical case important properties cohomology spaces structures braidings generalized lie brackets of these calculi are examined as well

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

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

regression analysis with clustered data clustered data are found in many different types of studies for example studies involving repeated measures inter rater agreement studies household surveys crossover designs and community randomized trials analyses based on population average and cluster specific models are commonly used for estimating treatment exposure effects with clustered data this paper discusses conditions when one or both types of models are appropriate for estimating causal effects and when there is agreement between population average and cluster specific analyses applications of survey sampling methods to the robust estimation of standard errors of estimated treatment parameters are discussed

tests for equality of several alpha coefficients when their sample estimates are dependent in a variety of measurement situations the researcher may wish to compare the reliabilities of several instruments administered to the same sample of subjects this paper presents eleven statistical procedures which test the equality ofm coefficient alphas when the sample alpha coefficients are dependent several of the procedures are derived in detail and numerical examples are given for two since all of the procedures depend on approximate asymptotic results monte carlo methods are used to assess the accuracy of the procedures for sample sizes of 50 100 and 200 both control of type i error and power are evaluated by computer simulation two of the procedures are unable to control type i errors satisfactorily the remaining nine procedures perform properly but three are somewhat superior in power and type i error control

interval estimation for treatment effects using propensity score matching in causal studies without random assignment of treatment causal effects can be estimated using matched treated and control samples where matches are obtained using estimated propensity scores propensity score matching can reduce bias in treatment effect estimators in cases where the matched samples have overlapping covariate distributions despite its application in many applied problems there is no universally employed approach to interval estimation when using propensity score matching in this article we present and evaluate approaches to interval estimation when using propensity score matching

all bicovariant differential calculuses on glq 3 c and slq 3 c all bicovariant first order differential calculuses on the quantum group glq 3 c are determined there are two distinct one parameter families of calculuses in terms of a suitable basis of 1 forms the commutation relations can be expressed with the help of the r matrix of glq 3 c some calculuses induce bicovariant differential calculuses on slq 3 c and on real forms of glq 3 c for the generic deformation parameter q there are six calculuses on slq 3 c on suq 3 there are only two the classical limit q to 1 of bicovariant calculuses on slq 3 c is not the ordinary calculus on sl 3 c one obtains a deformation of it which involves the cartan killing metric

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

dual and simultaneous sensitivity analysis for matched pairs summary when a study shows an association between a treatment and a response before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable u might explain the observed association sensitivity analysis clarifies the properties u must have in terms of its relationship to the response and its imbalance in the groups being compared a substantial literature has investigated the imbalance or association between u and group assignment this paper develops a dual sensitivity analysis for matched pairs focusing on the strength of the relationship between u and the response required to reduce an observed association to non significance a third simultaneous form of sensitivity analysis models both relationships between u and treatment assignment and u and response the simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships the methods are illustrated by several examples

model misspecification and robustness in causal inference comparing matching with doubly robust estimation in this paper we compare the robustness properties of a matching estimator with a doubly robust estimator we describe the robustness properties of matching and subclassification estimators by show

on the interpretation and observation of laws a law with factors x and concomitants z specifies a distribution given z of a potential value yx that is defined for each x whether or not it is observed an observed distribution of y given x and z agrees with the law if and only if given z the observed x is independent of yx or equivalently of the joint effect of ux of excluded variables on yx to establish such independence in non experimental data requires exhaustive exploration of the effects of concomitants causal and non causal r2 and f are irrelevant we show how the model free theory applies to linear models time series and simultaneous equations and point out its bayesian implications

causal inference for continuous time processes when covariates are observed only at discrete times most of the work on the structural nested model and g estimation for causal inference in longitudinal data assumes a discrete time underlying data generating process however in some observational studies it is more reasonable to assume that the data are generated from a continuous time process and are only observable at discrete time points when these circumstances arise the sequential randomization assumption in the observed discrete time data which is essential in justifying discrete time g estimation may not be reasonable under a deterministic model we discuss other useful assumptions that guarantee the consistency of discrete time g estimation in more general cases when those assumptions are violated we propose a controlling the future method that performs at least as well as g estimation in most scenarios and which provides consistent estimation in some cases where g estimation is severely inconsistent we apply the methods discussed in this paper to simulated data as well as to a data set collected following a massive flood in bangladesh estimating the effect of diarrhea on children s height results from different methods are compared in both simulation and the real application

representations and clebsch gordan coefficients for the jordanian quantum algebra representation theory for the jordanian quantum algebra is developed closed form expressions are given for the action of the generators of on the basis vectors of finite dimensional irreducible representations it is shown how representation theory of has a close connection to the combinatorial identities involving summation formulae a general formula is obtained for the clebsch gordan coefficients of these clebsch gordan coefficients are shown to coincide with those of su 2 for but for they are in general a non zero monomial in

generalized lie algebras of type an it is shown that the quantized enveloping algebra of sl n contains a generalized lie algebra defined by means of axioms similar to woronowicz s this gives rise to lie algebra like generators and relations for the locally finite part of the quantized enveloping algebra and suggests a canonical poincare birkhoff witt basis

the structure of quantum lie algebras for the classical series and the structure constants of quantum lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a lie algebra at q 1 we explain the relationship between the structure constants of quantum lie algebras and quantum clebsch gordan coefficients for we present a practical method for the determination of these quantum clebsch gordan coefficients and are thus able to give explicit expressions for the structure constants of the quantum lie algebras associated to the classical lie algebras and in the quantum case the structure constants of the cartan subalgebra are non zero and we observe that they are determined in terms of the simple quantum roots we introduce an invariant killing form on the quantum lie algebras and find that it takes values which are simple q deformations of the classical ones

addressing complications of intention to treat analysis in the combined presence of all or none treatment noncompliance and subsequent missing outcomes summary we study the combined impact that all or none compliance and subsequent missing outcomes can have on the estimation of the intention to treat effect of assignment in randomised studies in this setting a standard analysis which drops subjects with missing outcomes and ignores compliance information can be biased for the intention to treat effect to address all or none compliance that is followed by missing outcomes we construct a new estimation procedure for the intention to treat effect that maintains good randomisation based properties under more plausible nonignorable noncompliance and nonignorable missing outcome conditions the compound exclusion restriction on the effect of assignment and the latent ignorability of the missing data mechanism we present both theoretical results and a simulation study moreover we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings such as right censoring of a time to event outcome

covariate selection for the nonparametric estimation of an average treatment effect observational studies in which the effect of a nonrandomized treatment on an outcome of interest is estimated are common in domains such as labour economics and epidemiology such studies often rel

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

on quantum lie algebras and quantum root systems as a natural generalization of ordinary lie algebras we introduce the concept of quantum lie algebras we define these in terms of certain adjoint submodules of quantized enveloping algebras endowed with a quantum lie bracket given by the quantum adjoint action the structure constants of these algebras depend on the quantum deformation parameter q and they go over into the usual lie algebras when q 1 the notions of q conjugation and q linearity are introduced q linear analogues of the classical antipode and cartan involution are defined and a generalized killing form q linear in the first entry and linear in the second is obtained these structures allow the derivation of symmetries between the structure constants of quantum lie algebras the explicitly worked out examples of and illustrate the results

doubly robust estimators of causal exposure effects with missing data in the outcome exposure or a confounder we consider the estimation of the causal effect of a binary exposure on a continuous outcome confounding and missing data are both likely to occur in practice when observational data are used to estimate this causal effect in dealing with each of these problems model misspecification is likely to introduce bias we present augmented inverse probability weighted aipw estimators that account for both confounding and missing data with the latter occurring in a single variable only these estimators have an element of robustness to misspecification of the models used our estimators require two models to be specified to deal with confounding and two to deal with missing data only one of each of these models needs to be correctly specified when either the outcome or the exposure of interest is missing we derive explicit expressions for the aipw estimator when a confounder is missing explicit derivation is complex so we use a simple algorithm which can be applied using standard statistical software to obtain an approximation to the aipw estimator

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

bayesian analysis of cross section and clustered data treatment models this paper is concerned with the problem of determining the effect of a categorical treatment variable on a response given that the treatment is non randomly assigned and the response on any given subject is observed for one setting of the treatment we consider classes of models that are designed for such problems these models are subjected to a fully bayesian analysis based on markov chain monte carlo methods the analysis of the treatment effect is then based on amongst other things the posterior distribution of the potential outcomes counter factuals at the subject level which is obtained as a by product of the mcmc simulation procedure the analysis is extended to models with categorical treatments and binary and clustered outcomes the problem of model comparisons is also considered different aspects of the methodology are illustrated through two data examples

causality tests and observationally equivalent representations of econometric models abstract this article deals with the problem of observational equivalence of alternative econometric equation systems on the same data as a practical obstacle to econometricians success in applying definitions of causality by simon 1953 strotz and wold 1960 and granger 1969 to economic time series

duality for the jordanian matrix quantum group we find the hopf algebra dual to the jordanian matrix quantum group as an algebra it depends only on the sum of the two parameters and is split into two subalgebras with three generators and with one generator the subalgebra is a central hopf subalgebra of the subalgebra is not a hopf subalgebra and its co algebra structure depends on both parameters we discuss also two one parameter special cases g h and g h the subalgebra is a hopf algebra and coincides with the algebra introduced by ohn as the dual of the subalgebra is isomorphic to u sl 2 as an algebra but has a nontrivial co algebra structure and again is not a hopf subalgebra of

statistics and causal inference abstract problems involving causal inference have dogged at the heels of statistics since its earliest days correlation does not imply causation and yet causal conclusions drawn from a carefully designed experiment are often valid what can a statistical model say about causation this question is addressed by using a particular model for causal inference holland and rubin 1983 rubin 1974 to critique the discussions of other writers on causation and causal inference these include selected philosophers medical researchers statisticians econometricians and proponents of causal modeling

irreducible decomposition for tensor product representations of jordanian quantum algebras tensor products of irreducible representations of the jordanian quantum algebras and are considered for both the highest weight finite dimensional representations of and the lowest weight infinite dimensional ones of it is shown that tensor product representations are reducible and that the decomposition rules to irreducible representations are exactly the same as those of corresponding lie algebras

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

mutual information based matching for causal inference with observational data this paper presents an information theory driven matching methodology for making causal inference from observational data the paper adopts a potential outcomes framework view on evaluating the strength of cause effect relationships the population wide average effects of binary treatments are estimated by comparing two groups of units the treated and untreated control to reduce the bias in such treatment effect estimation one has to compose a control group in such a way that across the compared groups of units treatment is independent of the units covariates this requirement gives rise to a subset selection matching problem this paper presents the models and algorithms that solve the matching problem by minimizing the mutual information mi between the covariates and the treatment variable such a formulation becomes tractable thanks to the derived optimality conditions that tackle the non linearity of the sample based mi function computational experiments with mixed integer programming formulations and four matching algorithms demonstrate the utility of mi based matching for causal inference studies the algorithmic developments culminate in a matching heuristic that allows for balancing the compared groups in polynomial close to linear time thus allowing for treatment effect estimation with large data sets

estimating marginal causal effects in a secondary analysis of case control data when an initial case control study is performed data can be used in a secondary analysis to evaluate the effect of the case defining event on later outcomes in this paper we study the example in

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 linear theory for noncausality abstract different definitions of noncausality according to granger sims haugh and pierce are analyzed in terms of orthogonality in the hilbert space of square integrable variables conditions when necessary are given for their respective equivalence some problems of testability are mentioned finally noncausality is also analyzed in terms of rational expectations extending previous results of sims author