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

a universal method for structural static reanalysis of topological modifications this paper presents a universal method iterative combined approximation iterative ca approach for structural static reanalysis of all types of topological modifications the proposed procedure is basically an approximate two step method first the newly added degrees of freedom dofs are assumed to be linked to the original dofs of the modified structure by means of the guyan reduction so as to obtain the condensed equation second the displacements of the original dofs of the modified structure are solved by using the iterative ca approach and the displacements of the newly added dofs resulting from topological modification can be recovered four numerical examples are given to illustrate the applications of the present approach the results show that the proposed method is effective for structural static reanalysis of all types of the topological modifications and it is easy to implement on a computer copyright 2004 john wiley sons ltd

inference for the median residual life function in sequential multiple assignment randomized trials in survival analysis median residual lifetime is often used as a summary measure to assess treatment effectiveness it is not clear however how such a quantity could be estimated for a given dynamic treatment regimen using data from sequential randomized clinical trials we propose a method to estimate a dynamic treatment regimen specific median residual life merl function from sequential multiple assignment randomized trials we present the merl estimator which is based on inverse probability weighting as well as two variance estimates for the merl estimator one variance estimate follows from lunceford davidian and tsiatis 2002 survival function based variance estimate and the other uses the sandwich estimator the merl estimator is evaluated and its two variance estimates are compared through simulation studies showing that the estimator and both variance estimates produce approximately unbiased results in large samples to demonstrate our methods the estimator has been applied to data from a sequentially randomized leukemia clinical trial

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

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 efficient estimation of survival distributions in two stage randomisation designs in clinical trials with censored data summary two stage randomisation designs are useful in the evaluation of combination therapies where patients are initially randomised to an induction therapy and then depending upon their response and consent are randomised to a maintenance therapy in this paper we derive the best regular asymptotically linear estimator for the survival distribution and related quantities of treatment regimes we propose an estimator which is easily computable and is more efficient than existing estimators large sample properties of the proposed estimator are derived and comparisons with other estimators are made using simulation

examination of percentile residual life we initiate a nonparametric large sample estimation theory for the percentile residual lifetime we introduce the empirical percentile residual life process and determine its asymptotic distribution resulting in asymptotically distribution free confidence intervals and confidence bands for the percentile residual lifetime we illustrate the methods using strike duration data from the work of d c schmittlein and d g morrison

percentile residual life functions the percentile 0 1 residual life function at time t is defined as the percentile of the remaining life given survival up to time t note that percentile is used in place of 100 percentile two classes of life distributions defined by the percentile residual life function are the decreasing percentile residual life dprl class and the new better than used with respect to the percentile nbup class these two classes are respectively analogous to the well known decreasing mean residual life dmrl class and the new better than used in expectation nbue class that involve the mean residual life function we obtain properties of the percentile residual life function and of the dprl nbup and their dual classes some results differ notably from corresponding results for the mean residual life function

exact and efficient isogeometric reanalysis of accurate shape and boundary modifications abstract in the traditional design through analysis pipeline geometric models and modifications are approximately represented and transformed with computational models besides after each modification the latest design often needs to be completely analyzed again leading to reanalysis these procedures produce many errors and are extremely time consuming therefore in this paper we propose a novel and an exact and efficient isogeometric reanalysis methodology of accurate shape and boundary modifications that improves the totality of integration of design and analysis greatly geometric models and shape modifications are exactly represented and transformed and the corresponding computational models will change simultaneously when the geometric models are modified thereby reducing error and time in model representation and transformation furthermore we extend and propose the isogeometric based exact reanalysis method termed indirect factorization updating ifu with the combination of isogeometric based reanalysis the method can efficiently obtain the exact solution of the modified structure without solving the complete set of modified equations of the new structure it is also applicable to all techniques for representing the cad geometry model and complex problems several examples illustrate and verify the accuracy and efficiency of this proposed method and furthermore the larger the scale of the problem the more advantageous the end result will be

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

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

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

technical note when does the βth percentile residual life function determine the distribution knowledge of the th percentile residual life function does not uniquely determine the underlying distribution additional information about the tail behavior of the distribution is needed knowledge of both the 1 and 2 percentile residual life functions does uniquely determine the distribution provided that 1 and 2 are noncommensurate this corrects and extends the results of schmittlein and morrison schmittlein d c d g morrison 1981 the median residual lifetime a characterization theorem and an application opns res 29 392 399

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

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

classifying regular languages by a split game in this paper we introduce the split game a variant of the ehrenfeucht fraisse game from logic which is useful for analyzing the expressive power of classes of generalized regular expressions an extension of the split game to generalized w regular expressions is also established to gain insight into how the split game can be applied to attack the long standing generalized star height 2 problem we propose and solve the omega power problem a similar but tractable problem in the context of w languages namely we show that omega powers together with boolean combinations and concatenations are not sufficient to express the class of w regular languages

remark on the star height problem abstract a method is presented which allows to construct general regular expressions of star height 1 for a class of rather complicated regular events general regular expressions include an operation symbol for complement if events of greater general star height exist which is still open they must be more complex than those accessible by this method an event which seems to be of this kind is suggested at the end of the paper

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

the median residual lifetime a characterization theorem and an application the concept of the median residual lifetime for a probability distribution is outlined and shown to have several advantages over its more common counterpart the mean residual lifetime a characterization theorem shows that a pareto distribution of the second kind or equivalently a gamma mixture of exponentials is the unique distribution with a linearly increasing median residual lifetime an empirical example from the literature on strike durations is presented

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

more languages of generalised star height 1 abstract suppose that membership of a word w in a language l is specified in terms of the number modulo some integer k of occurrences of a fixed word w as a factor of w then the language obtained for any m by adding arbitrary numbers of copies of a m anywhere in the words of l has generalized star height at most 1

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

on least squares regression with censored data summary the semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified the present paper describes simple and reliable inference procedures based on the least squares principle for this model with right censored data the proposed estimator of the vector valued regression parameter is an iterative solution to the buckley james estimating equation with a preliminary consistent estimator as the starting value the estimator is shown to be consistent and asymptotically normal a novel resampling procedure is developed for the estimation of the limiting covariance matrix extensions to marginal models for multivariate failure time data are considered the performance of the new inference procedures is assessed through simulation studies illustrations with medical studies are provided

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

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 preconditioned conjugate gradient approach to structural reanalysis for general layout modifications this paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications it is suitable for all types of layout modifications including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently the approach is based on the preconditioned conjugate gradient technique the preconditioner is constructed and an efficient implementation for applying the preconditioner is presented which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only in particular the approach can adaptively monitor the accuracy of approximate solutions numerical examples show that the condition number of the preconditioned matrix is remarkably reduced therefore the fast convergence and accurate results can be achieved by the approach copyright 2006 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

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

some results on the generalized star height problem abstract we prove some results related to the generalized star height problem in this problem as opposed to the restricted star height problem complementation is considered as a basic operator we first show that the class of languages of star height n is closed under certain operations left and right quotients inverse alphabetic morphisms injective star free substitutions it is known that languages recognized by a commutative group are of star height 1 we extend this result to nilpotent groups of class 2 and to the groups that divide a semidirect product of a commutative group by z 2 z n in the same direction we show that one of the languages that were conjectured to be of star height 2 during the past ten years is in fact of star height 1 next we show that if a rational language l is recognized by a monoid of the variety generated by wreath products of the form m g n where m and n are aperiodic monoids and g is a commutative group the l is of star height 1 finally we show that every rational language is the inverse image under some morphism between free monoids of a language of resticted star height 1

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

estimating 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

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