multimodality image registration by maximization of mutual information a new approach to the problem of multimodality medical image registration is proposed using a basic concept from information theory mutual information mi or relative entropy as a new matching criterion the method presented in this paper applies mi to measure the statistical dependence or information redundancy between the image intensities of corresponding voxels in both images which is assumed to be maximal if the images are geometrically aligned maximization of mi is a very general and powerful criterion because no assumptions are made regarding the nature of this dependence and no limiting constraints are imposed on the image content of the modalities involved the accuracy of the mi criterion is validated for rigid body registration of computed tomography ct magnetic resonance mr and photon emission tomography pet images by comparison with the stereotactic registration solution while robustness is evaluated with respect to implementation issues such as interpolation and optimization and image content including partial overlap and image degradation our results demonstrate that subvoxel accuracy with respect to the stereotactic reference solution can be achieved completely automatically and without any prior segmentation feature extraction or other preprocessing steps which makes this method very well suited for clinical applications

randomization inference and sensitivity analysis for composite null hypotheses with binary outcomes in matched observational studies abstractwe present methods for conducting hypothesis testing and sensitivity analyses for composite null hypotheses in matched observational studies when outcomes are binary causal estimands discussed include the causal risk difference causal risk ratio and the effect ratio we show that inference under the assumption of no unmeasured confounding can be performed by solving an integer linear program while inference allowing for unmeasured confounding of a given strength requires solving an integer quadratic program through simulation studies and data examples we demonstrate that our formulation allows these problems to be solved in an expedient manner even for large datasets and for large strata we further exhibit that through our formulation one can assess the impact of various assumptions about the potential outcomes on the performed inference r scripts are provided that implement our methods supplementary materials for this article are available online

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

exogeneity in structural equation models the practical relevance of several concepts of exogeneity of treatments for the estimation of causal parameters based on observational data are discussed we show that the traditional concepts such as strong ignorability and weak and super exogeneity are too restrictive if interest lies in average effects i e not on distributional effects of the treatment we suggest a new definition of exogeneity kl exogeneity it does not rely on distributional assumptions and is not based on counterfactual random variables as a consequence it can be empirically tested using a proposed test that is simple to implement and is distribution free

two stage least squares estimation of average causal effects in models with variable treatment intensity abstract two stage least squares tsls is widely used in econometrics to estimate parameters in systems of linear simultaneous equations and to solve problems of omitted variables bias in single equation estimation we show here that tsls can also be used to estimate the average causal effect of variable treatments such as drug dosage hours of exam preparation cigarette smoking and years of schooling the average causal effect in which we are interested is a conditional expectation of the difference between the outcomes of the treated and what these outcomes would have been in the absence of treatment given mild regularity assumptions the probability limit of tsls is a weighted average of per unit average causal effects along the length of an appropriately defined causal response function the weighting function is illustrated in an empirical example based on the relationship between schooling and earnings

inference on a new class of sample average treatment effects we derive new variance formulas for inference on a general class of estimands of causal average treatment effects in a randomized control trial we generalize the seminal work of robins and show th

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

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

general forms of finite population central limit theorems with applications to causal inference abstractfrequentists inference often delivers point estimators associated with confidence intervals or sets for parameters of interest constructing the confidence intervals or sets requires understanding the sampling distributions of the point estimators which in many but not all cases are related to asymptotic normal distributions ensured by central limit theorems although previous literature has established various forms of central limit theorems for statistical inference in super population models we still need general and convenient forms of central limit theorems for some randomization based causal analyses of experimental data where the parameters of interests are functions of a finite population and randomness comes solely from the treatment assignment we use central limit theorems for sample surveys and rank statistics to establish general forms of the finite population central limit theorems that are particularly useful for proving asymptotic distributions of randomization tests under th

comparison of adaptive treatment strategies based on longitudinal outcomes in sequential multiple assignment randomized trials in sequential multiple assignment randomized trials longitudinal outcomes may be the most important outcomes of interest because this type of trials is usually conducted in areas of chronic diseases or conditions we propose to use a weighted generalized estimating equation gee approach to analyzing data from such type of trials for comparing two adaptive treatment strategies based on generalized linear models although the randomization probabilities are known we consider estimated weights in which the randomization probabilities are replaced by their empirical estimates and prove that the resulting weighted gee estimator is more efficient than the estimators with true weights the variance of the weighted gee estimator is estimated by an empirical sandwich estimator the time variable in the model can be linear piecewise linear or more complicated forms this provides more flexibility that is important because in the adaptive treatment setting the treatment changes over time and hence a single linear trend over the whole period of study may not be practical simulation results show that the weighted gee estimators of regression coefficients are consistent regardless of the specification of the correlation structure of the longitudinal outcomes the weighted gee method is then applied in analyzing data from the clinical antipsychotic trials of intervention effectiveness copyright 2016 john wiley sons ltd

colorings of simplicial complexes and vector bundles over davis januszkiewicz spaces we show that coloring properties of a simplicial complex k are reflected by splitting properties of a bundle over the associated davis januszkiewicz space whose chern classes are given by the elementary symmetric polynomials in the generators of the stanley reisner algebra of k

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

the dual polyhedral product cocategory and nilpotence abstract the notion of a dual polyhedral product is introduced as a generalization of hovey s definition of lusternik schnirelmann cocategory properties established from homotopy decompositions that relate the based loops on a polyhedral product to the based loops on its dual are used to show that if x is a simply connected space then the weak cocategory of x equals the homotopy nilpotency class of x this answers a fifty year old problem posed by ganea the methods are applied to determine the homotopy nilpotency class of quasi p regular exceptional lie groups and sporadic p compact groups

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

the polyhedral product functor a method of decomposition for moment angle complexes arrangements and related spaces this article gives a natural decomposition of the suspension of generalized moment angle complexes or partial product spaces which arise as polyhedral product functors described below the geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of goresky macpherson concerning complements of certain subspace arrangements as well as davis januszkiewicz and buchstaber panov concerning moment angle complexes since the stable decompositions here are geometric they provide corresponding homological decompositions for generalized moment angle complexes for any homology theory

on removing interpolation and resampling artifacts in rigid image registration we show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts these artifacts negatively affect the accuracy of registration by producing local optima altering the gradient shifting the global optimum and making rigid registration asymmetric in this paper after an extensive literature review we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically we show the sum of squared differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration we then discuss aliasing that occurs in rotation which is due to the fact that an image represented in the cartesian grid is sampled with different rates in different directions and propose the use of oscillatory isotropic interpolation kernels which allow better recovery of true global optima by overcoming this type of aliasing through our experiments on brain fingerprint and white noise images we illustrate the superior performance of the integral registration cost function in both the cartesian and spherical coordinates and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration

volatility and correlation based systemic risk measures in the us market this paper deals with the problem of how to use simple systemic risk measures to assess portfolio risk characteristics using three simple examples taken from previous literature one based on raw and partial correlations another based on the eigenvalue decomposition of the covariance matrix and the last one based on an eigenvalue entropy a granger causation analysis revealed some of them are not always a good measure of risk in the sp therefore in the sense of risk as volatility the indicators are not always suitable nevertheless their results towards returns are similar to previous works that accept them a deeper analysis has shown that any symmetric measure based on eigenvalue decomposition of correlation matrices however is not useful as a measure of correlation risk the empirical counterpart analysis of this proposition stated that negative correlations are usually small and therefore do not heavily distort the behavior of the indicator

balancing covariates via propensity score weighting abstractcovariate balance is crucial for unconfounded descriptive or causal comparisons however lack of balance is common in observational studies this article considers weighting strategies for balancing covariates we define a general class of weights the balancing weights that balance the weighted distributions of the covariates between treatment groups these weights incorporate the propensity score to weight each group to an analyst selected target population this class unifies existing weighting methods including commonly used weights such as inverse probability weights as special cases general large sample results on nonparametric estimation based on these weights are derived we further propose a new weighting scheme the overlap weights in which each unit s weight is proportional to the probability of that unit being assigned to the opposite group the overlap weights are bounded and minimize the asymptotic variance of the weighted average treatment effect among the class of balancing wei

effect analysis and causation in linear structural equation models this paper considers total and direct effects in linear structural equation models adopting a causal perspective that is implicit in much of the literature on the subject the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature drawing a distinction between concomitants and factors the paper concludes that a concomitant has neither total nor direct effects on other variables when a variable is a factor and one or more intervening variables are concomitants the notion of a direct effect is not causally meaningful even when the notion of a direct effect is meaningful the usual estimate of this quantity may be inappropriate the total effect is usually interpreted as an equilibrium multiplier in the case where there are simultaneity relations among the dependent variables in tghe model the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers and thus the usual interpretation is incorrect to remedy some of these deficiencies a new effect the total effect of a factorx on an outcomey holding a set of variablesf constant is defined when defined the total and direct effects are a special case of this new effect and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier

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

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

efficient nonparametric estimation of causal effects in randomized trials with noncompliance causal approaches based on the potential outcome framework provide a useful tool for addressing noncompliance problems in randomized trials we propose a new estimator of causal treatment effects in randomized clinical trials with noncompliance we use the empirical likelihood approach to construct a profile random sieve likelihood and take into account the mixture structure in outcome distributions so that our estimator is robust to parametric distribution assumptions and provides substantial finite sample efficiency gains over the standard instrumental variable estimator our estimator is asymptotically equivalent to the standard instrumental variable estimator and it can be applied to outcome variables with a continuous ordinal or binary scale we apply our method to data from a randomized trial of an intervention to improve the treatment of depression among depressed elderly patients in primary care practices

confidence intervals for causal parameters consider an unbiased follow up study designed to investigate the causal effect of a dichotomous exposure on a dichotomous disease outcome under a deterministic outcome model a standard 95 per cent binomial confidence interval may fail to cover the causal parameter of interest at the nominal rate when we take the causal parameter to be a parameter associated with the observed study population regardless of whether the observed study population was sampled from a larger superpopulation i propose new interval estimators that in this setting improve upon the performance of the standard binomial confidence interval

sharp nonparametric bounds and randomization inference for treatment effects on an ordinal outcome in clinical research investigators are interested in inferring the average causal effect of a treatment however the causal parameter that can be used to derive the average causal effect is not well defined for ordinal outcomes although some definitions have been proposed they are limited in that they are not identical to the well defined causal risk for a binary outcome which is the simplest ordinal outcome in this paper we propose the use of a causal parameter for an ordinal outcome defined as the proportion that a potential outcome under one treatment condition would not be smaller than that under the other condition for a binary outcome this proportion is identical to the causal risk unfortunately the proposed causal parameter cannot be identified even under randomization therefore we present a numerical method to calculate the sharp nonparametric bounds within a sample reflecting the impact of confounding when the assumption of independent potential outcomes is included the causal parameter can be identified when randomization is in play then we present exact tests and the associated confidence intervals for the relative treatment effect using the randomization based approach which are an extension of the existing methods for a binary outcome our methodologies are illustrated using data from an emetic prevention clinical trial

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

accounting for covariates observed post randomization for discrete and continuous repeated measures data adjusting for covariates observed post randomization is a difficult issue in randomized clinical trials one approach is to enter these covariates as time dependent covariates in a general linear model however this approach fails to account for interactions between the primary end point and confounding variable as they evolve over time in this paper we adopt the view that since the confounder is observed following randomization it should be treated as an outcome and analysed accordingly we consider the repeated measures design where both the primary end point and the confounding measure are observed repeatedly over patient follow up a generalized estimating equation model is applied to allow each set of repeated measures to be modelled in terms of important explanatory variables seemingly unrelated regression combines the two models into an overall framework for analysis inference is then performed by imposing restrictions on the confounder regression parameters to reflect the behaviour profile of interest estimation and identification procedures are described and the methodology is illustrated with an example

response to comment on randomization inference for treatment effects on a binary outcome we thank professor yasutaka chiba 1 for commenting on rigdon and hudgens rh 2 chiba 1 described a certain exact confidence interval reported in rh as somewhat unnatural chiba also presented an alternative approach to constructing confidence intervals 3 in this response we i provide a simple explanation why the confidence interval in rh appeared unnatural and ii explain the relationship between the rh 2 and chiba 3 confidence intervals essentially the two approaches are equivalent except rh entails inverting one two sided test whereas chiba inverts two one sided tests we present a more computationally efficient method rlh for computing the rh intervals based on chiba s principal stratification formulation of the problem we also propose a third method based on blaker 4 which inverts a single two sided test but forms a confidence interval that is at least as narrow as inverting two one sided tests simulation results show the rlh intervals tend to be as narrow or narrower than the chiba and blaker intervals on average

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

an information theoretic approach for the evaluation of surrogate endpoints based on causal inference in this work a new metric of surrogacy the so called individual causal association ica is introduced using information theoretic concepts and a causal inference model for a binary surrogate and true endpoint the ica has a simple and appealing interpretation in terms of uncertainty reduction and in some scenarios it seems to provide a more coherent assessment of the validity of a surrogate than existing measures the identifiability issues are tackled using a two step procedure in the first step the region of the parametric space of the distribution of the potential outcomes compatible with the data at hand is geometrically characterized further in a second step a monte carlo approach is proposed to study the behavior of the ica on the previous region the method is illustrated using data from the collaborative initial glaucoma treatment study a newly developed and user friendly r package surrogate is provided to carry out the evaluation exercise

causal inference without counterfactuals abstract a popular approach to the framing and answering of causal questions relies on the idea of counterfactuals outcomes that would have been observed had the world developed differently for example if the patient had received a different treatment by definition one can never observe such quantities nor assess empirically the validity of any modeling assumptions made about them even though one s conclusions may be sensitive to these assumptions here i argue that for making inference about the likely effects of applied causes counterfactual arguments are unnecessary and potentially misleading an alternative approach based on bayesian decision analysis is presented properties of counterfactuals are relevant to inference about the likely causes of observed effects but close attention then must be given to the nature and context of the query as well as to what conclusions can and cannot be supported empirically in particular even in the absence of statistical uncertainty such inferences m

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

a continuous method for reducing interpolation artifacts in mutual information based rigid image registration we propose an approach for computing mutual information in rigid multimodality image registration images to be registered are modeled as functions defined on a continuous image domain analytic forms of the probability density functions for the images and the joint probability density function are first defined in 1d we describe how the entropies of the images the joint entropy and mutual information can be computed accurately by a numerical method we then extend the method to 2d and 3d the mutual information function generated is smooth and does not seem to have the typical interpolation artifacts that are commonly observed in other standard models the relationship between the proposed method and the partial volume pv model is described in addition we give a theoretical analysis to explain the nonsmoothness of the mutual information function computed by the pv model numerical experiments in 2d and 3d are presented to illustrate the smoothness of the mutual information function which leads to robust and accurate numerical convergence results for solving the image registration problem

multiscale image segmentation by integrated edge and region detection this paper is concerned with the detection of low level structure in images it describes an algorithm for image segmentation at multiple scales the detected regions are homogeneous and surrounded by closed edge contours previous approaches to multiscale segmentation represent an image at different scales using a scale space however structure is only represented implicitly in this representation structures at coarser scales are inherently smoothed and the problem of structure extraction is unaddressed this paper argues that the issues of scale selection and structure detection cannot be treated separately a new concept of scale is presented that represents image structures at different scales and not the image itself this scale is integrated into a nonlinear transform which makes structure explicit in the transformed domain structures that are stable locally invariant to changes in scale are identified as being perceptually relevant the transform can be viewed as collecting spatially distributed evidence for edges and regions and making it available at contour locations thereby facilitating integrated detection of edges and regions without restrictive models of geometry or homogeneity in this sense it performs gestalt analysis all scale parameters of the transform are automatically determined and the structure of any arbitrary geometry can be identified without any smoothing even at coarse scales

randomization inference with natural experiments an analysis of ballot effects in the 2003 california recall election since the 2000 u s presidential election social scientists have rediscovered a long tradition of research examining the effects of ballot format on voting using a new dataset collected by the new york times we investigate the causal effect of being listed on the first ballot page in the 2003 california gubernatorial recall election california law mandates a unique randomization procedure of ballot order that when appropriately modeled can be used to approximate a classical randomized experiment in a real world setting we apply randomization inference based on fisher s exact test which directly incorporates the exact randomization procedure and yields accurate nonparametric confidence intervals our results suggest that being listed on the first ballot page causes a statistically significant increase in vote shares for more than 40 of the minor candidates whereas there is no significant effect for the top two candidates we also investigate how randomization inference differs from conventional e

further analysis of interpolation effects in mutual information based image registration this paper presents an analysis of the mutual information mi metric in rigid body registration of two digital images in particular local fluctuations of the mi value due to interpolation in contrast to existing work in this area this paper starts with two hypothetical continuous images based on which both sampling and interpolation effects are analyzed this analysis indicates that an ideal interpolator may not be able to completely suppress the undesirable local minima of the mi metric if the sampling effect is not negligible several preprocessing methods are discussed for reducing the interpolation effects

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

causality conditional independence and graphical separation in settable systems we study the connections between causal relations and conditional independence within the settable systems extension of the pearl causal model pcm our analysis clearly distinguishes between causal notions and probabilistic notions and it does not formally rely on graphical representations as a foundation we provide definitions in terms of suitable functional dependence for direct causality and for indirect and total causality via and exclusive of a set of variables based on these foundations we provide causal and stochastic conditions formally characterizing conditional dependence among random vectors of interest in structural systems by stating and proving the conditional reichenbach principle of common cause obtaining the classical reichenbach principle as a corollary we apply the conditional reichenbach principle to show that the useful tools of d separation and d separation can be employed to establish conditional independence within suitably restricted settable systems analogous to markovian pcms

latent variables causal models and overidentifying constraints abstract when is a statistical dependency between two variables best explained by the supposition that one of these variables causes the other as opposed to the supposition that there is a possibly unmeasured common cause acting on both variables in this paper we describe an approach towards model specification developed more fully in our book discovering causal structure and illustrate its application to the aforementioned question briefly the approach is to determine constraints satisfied by the variance covariance matrix of a sample and then to conduct a quasi automated search for the causal specifications that will best explain those constraints

effects attributable to treatment inference in experiments and observational studies with a discrete pivot summary in randomisation and permutation inference pivotal arguments remove the hypothesised treatment effect thereby basing inferences on the null distribution in which the treatment has no effect this is common for instance with additive treatment effects the current paper uses attributable effects to expand substantially the scope of pivotal arguments attributable effects are defined for three cases namely the 2 x 2 contingency table displacement effects and the mann whitney wilcoxon statistic and in each case removing an appropriate attributable effect restores the familiar null randomisation distribution of the associated statistic yielding exact inferences the procedure extends immediately for use in sensitivity analysis in nonrandomised observational studies

exact confidence intervals for the average causal effect on a binary outcome based on the physical randomization of completely randomized experiments in a recent article in statistics in medicine rigdon and hudgens propose two approaches to obtaining exact confidence intervals for the average causal effect on a binary outcome they construct the first confidence interval by combining with the bonferroni adjustment the prediction sets for treatment effects among treatment and control groups and the second one by inverting a series of randomization tests with sample size n their second approach requires performing o n4 randomization tests we demonstrate that the physical randomization also justifies other ways to constructing exact confidence intervals that are more computationally efficient by exploiting recent advances in hypergeometric confidence intervals and the stochastic order information of randomization tests we propose approaches that either do not need to invoke monte carlo or require performing at most o n2 randomization tests we provide technical details and r code in the supporting information

causation entropy identifies indirect influences dominance of neighbors and anticipatory couplings abstract inference of causality is central in nonlinear time series analysis and science in general a popular approach to infer causality between two processes is to measure the information flow between them in terms of transfer entropy using dynamics of coupled oscillator networks we show that although transfer entropy can successfully detect information flow in two processes it often results in erroneous identification of network connections under the presence of indirect interactions dominance of neighbors or anticipatory couplings such effects are found to be profound for time dependent networks to overcome these limitations we develop a measure called causation entropy and show that its application can lead to reliable identification of true couplings

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

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

higher order whitehead products and l structures on the homology of a dgl abstract we detect higher order whitehead products on the homology h of a differential graded lie algebra l in terms of higher brackets in the transferred l structure on h via a given homotopy retraction of l onto h

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

continuous sampling in mutual information registration mutual information is a popular and widely used metric in retrospective image registration this metric excels especially with multimodal data due to the minimal assumptions about the correspondence between the image intensities in certain situations the mutual information metric is known to produce artifacts that rule out subsample registration accuracy various methods have been developed to mitigate these artifacts including higher order kernels for smoother sampling of the metric this study introduces a novel concept of continuous sampling to provide new insight into the mutual information methods currently in use in particular the connection between the partial volume interpolation and the recently introduced higher order partial volume type kernels is revealed

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

a potential tale of two by two tables from completely randomized experiments causal inference in completely randomized treatment control studies with binary outcomes is discussed from fisherian neymanian and bayesian perspectives using the potential outcomes model a randomization based justification of fisher s exact test is provided arguing that the crucial assumption of constant causal effect is often unrealistic and holds only for extreme cases some new asymptotic and bayesian inferential procedures are proposed the proposed procedures exploit the intrinsic nonadditivity of unit level causal effects can be applied to linear and nonlinear estimands and dominate the existing methods as verified theoretically and also through simulation studies supplementary materials for this article are available online

discrete optimization for interpretable study populations and randomization inference in an observational study of severe sepsis mortality abstractmotivated by an observational study of the effect of hospital ward versus intensive care unit admission on severe sepsis mortality we develop methods to address two common problems in observational studies 1 when there is a lack of covariate overlap between the treated and control groups how to define an interpretable study population wherein inference can be conducted without extrapolating with respect to important variables and 2 how to use randomization inference to form confidence intervals for the average treatment effect with binary outcomes our solution to problem 1 incorporates existing suggestions in the literature while yielding a study population that is easily understood in terms of the covariates themselves and can be solved using an efficient branch and bound algorithm we address problem 2 by solving a linear integer program to use the worst case variance of the average treatment effect among values for unobserved potential outcomes that are compatible with the null hy

dealing with limited overlap in estimation of average treatment effects summary estimation of average treatment effects under unconfounded or ignorable treatment assignment is often hampered by lack of overlap in the covariate distributions between treatment groups this lack of overlap can lead to imprecise estimates and can make commonly used estimators sensitive to the choice of specification in such cases researchers have often used ad hoc methods for trimming the sample we develop a systematic approach to addressing lack of overlap we characterize optimal subsamples for which the average treatment effect can be estimated most precisely under some conditions the optimal selection rules depend solely on the propensity score for a wide range of distributions a good approximation to the optimal rule is provided by the simple rule of thumb to discard all units with estimated propensity scores outside the range 0 1 0 9

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

randomization inference for treatment effects on a binary outcome two methods are developed for constructing randomization based confidence sets for the average effect of a treatment on a binary outcome the methods are nonparametric and require no assumptions about random sampling from a larger population both of the resulting 1 confidence sets are exact in the sense that the probability of containing the true treatment effect is at least 1 both types of confidence sets are also guaranteed to have width no greater than one in contrast a previously proposed asymptotic confidence interval is not exact and may have width greater than one the first approach combines bonferroni adjusted prediction sets for the attributable effects in the treated and untreated the second method entails inverting a permutation test simulations are presented comparing the two randomization based confidence sets with the asymptotic interval as well as the standard wald confidence interval and a commonly used exact interval for the difference in binomial proportions results show for small to moderate sample sizes that the permutation confidence set attains the narrowest width on average among the methods that maintain nominal coverage extensions that allow for stratifying on categorical baseline covariates are also discussed

a tutorial on propensity score estimation for multiple treatments using generalized boosted models the use of propensity scores to control for pretreatment imbalances on observed variables in non randomized or observational studies examining the causal effects of treatments or interventions has become widespread over the past decade for settings with two conditions of interest such as a treatment and a control inverse probability of treatment weighted estimation with propensity scores estimated via boosted models has been shown in simulation studies to yield causal effect estimates with desirable properties there are tools e g the twang package in r and guidance for implementing this method with two treatments however there is not such guidance for analyses of three or more treatments the goals of this paper are twofold 1 to provide step by step guidance for researchers who want to implement propensity score weighting for multiple treatments and 2 to propose the use of generalized boosted models gbm for estimation of the necessary propensity score weights we define the causal quantities that may be of interest to studies of multiple treatments and derive weighted estimators of those quantities we present a detailed plan for using gbm to estimate propensity scores and using those scores to estimate weights and causal effects we also provide tools for assessing balance and overlap of pretreatment variables among treatment groups in the context of multiple treatments a case study examining the effects of three treatment programs for adolescent substance abuse demonstrates the methods

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

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

randomization tests for weak null hypotheses in randomized experiments the fisher randomization test frt is appropriate for any test statistic under a sharp null hypothesis that can recover all missing potential outcomes however it is often sought after to test a

configuration spaces and polyhedral products abstract this paper aims to find the most general combinatorial conditions under which a moment angle complex d 2 s 1 k is a co h space thus splitting unstably in terms of its full subcomplexes in this way we study to which extent the conjecture holds that a moment angle complex over a golod simplicial complex is a co h space our main tool is a certain generalisation of the theory of labelled configuration spaces

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

a bayesian perspective on the analysis of unreplicated factorial experiments using potential outcomes unreplicated factorial designs have been widely used in scientific and industrial settings when it is important to distinguish active or real factorial effects from inactive or noise factorial effects used to estimate residual or error terms we propose a new approach to screen for active factorial effects from such experiments that uses the potential outcomes framework and is based on sequential posterior predictive model checks one advantage of the proposed method is its ability to broaden the standard definition of active effects and to link their definition to the population of interest another important aspect of this approach is its conceptual connection to fisherian randomization tests extensive simulation studies are conducted which demonstrate the superiority of the proposed approach over existing ones in the situations considered

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

decompositions of polyhedral products for shifted complexes abstract the conjecture of bahri bendersky cohen and gitler 2010 3 on wedge decompositions of polyhedral products of shifted complexes is settled affirmatively as a corollary it is proved that the homotopy type of the complement of a coordinate subspace arrangement associated with a shifted complex tensored with r r for any r 1 has the homotopy type of a wedge of spheres