stable weights that balance covariates for estimation with incomplete outcome data weighting methods that adjust for observed covariates such as inverse probability weighting are widely used for causal inference and estimation with incomplete outcome data part of the appeal of such methods is that one set of weights can be used to estimate a range of treatment effects based on different outcomes or a variety of population means for several variables however this appeal can be diminished in practice by the instability of the estimated weights and by the difficulty of adequately adjusting for observed covariates in some settings to address these limitations this article presents a new weighting method that finds the weights of minimum variance that adjust or balance the empirical distribution of the observed covariates up to levels prespecified by the researcher this method allows the researcher to balance very precisely the means of the observed covariates and other features of their marginal and joint distributions such as variances and correlations and also for example the

randomization inference for treatment effect variation summary applied researchers are increasingly interested in whether and how treatment effects vary in randomized evaluations especially variation that is not explained by observed covariates we propose a model free approach for testing for the presence of such unexplained variation to use this randomization based approach we must address the fact that the average treatment effect which is generally the object of interest in randomized experiments actually acts as a nuisance parameter in this setting we explore potential solutions and advocate for a method that guarantees valid tests in finite samples despite this nuisance we also show how this method readily extends to testing for heterogeneity beyond a given model which can be useful for assessing the sufficiency of a given scientific theory we finally apply our method to the national head start impact study which is a large scale randomized evaluation of a federal preschool programme finding that there is indeed significant unexplained treatment effect variation

likelihood based analysis of causal effects of job training programs using principal stratification government sponsored job training programs must be subject to evaluation to assess whether their effectiveness justifies their cost to the public the evaluation usually focuses on employment and total earnings although the effect on wages is also of interest because this effect reflects the increase in human capital due to the training program whereas the effect on total earnings may be simply reflecting the increased likelihood of employment without any effect on wage rates estimating the effects of training programs on wages is complicated by the fact that even in a randomized experiment wages are truncated or less accurately censored by nonemployment that is they are only observed and well defined for individuals who are employed in this article we develop a likelihood based approach to estimate the wage effect of the us federally funded job corps training program using principal stratification our estimands are formulated in terms of 1 the effect of the training program on wages

causal mediation analysis in the multilevel intervention and multicomponent mediator case summary mediation analysis is an important tool in social and medical sciences as it helps to understand why an intervention works the commonly used approach given by baron and kenny requires the strong assumption sequential ignorability to yield causal interpretation ten have and his colleagues proposed a rank preserving model to relax this assumption however the rank preserving model is restricted to the case with binary intervention and single mediator and needs another strong assumption rank preserving we propose a new model that can relax this assumption and can handle both multilevel intervention and multicomponent mediators as an estimating equation based method our model can handle both correlated data with the generalized estimating equation and missing data with inverse probability weighting finally our method can also be used in many other research settings using mathematical models similar to mediation analysis such as treatment compliance and post randomized treatment component analysis for the causal mediation model proposed we first show identifiability for the parameters in the model we then propose a semiparametric method for estimating the model parameters and derive asymptotic results for the estimators proposed simulation shows good performance for the proposed estimators in finite sample sizes finally we apply the method proposed to two real world clinical studies the college student drinking study and the improving mood promoting access to collaborative treatment for late life depression study

in praise of simplicity not mathematistry ten simple powerful ideas for the statistical scientist ronald fisher was by all accounts a first rate mathematician but he saw himself as a scientist not a mathematician and he railed against what george box called in his fisher lecture mathematistry mathematics is the indispensable foundation of statistics but for me the real excitement and value of our subject lies in its application to other disciplines we should not view statistics as another branch of mathematics and favor mathematical complexity over clarifying formulating and solving real world problems valuing simplicity i describe 10 simple and powerful ideas that have influenced my thinking about statistics in my areas of research interest missing data causal inference survey sampling and statistical modeling in general the overarching theme is that statistics is a missing data problem and the goal is to predict unknowns with appropriate measures of uncertainty

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

geodesic active regions and level set methods for supervised texture segmentation this paper presents a novel variational framework to deal with frame partition problems in computer vision this framework exploits boundary and region based segmentation modules under a curve based optimization objective function the task of supervised texture segmentation is considered to demonstrate the potentials of the proposed framework the textured feature space is generated by filtering the given textured images using isotropic and anisotropic filters and analyzing their responses as multi component conditional probability density functions the texture segmentation is obtained by unifying region and boundary based information as an improved geodesic active contour model the defined objective function is minimized using a gradient descent method where a level set approach is used to implement the obtained pde according to this pde the curve propagation towards the final solution is guided by boundary and region based segmentation forces and is constrained by a regularity force the level set implementation is performed using a fast front propagation algorithm where topological changes are naturally handled the performance of our method is demonstrated on a variety of synthetic and real textured frames

causal inference by using invariant prediction identification and confidence intervals summary what is the difference between a prediction that is made with a causal model and that with a non causal model suppose that we intervene on the predictor variables or change the whole environment the predictions from a causal model will in general work as well under interventions as for observational data in contrast predictions from a non causal model can potentially be very wrong if we actively intervene on variables here we propose to exploit this invariance of a prediction under a causal model for causal inference given different experimental settings e g various interventions we collect all models that do show invariance in their predictive accuracy across settings and interventions the causal model will be a member of this set of models with high probability this approach yields valid confidence intervals for the causal relationships in quite general scenarios we examine the example of structural equation models in more detail and provide sufficient assumptions under which the set of causal predictors becomes identifiable we further investigate robustness properties of our approach under model misspecification and discuss possible extensions the empirical properties are studied for various data sets including large scale gene perturbation experiments

toward causal inference with interference a fundamental assumption usually made in causal inference is that of no interference between individuals or units that is the potential outcomes of one individual are assumed to be unaffected by the treatment assignment of other individuals however in many settings this assumption obviously does not hold for example in the dependent happenings of infectious diseases whether one person becomes infected depends on who else in the population is vaccinated in this article we consider a population of groups of individuals where interference is possible between individuals within the same group we propose estimands for direct indirect total and overall causal effects of treatment strategies in this setting relations among the estimands are established for example the total causal effect is shown to equal the sum of direct and indirect causal effects using an experimental design with a two stage randomization procedure first at the group level then at the individual level within groups unbiased estimators of the proposed estimands are presented variances of the estimators are also developed the methodology is illustrated in two different settings where interference is likely assessing causal effects of housing vouchers and of vaccines

localizing region based active contours in this paper we propose a natural framework that allows any region based segmentation energy to be re formulated in a local way we consider local rather than global image statistics and evolve a contour based on local information localized contours are capable of segmenting objects with heterogeneous feature profiles that would be difficult to capture correctly using a standard global method the presented technique is versatile enough to be used with any global region based active contour energy and instill in it the benefits of localization we describe this framework and demonstrate the localization of three well known energies in order to illustrate how our framework can be applied to any energy we then compare each localized energy to its global counterpart to show the improvements that can be achieved next an in depth study of the behaviors of these energies in response to the degree of localization is given finally we show results on challenging images to illustrate the robust and accurate segmentations that are possible with this new class of active contour models

posterior predictive p values extending work of rubin this paper explores a bayesian counterpart of the classical p value namely a tail area probability of a test statistic under a null hypothesis the bayesian formulation using posterior predictive replications of the data allows a test statistic to depend on both data and unknown nuisance parameters and thus permits a direct measure of the discrepancy between sample and population quantities the tail area probability for a test statistic is then found under the joint posterior distribution of replicate data and the nuisance parameters both conditional on the null hypothesis this posterior predictive p value can also be viewed as the posterior mean of a classical p value averaging over the posterior distribution of nuisance parameters under the null hypothesis and thus it provides one general method for dealing with nuisance parameters two classical examples including the behrens fisher problem are used to illustrate the posterior predictive p value and some of its interesting properties which also reveal a new bayesian interpretation for some classical p values an application to multiple imputation inference is also presented a frequency evaluation shows that in general if the replication is defined by new nuisance parameters and new data then the type i frequentist error of an level posterior predictive test is often close to but less than and will never exceed 2

valid randomization based p values for partially post hoc subgroup analyses by partially post hoc subgroup analyses we mean analyses that compare existing data from a randomized experiment from which a subgroup specification is derived to new subgroup only experimental data we describe a motivating example in which partially post hoc subgroup analyses instigated statistical debate about a medical device s efficacy we clarify the source of such analyses invalidity and then propose a randomization based approach for generating valid posterior predictive p values for such partially post hoc subgroups lastly we investigate the approach s operating characteristics in a simple illustrative setting through a series of simulations showing that it can have desirable properties under both null and alternative hypotheses

on the nature and discovery of structure abstract extending principles of experimentation we discuss conditions under which nonexperimental data allow consistent estimation of effects of the kind revealed by experimentation and relevant to decisions we show how implications of these conditions are often overlooked and how failure to distinguish between factors and concomitants makes almost anything said about a model ambiguous if not wrong the effects to be estimated dictate the factors to be included consistency and efficiency determine the concomitants whose effects are not to be estimated concomitants may affect but must not be affected by the factors effects of excluded variables on an included variable may cause inconsistency if the included variable is a factor can only reduce inconsistency if the included variable is a concomitant exclusion of a variable because it is highly correlated with another may sometimes be legitimate if both variables are concomitants never if either is a factor a condition for consistent estimatio

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

estimation of average treatment effect with incompletely observed longitudinal data application to a smoking cessation study we study the problem of estimation and inference on the average treatment effect in a smoking cessation trial where an outcome and some auxiliary information were measured longitudinally and both were subject to missing values dynamic generalized linear mixed effects models linking the outcome the auxiliary information and the covariates are proposed the maximum likelihood approach is applied to the estimation and inference on the model parameters the average treatment effect is estimated by the g computation approach and the sensitivity of the treatment effect estimate to the nonignorable missing data mechanisms is investigated through the local sensitivity analysis approach the proposed approach can handle missing data that form arbitrary missing patterns over time we applied the proposed method to the analysis of the smoking cessation trial

matching and weighting with functions of error prone covariates for causal inference abstractmatching estimators are commonly used to estimate causal effects in nonexperimental settings covariate measurement error can be problematic for matching estimators when observational treatment groups differ on latent quantities observed only through error prone surrogates we establish necessary and sufficient conditions for matching and weighting with functions of observed covariates to yield unconfounded causal effect estimators generalizing results from the standard i e no measurement error case we establish that in common covariate measurement error settings including continuous variables with continuous measurement error discrete variables with misclassification and factor and item response theory models no single function of the observed covariates computed for all units in a study is appropriate for matching however we demonstrate that in some circumstances it is possible to create different functions of the observed covariates for treatment and control units to construct a va

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

doubly robust conditional logistic regression epidemiologic research often aims to estimate the association between a binary exposure and a binary outcome while adjusting for a set of covariates eg confounders when data are clustered as in for instance matched case control studies and co twin control studies it is common to use conditional logistic regression in this model all cluster constant covariates are absorbed into a cluster specific intercept whereas cluster varying covariates are adjusted for by explicitly adding these as explanatory variables to the model in this paper we propose a doubly robust estimator of the exposure outcome odds ratio in conditional logistic regression models this estimator protects against bias in the odds ratio estimator due to misspecification of the part of the model that contains the cluster varying covariates the doubly robust estimator uses two conditional logistic regression models for the odds ratio one prospective and one retrospective and is consistent for the exposure outcome odds ratio if at least one of these models is correctly specified not necessarily both we demonstrate the properties of the proposed method by simulations and by re analyzing a publicly available dataset from a matched case control study on induced abortion and infertility

facilitating score and causal inference trees for large observational studies assessing treatment effects in observational studies is a multifaceted problem that not only involves heterogeneous mechanisms of how the treatment or cause is exposed to subjects known as propensity but also differential causal effects across sub populations we introduce a concept termed the facilitating score to account for both the confounding and interacting impacts of covariates on the treatment effect several approaches for estimating the facilitating score are discussed in particular we put forward a machine learning method called causal inference tree cit to provide a piecewise constant approximation of the facilitating score with interpretable rules cit splits data in such a way that both the propensity and the treatment effect become more homogeneous within each resultant partition causal inference at different levels can be made on the basis of cit together with an aggregated grouping procedure cit stratifies data into strata where causal effects can be conveniently assessed within each besides a feasible way of predicting individual causal effects ice is made available by aggregating ensemble cit models both the stratified results and the estimated ice provide an assessment of heterogeneity of causal effects and can be integrated for estimating the average causal effect ace mean square consistency of cit is also established we evaluate the performance of proposed methods with simulations and illustrate their use with the nsw data in dehejia and wahba 1999 where the objective is to assess the impact of a labor training program the national supportedwork nsw demonstration on post intervention earnings

new g formula for the sequential causal effect and blip effect of treatment in sequential causal inference in sequential causal inference two types of causal effects are of practical interest namely the causal effect of the treatment regime called the sequential causal effect and the blip effect of

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

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

new efficient multipoint iterative methods for solving nonlinear systems it is attempted to put forward a new multipoint iterative method for approximating solutions of nonlinear systems the main feature of the extended methods is that it uses only one lu factorization which preserves and reduces computational complexities moreover the first step is designed in such a way that in most cases singularity of the denominator is avoided therefore we try to generalize the suggested method so that we can increase the order of convergence from four to six and eight but we do not need any new lu factorization also we justify this advantage of the convergence analysis versus some numerical methods with different examples

causal inference using potential outcomes design modeling decisions causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units observed values of the potential outcomes are revealed by the assignment mechanism a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes fisher made tremendous contributions to causal inference through his work on the design of randomized experiments but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well as noted by kempthorne in his 1976 discussion of savage s fisher lecture fisher never bridged his work on experimental design and his work on parametric modeling a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework where the potential outcomes and covariates are given a bayesian distribution to complete the model specification also this framework crisply separates scientific inference for causal effects and decisions based on s

image segmentation using active contours driven by the bhattacharyya gradient flow this paper addresses the problem of image segmentation by means of active contours whose evolution is driven by the gradient flow derived from an energy functional that is based on the bhattacharyya distance in particular given the values of a photometric variable or of a set thereof which is to be used for classifying the image pixels the active contours are designed to converge to the shape that results in maximal discrepancy between the empirical distributions of the photometric variable inside and outside of the contours the above discrepancy is measured by means of the bhattacharyya distance that proves to be an extremely useful tool for solving the problem at hand the proposed methodology can be viewed as a generalization of the segmentation methods in which active contours maximize the difference between a finite number of empirical moments of the ldquoinsiderdquo and ldquooutsiderdquo distributions furthermore it is shown that the proposed methodology is very versatile and flexible in the sense that it allows one to easily accommodate a diversity of the image features based on which the segmentation should be performed as an additional contribution a method for automatically adjusting the smoothness properties of the empirical distributions is proposed such a procedure is crucial in situations when the number of data samples supporting a certain segmentation class varies considerably in the course of the evolution of the active contour in this case the smoothness properties of the empirical distributions have to be properly adjusted to avoid either over or underestimation artifacts finally a number of relevant segmentation results are demonstrated and some further research directions are discussed

bias in estimating the causal hazard ratio when using two stage instrumental variable methods two stage instrumental variable methods are commonly used to estimate the causal effects of treatments on survival in the presence of measured and unmeasured confounding two stage residual inclusion 2sri has been the method of choice over two stage predictor substitution 2sps in clinical studies we directly compare the bias in the causal hazard ratio estimated by these two methods under a principal stratification framework we derive a closed form solution for asymptotic bias of the causal hazard ratio among compliers for both the 2sps and 2sri methods when survival time follows the weibull distribution with random censoring when there is no unmeasured confounding and no always takers our analytic results show that 2sri is generally asymptotically unbiased but 2sps is not however when there is substantial unmeasured confounding 2sps performs better than 2sri with respect to bias under certain scenarios we use extensive simulation studies to confirm the analytic results from our closed form solutions we apply these two methods to prostate cancer treatment data from surveillance epidemiology and end results medicare and compare these 2sri and 2sps estimates with results from two published randomized trials copyright 2015 john wiley sons ltd

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

identification and estimation of local average treatment effects we investigate conditions sufficient for identification of average treatment effects using instrumental variables first we show that the existence of valid instruments is not sufficient to identify any meaningful average treatment effect we then establish that the combination of an instrument and a condition on the relation between the instrument and the participation status is sufficient for identification of a local average treatment effect for those who can be induced to change their participation status by changing the value of the instrument finally we derive the probability limit of the standard iv estimator under these conditions it is seen to be a weighted average of local average treatment effects this abstract was borrowed from another version of this item

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

compensation and amplification of attenuation bias in causal effect estimates covariate adjusted treatment effects are commonly estimated in non randomized studies it has been shown that measurement error in covariates can bias treatment effect estimates when not appropriately accounted for so far these delineations primarily assumed a true data generating model that included just one single covariate it is however more plausible that the true model consists of more than one covariate we evaluate when a further covariate may reduce bias due to measurement error in another covariate and in which cases it is not recommended to include a further covariate we analytically derive the amount of bias related to the fallible covariate s reliability and systematically disentangle bias compensation and amplification due to an additional covariate with a fallible covariate it is not always beneficial to include an additional covariate for adjustment as the additional covariate can extensively increase the bias the mechanisms for an increased bias due to an additional covariate can be complex even in a simple setting of just two covariates a high reliability of the fallible covariate or a high correlation between the covariates cannot in general prevent from substantial bias we show distorting effects of a fallible covariate in an empirical example and discuss adjustment for latent covariates as a possible solution

statistical inference based on randomly generated auxiliary variables summary in most real life studies auxiliary variables are available and are employed to explain and understand missing data patterns and to evaluate and control causal relationships with variables of interest usually their availability is assumed to be a fact even if the variables are measured without the objectives of the study in mind as a result inference with missing data and causal inference require some assumptions that cannot easily be validated or checked in this paper a framework is constructed in which auxiliary variables are treated as a selection possibly random from the universe of variables on a population this framework provides conditions to make statistical inference beyond the traces of bias or effects found by the auxiliary variables themselves the utility of the framework is demonstrated for the analysis and reduction of non response in surveys however the framework may be more generally used to understand the strength of association between variables important roles are played by the diversity and diffusion of the population of interest features that are defined in the paper and the estimation of which is discussed

a semiparametric approach to model effect modification one fundamental statistical question for research areas such as precision medicine and health disparity is about discovering effect modification of treatment or exposure by observed covariates we

bayesianly justifiable and relevant frequency calculations for the applied statistician a common reaction among applied statisticians is that the bayesian statistician s energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying bayes s theorem to calculate conditional distributions of unknowns given knowns i feel however that the applied bayesian statistician s tool kit should be more extensive and include tools that may be usefully labeled frequency calculations three types of bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician

doubly robust type estimation for covariate adjustment in latent variable modeling due to the difficulty in achieving a random assignment a quasi experimental or observational study design is frequently used in the behavioral and social sciences if a nonrandom assignment depends on the covariates multiple group structural equation modeling that includes the regression function of the dependent variables on the covariates that determine the assignment can provide reasonable estimates under the condition of correct specification of the regression function however it is usually difficult to specify the correct regression function because the dimensions of the dependent variables and covariates are typically large therefore the propensity score adjustment methods have been proposed since they do not require the specification of the regression function and have been applied to several applied studies however these methods produce biased estimates if the assignment mechanism is incorrectly specified in order to make a more robust inference it would be more useful to develop an estimation method that integrates the regression approach with the propensity score methodology in this study we propose a doubly robust type estimation method for marginal multiple group structural equation modeling this method provides a consistent estimator if either the regression function or the assignment mechanism is correctly specified a simulation study indicates that the proposed estimation method is more robust than the existing methods

positive association among three binary variables and cross product ratios we show that when the three way association level among the three binary variables x u 1 and u 2 is fixed dp pr x 1 u 1 1 pr x 11 u 1 0 increases as the cross product ratio of u 1 and u 2 increases under the assumption that x is positively associated with u 1 and u 2 we then discuss some implications of this property

modeling partial compliance through copulas in a principal stratification framework within the principal stratification framework for causal inference modeling partial compliance is challenging because the continuous nature of the principal strata raises subtle specification issues in this context we propose an approach based on the assumption that the joint distribution of the degree of compliance to the treatment and the degree of compliance to the control follows a plackett copula so that their association is modeled in a flexible way through a single parameter moreover given the two compliances the distribution of the outcomes is parameterized in a flexible way through a regression model which may include interaction and quadratic terms and may also be heteroscedastic in order to estimate the parameters of the resulting model and then the causal effect of the treatment we adopt a maximum likelihood approach via the em algorithm in applying this approach the marginal distributions of the two compliances are estimated by their empirical distribution functions so that no co

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

semiparametric bayesian estimation for marginal parametric potential outcome modeling application to causal inference we propose a new semiparametric bayesian model for causal inference in which assignment to treatment depends on potential outcomes the model uses the probit stick breaking process mixture proposed by chung and dunson 2009 a variant of the dirichlet process mixture modeling in contrast to previous bayesian models the proposed model directly estimates the parameters of the marginal parametric model of potential outcomes while it relaxes the strong ignorability assumption and requires no parametric model assumption for the assignment model and conditional distribution of the covariate vector the proposed estimation method is more robust than maximum likelihood estimation in that it does not require knowledge of the full joint distribution of potential outcomes covariates and assignments in addition the method is more efficient than fully nonparametric bayes methods we apply this model to infer the differential effects of cognitive and noncognitive skills on the wages of production and nonprodu

a general statistical framework for subgroup identification and comparative treatment scoring summary many statistical methods have recently been developed for identifying subgroups of patients who may benefit from different available treatments compared with the traditional outcome modeling approaches these methods focus on modeling interactions between the treatments and covariates while by pass or minimize modeling the main effects of covariates because the subgroup identification only depends on the sign of the interaction however these methods are scattered and often narrow in scope in this article we propose a general framework by weighting and a learning for subgroup identification in both randomized clinical trials and observational studies our framework involves minimum modeling for the relationship between the outcome and covariates pertinent to the subgroup identification under the proposed framework we may also estimate the magnitude of the interaction which leads to the construction of scoring system measuring the individualized treatment effect the proposed methods are quite flexible and include many recently proposed estimators as special cases as a result some estimators originally proposed for randomized clinical trials can be extended to observational studies and procedures based on the weighting method can be converted to an a learning method and vice versa our approaches also allow straightforward incorporation of regularization methods for high dimensional data as well as possible efficiency augmentation and generalization to multiple treatments we examine the empirical performance of several procedures belonging to the proposed framework through extensive numerical studies