the control of confounding by intermediate variables in epidemiologic studies of the effect of an exposure on disease the crude association of exposure with disease may fail to reflect a causal association due to confounding by one or more covariates most previous discussions of confounding in the epidemiologic literature have considered only point exposure studies that is studies that measure exposure and covariate status only once at start of follow up in this paper we offer definitions of confounding suitable for longitudinal studies that obtain data on exposure covariate and vital status at several points in time an important difference between longitudinal studies and point exposure studies is that in longitudinal studies a time dependent covariate can be simultaneously a confounder and an intermediate variable on the causal pathway from exposure to disease in this paper i propose an estimator the extended standardized risk difference that provides control for confounding by a covariate that is simultaneously a confounder and an intermediate variable

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

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

the foundations of confounding in epidemiology abstract a statistically coherent view of confounding motivated by the over controversy over the proper control of confounding in the presence of prior knowledge is presented confounding by a covariate c in the presence of data on c is distinguished from confounding in the absence of data on c a covariate c is defined to be a nonconfounder in the absence of data on c if the population parameter of interest can be unbiasedly estimated asymptotically absent data on c under this definition c may be a confounder for some parameters of interest and a nonconfounder for others if c is a confounder for a parameter of interest that has a causal interpretation we call c a causal confounder when data on c are available c is defined to be a nonconfounder for a particular parameter of interest if and only if inference on the parameter of interest does not depend on the data through c bayesians frequentists and pure likelihoodists will in general agree on the prior knowledge necessary to render c a non confounder in particular c will in general be a nonconfounder precisely when the crude data ignoring c are s sufficient for the parameter of interest the intuitive view held by many practicing epidemiologists that confounding by c represents a bias of the unadjusted crude estimator is in a sense correct provided inference is performed conditional on approximate ancillary statistics that measure the degree to which associations in the data differ due to sampling variability from those population associations known a priori

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

regularized positive definite fourth order tensor field estimation from dw mri in diffusion weighted magnetic resonance image dw mri processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the dw mri data from this tensor approximation one can compute useful scalar quantities e g anisotropy mean diffusivity which have been clinically used for monitoring encephalopathy sclerosis ischemia and other brain disorders it is now well known that this 2nd order tensor approximation fails to capture complex local tissue structures e g crossing fibers and as a result the scalar quantities derived from these tensors are grossly inaccurate at such locations in this paper we employ a 4th order symmetric positive definite spd tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the dw mri data guaranteeing the spd property several articles have been reported in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positivity of the estimates which is a fundamental constraint since negative values of the diffusivity are not meaningful in this paper we represent the 4th order tensors as ternary quartics and then apply hilbert s theorem on ternary quartics along with the iwasawa parametrization to guarantee an spd 4th order tensor approximation from the dw mri data the performance of this model is depicted on synthetic data as well as real dw mris from a set of excised control and injured rat spinal cords showing accurate estimation of scalar quantities such as generalized anisotropy and trace as well as fiber orientations

axioms of causal relevance this paper develops axioms and formal semantics for statements of the form x is causally irrelevant to y in context z which we interpret to mean changing x will not affect y once z is held constant the axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance as in finding x will not alter our belief in y once we know z two versions of causal irrelevance are analyzed probabilistic and deterministic we show that unless stability is assumed the probabilistic definition yields a very loose structure that is governed by just two trivial axioms under the stability assumption probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs under the deterministic definition causal irrelevance complies with all of the axioms of path interception in cyclic graphs except transitivity we compare our formalism to that of lewis 1973 and offer a graphical method of proving theorems about causal relevance

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

causal inference for complex longitudinal data the continuous case we extend robins theory of causal inference for complex longitudinal data to the case of continuously varying as opposed to discrete covariates and treatments in particular we establish versions of the key results of the discrete theory the g computation formula and a collection of powerful characterizations of the g null hypothesis of no treatment eect this is accomplished under natural continuity hypotheses concerning the conditional distributions of the outcome variable and of the covariates given the past we also show that our assumptions concerning counterfactual variables place no restriction on the joint distribution of the observed variables thus in a precise sense these assumptions are for free or if you prefer harmless

uniform consistency in causal inference there is a long tradition of representing causal relationships by directed acyclic graphs wright 1934 spirtes 1994 spirtes et al 1993 and pearl verma 1991 describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables and or an unknown time order and that under weak conditions for certain combinations of directed acyclic graphs and probability distributions are asymptotically in sample size consistent these results are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables we resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures we show that the asymptotically consistent procedures are pointwise consistent but uniformly consistent tests do not exist thus no finite sample size can ever be guaranteed to approximate the asymptotic results we also show the nonexistence of valid consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators our results make no assumption about the form of the tests or estimators in particular the tests could be classical independence tests they could be bayes tests or they could be tests based on scoring methods such as bic or aic the implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper the results hinge on the following fact it is possible to find for each sample size n distributions p and q such that p and q are empirically indistinguishable and yet p and q correspond to different causal effects

estimation of controlled direct effects in time varying treatments using structural nested mean models application to a primary prevention trial for coronary events with pravastatin for the estimation of controlled direct effects i e direct effects controlling intermediates that are set at a fixed level for all members of the population without bias two fundamental assumptions must hold the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome even if these assumptions hold one would nonetheless fail to estimate direct effects using standard methods for example stratification or regression modeling when the treatment influences confounding factors for such situations the sequential g estimation method for structural nested mean models has been developed for estimating controlled direct effects in point treatment situations in this study we demonstrate that this method can be applied to longitudinal data with time varying treatments and repeatedly measured intermediate variables we sequentially estimate the parameters in two structural nested mean models one for a repeatedly measured intermediate and the other one for direct effects of a time varying treatment the method was applied to data from a large primary prevention trial for coronary events in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia

identifying the average treatment effect in ordered treatment models without unconfoundedness we show identification of the average treatment effect ate when treatment is specified by ordered choice in cross section or panel models treatment is determined by location of a latent variable containing a continuous instrument relative to two or more thresholds we place no functional form restrictions on latent errors and potential outcomes unconfoundedness of treatment does not hold and identification at infinity for the treated is not possible yet we still show nonparametric point identification and estimation of the ate we apply our model to reinvestigate the inverted u relationship between competition and innovation and find no inverted u in us data

analyzing sequentially randomized trials based on causal effect models for realistic individualized treatment rules in this paper we argue that causal effect models for realistic individualized treatment rules represent an attractive tool for analyzing sequentially randomized trials unlike a number of methods proposed previously this approach does not rely on the assumption that intermediate outcomes are discrete or that models for the distributions of these intermediate outcomes given the observed past are correctly specified in addition it generalizes the methodology for performing pairwise comparisons between individualized treatment rules by allowing the user to posit a marginal structural model for all candidate treatment rules simultaneously this is particularly useful if the number of such rules is large in which case an approach based on individual pairwise comparisons would be likely to suffer from too much sampling variability to provide an informative answer in addition such causal effect models represent an interesting alternative to methods previously proposed for selecting an optimal individualized treatment rule in that they immediately give the user a sense of how the optimal outcome is estimated to change in the neighborhood of the identified optimum we discuss an inverse probability of treatment weighted iptw estimator for these causal effect models which is straightforward to implement using standard statistical software and develop an approach for constructing valid asymptotic confidence intervals based on the influence curve of this estimator the methodology is illustrated in two simulation studies that are intended to mimic an hiv aids trial

estimation of the causal effect of a time varying exposure on the marginal mean of a repeated binary outcome abstract we provide sufficient conditions for estimating from longitudinal data the causal effect of a time dependent exposure or treatment on the marginal probability of response for a dichotomous outcome we then show how one can estimate this effect under these conditions using the g computation algorithm of robins we also derive the conditions under which some current approaches to the analysis of longitudinal data such as the generalized estimating equations gee approach of zeger and liang the feedback model techniques of liang and zeger and within subject conditional methods can provide valid tests and estimates of causal effects we use our methods to estimate the causal effect of maternal stress on the marginal probability of a child s illness from the mothers stress and children s morbidity data and compare our results with those previously obtained by zeger and liang using a gee approach

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

empirical and counterfactual conditions for sufficient cause interactions summary sufficient component causes are discussed within the deterministic potential outcomes framework so as to formalize notions of sufficient causes synergism and sufficient cause in teractions doing so allows for the derivation of counterfactual and empirical conditions for detecting the presence of sufficient cause interactions the conditions are novel in that unlike other conditions in the literature they make no assumption about monotonicity the conditions can also be generalized and the conditions for three way sufficient cause interactions are given explicitly the statistical tests derived for sufficient cause interactions are compared with and contrasted to interaction terms in standard statistical models

bayesian inference for causal effects in randomized experiments with noncompliance for most of this century randomization has been a cornerstone of scientific experimentation especially when dealing with humans as experimental units in practice however noncompliance is relatively common with human subjects complicating traditional theories of inference that require adherence to the random treatment assignment in this paper we present bayesian inferential methods for causal estimands in the presence of noncompliance when the binary treatment assignment is random and hence ignorable but the binary treatment received is not ignorable we assume that both the treatment assigned and the treatment received are observed we describe posterior estimation using em and data augmentation algorithms also we investigate the role of two assumptions often made in econometric instrumental variables analyses the exclusion restriction and the monotonicity assumption without which the likelihood functions generally have substantial regions of maxima we apply our procedures to real and artificial data thereby demonstrating the technology and showing that our new methods can yield valid inferences that differ in practically important ways from those based on previous methods for analysis in the presence of noncompliance including intention to treat analyses and analyses based on econometric instrumental variables techniques finally we perform a simulation to investigate the operating characteristics of the competing procedures in a simple setting which indicates relatively dramatic improvements in frequency operating characteristics attainable using our bayesian procedures

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

endogenous selection or treatment model estimation in a sample selection or treatment effects model common unobservables may affect both the outcome and the probability of selection in unknown ways this paper shows that the distribution function of potential outcomes conditional on covariates can be identified given an observed variable v that affects the treatment or selection probability in certain ways and is conditionally independent of the error terms in a model of potential outcomes selection model estimators based on this identification are provided which take the form of simple weighted averages gmm or two stage least squares these estimators permit endogenous and mismeasured regressors empirical applications are provided to estimation of a firm investment model and a schooling effects on wages model

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

conditioning likelihood and coherence a review of some foundational concepts 2000 conditioning likelihood and coherence a review of some foundational concepts journal of the american statistical association vol 95 no 452 pp 1340 1346

opportunities and pitfalls in the quantification of fiber integrity what can we gain from q ball imaging the quantification of fiber integrity is central to the clinical application of diffusion imaging compared to diffusion tensor imaging dti q ball imaging qbi allows for the depiction of multiple fiber directions within a voxel however this advantage has not yet been shown to translate directly to superior quantification of fiber integrity furthermore recent developments in qbi reconstruction with solid angle consideration have led to sharper and intrinsically normalized orientation distribution functions the implications of this technique on quantification are also unknown to investigate this the generalized fractional anisotropy gfa from the original and the more recent qbi reconstruction scheme and the dti derived fractional anisotropy fa were evaluated comparatively using monte carlo simulations and real mri measurements of crossing fiber phantoms contrast to noise ratio accuracy independence of the acquisition setup and the relation of single fiber anisotropies to measured anisotropy in crossings were assessed in homogeneous single fiber regions at b values around 1000 s mm2 the fa performed best while the original qbi reconstruction does not show a clear advantage even at higher b values and in crossing regions the new reconstruction scheme yields superior properties and is recommended for quantification at higher b values and especially in regions of heterogeneous fiber configuration

signed directed acyclic graphs for causal inference formal rules governing signed edges on causal directed acyclic graphs are described in this paper and it is shown how these rules can be useful in reasoning about causality specifically the notions of a monotonic effect a weak monotonic effect and a signed edge are introduced results are developed relating these monotonic effects and signed edges to the sign of the causal effect of an intervention in the presence of intermediate variables the incorporation of signed edges into the directed acyclic graph causal framework furthermore allows for the development of rules governing the relationship between monotonic effects and the sign of the covariance between two variables it is shown that when certain assumptions about monotonic effects can be made then these results can be used to draw conclusions about the presence of causal effects even when data is missing on confounding variables

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

criteria for confounders in epidemiological studies the paper addresses a formal definition of a confounder based on the qualitative definition that is commonly used in standard epidemiology text books to derive the criterion for a factor to be a confounder given by miettinen and cook and to clarify inconsistency between various criteria for a confounder we introduce the concepts of an irrelevant factor an occasional confounder and a uniformly irrelevant factor we discuss criteria for checking these and show that miettinen and cook s criterion can also be applied to occasional confounders moreover we consider situations with multiple potential confounders and we obtain two necessary conditions that are satisfied by each confounder set none of the definitions and results presented in this paper require the ignorability and sufficient control confounding assumptions which are commonly employed in observational and epidemiological studies

grouped data estimation and testing in simple labor supply models abstract inappropriate identifying assumptions and measurement error in hourly wage data may account for the poor performance of some empirical labor supply models this paper discusses an efficient generalization of wald s method of fitting straigth lines that is robust to measurement error imposes mild identifying assumptions and is useful for the estimation of labor supply models with panel data a two stage least squares tsls equivalent of the efficient wald estimator is presented and a tsls overidentification test statistic is shown to be a test statistic for the equality of alternative wald estimates of the same parameter in an emperical example estimated labor supply elasticities range from 0 6 to 0 8 a test for measurement error based on the difference between efficient wald and analysis of covariance estimators is also proposed application of the test indicates that measurement error may be responsible for low or negative estimates of labor supply elasticities

dynamic treatment effects this paper develops robust models for estimating and interpreting treatment effects arising from both ordered and unordered multi stage decision problems identification is secured through instrumental variables and or conditional independence matching assumptions we decompose treatment effects into direct effects and continuation values associated with moving to the next stage of a decision problem using our framework we decompose the iv estimator showing that iv generally does not estimate economically interpretable or policy relevant parameters in prototypical dynamic discrete choice models unless policy variables are instruments continuation values are an empirically important component of estimated total treatment effects of education we use our analysis to estimate the components of what late estimates in a dynamic discrete choice model

semiparametric estimation of a binary response model with a change point due to a covariate threshold this paper is concerned with semiparametric estimation of a threshold binary response model the estimation method considered in the paper is semiparametric since the parameters for a regression function are finite dimensional while allowing for heteroskedasticity of unknown form in particular the paper considers manski 1975 1985 s maximum score estimator the model in this paper is irregular because of a change point due to an unknown threshold in a covariate this irregularity coupled with the discontinuity of the objective function of the maximum score estimator complicates the analysis of the asymptotic behavior of the estimator sufficient conditions for the identification of parameters are given and the consistency of the estimator is obtained it is shown that the estimator of the threshold parameter is n consistent and the estimator of the remaining regression parameters is cube root n consistent furthermore we obtain the asymptotic distribution of the estimators it turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator

improved estimation of controlled direct effects in the presence of unmeasured confounding of intermediate variables adjusting for a causal intermediate is a common analytic strategy for estimating an average causal direct effect acde the acde is the component of the total exposure effect that is not relayed through the specified intermediate even if the total effect is unconfounded the usual acde estimate may be biased when an unmeasured variable affects the intermediate and outcome variables using linear programming optimization to compute non parametric bounds we develop new acde estimators for binary measured variables in this causal structure and use root mean square confounding bias rmsb to compare their performance with the usual stratified estimator in simulated distributions of target populations comprised of the 64 possible potential response types as well as distributions of target populations restricted to subsets of 18 or 12 potential response types defined by monotonicity or no interactions assumptions of unit level causal effects we also consider target population distributions conditioned on fixed outcome risk among the unexposed or fixed true acde in one stratum of the intermediate results show that a midpoint estimator constructed from the optimization bounds has consistently lower rmsb than the usual stratified estimator both unconditionally and conditioned on any risk in the unexposed when conditioning on true acde this midpoint estimator performs more poorly only when conditioned on an extreme true acde in one stratum of the intermediate yet outperforms the stratified estimator in the other stratum when interaction is permitted an alternate limit modified crude estimator can never perform less favourably than the stratified estimator and often has lower rmsb

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

single and multiple shell uniform sampling schemes for diffusion mri using spherical codes in diffusion mri dmri a good sampling scheme is important for efficient acquisition and robust reconstruction diffusion weighted signal is normally acquired on single or multiple shells in q space signal samples are typically distributed uniformly on different shells to make them invariant to the orientation of structures within tissue or the laboratory coordinate frame the electrostatic energy minimization eem method originally proposed for single shell sampling scheme in dmri was recently generalized to multi shell schemes called generalized eem geem geem has been successfully used in the human connectome project however eem does not directly address the goal of optimal sampling i e achieving large angular separation between sampling points in this paper we propose a more natural formulation called spherical code sc to directly maximize the minimal angle between different samples in single or multiple shells we consider not only continuous problems to design single or multiple shell sampling schemes but also discrete problems to uniformly extract sub sampled schemes from an existing single or multiple shell scheme and to order samples in an existing scheme we propose five algorithms to solve the above problems including an incremental sc isc a sophisticated greedy algorithm called iterative maximum overlap construction imoc an 1 opt greedy method a mixed integer linear programming method and a constrained non linear optimization method to our knowledge this is the first work to use the sc formulation for single or multiple shell sampling schemes in dmri experimental results indicate that sc methods obtain larger angular separation and better rotational invariance than the state of the art eem and geem the related codes and a tutorial have been released in dmritool 1 1 https diffusionmritool github io tutorial qspacesampling html

nonparametric iv estimation of local average treatment effects with covariates in this paper nonparametric instrumental variable estimation of local average treatment effects late is extended to incorporate covariates estimation of late is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models including covariates in the estimation of late is necessary when the instrumental variable itself is confounded such that the iv assumptions are valid only conditional on covariates previous approaches to handle covariates in the estimation of late relied on parametric or semiparametric methods in this paper a nonparametric estimator for the estimation of late with covariates is suggested that is root n asymptotically normal and efficient

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

testing for imbalance of covariates in controlled experiments results of a controlled experiment are often adjusted for covariates found by a preliminary test to differ significantly between the treatment and control groups the resulting test s true significance level is lower than the nominal level greater power can be achieved by always adjusting for a covariate that is highly correlated with the response regardless of its distribution between groups

extended conditional independence and applications in causal inference the goal of this paper is to integrate the notions of stochastic conditional independence and variation conditional independence under a more general notion of extended conditional independence we show that under appropriate assumptions the calculus that applies for the two cases separately axioms of a separoid still applies for the extended case these results provide a rigorous basis for a wide range of statistical concepts including ancillarity and sufficiency and in particular the decision theoretic framework for statistical causality which uses the language and calculus of conditional independence in order to express causal properties and make causal inferences

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

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

geometrical theory of asymptotic ancillarity and conditional inference summary differential geometry is applied to the problems of defining higher order asymptotic ancillarity and of obtaining the asymptotic conditional distribution of an efficient estimator in multiparameter curved exponential families it is shown that a fundamental role is played in the asymptotic theory of estimation by a one parameter family of affine connexions and curvatures of subspaces asymptotic ancillary statistics of higher order are explicitly constructed with the help of the geometry the conditional distribution of an estimator is given in terms of the exponential curvature of the model and the mixture curvature of the ancillary subspaces associated with the estimator

bayesian inference for a generalized population attributable fraction the impact of early vitamin a levels on chronic lung disease in very low birthweight infants in this paper the population attributable fraction is studied using the potential responses framework of rubin s causal model this framework facilitates definition of a general measure of population attributable effect which can accommodate many valued and multivariate exposures as well as many valued responses inferential issues are considered from the bayesian perspective finite population inference is emphasized with inference in the case of a fully observed population given particular attention the key inferential issue concerns computation of the posterior distribution of unobserved potential responses given observed responses exposures and covariates a dependency on model parameters about which observed data are uninformative is highlighted and this reflects the unobservable nature of causal effects in an application to a small cohort study of respiratory problems in very low birthweight infants posterior inferences were found to be insensitive to assumptions concerning the joint distribution of potential response variables but sensitive to the assumption of weak ignorability a weaker form of the more familiar assumption of no confounding by omitted covariates in a model based set up the weak ignorability assumption is identified with setting a model parameter to zero and consequently uncertainty concerning this assumption can in principle be handled via the prior distribution for the model parameters

about the geometry of asymmetric fiber orientation distributions fiber orientation distributions fods based on diffusion sensitized magnetic resonance imaging are usually symmetric primarily due to the nature of the diffusion in contrast the underlying fiber configurations are not as bending or fanning configurations are inherently asymmetric we propose to dismiss the symmetry of the fod to additionally encode the asymmetry of the underlying fiber configuration this is of particular importance for low resolution images that are common in diffusion weighted imaging we set up the mathematical foundations and geometric interpretations of asymmetric fods and show how one can benefit from these considerations we infer a continuity condition that is used as a prior during fod estimation by constrained spherical deconvolution this new prior shows superior performance in comparison to other spatial regularization strategies in reliability and accuracy

on the definition of a confounder the causal inference literature has provided a clear formal definition of confounding expressed in terms of counterfactual independence the causal inference literature has not however produced a clear formal definition of a confounder as it has given priority to the concept of confounding over that of a confounder we consider a number of candidate definitions arising from various more informal statements made in the literature we consider the properties satisfied by each candidate definition principally focusing on i whether under the candidate definition control for all confounders suffices to control for confounding and ii whether each confounder in some context helps eliminate or reduce confounding bias several of the candidate definitions do not have these two properties only one candidate definition of those considered satisfies both properties we propose that a confounder be defined as a pre exposure covariate c for which there exists a set of other covariates x such that effect of the exposure on the outcome is unconfounded conditional on x c but such that for no proper subset of x c is the effect of the exposure on the outcome unconfounded given the subset a variable that helps reduce bias but not eliminate bias we propose referring to as a surrogate confounder

a powerful and robust test statistic for randomization inference in group randomized trials with matched pairs of groups summary for group randomized trials randomization inference based on rank statistics provides robust exact inference against nonnormal distributions however in a matched pair design the currently available rank based statistics lose significant power compared to normal linear mixed model lmm test statistics when the lmm is true in this article we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed mann whitney wilcoxon statistics under certain assumptions this test is almost as powerful as the lmm even when the lmm is true but it is much more powerful for heavy tailed distributions a simulation study is conducted to examine the power

identifying effects of multivalued treatments multivalued treatment models have typically been studied under restrictive assumptions ordered choice and more recently unordered monotonicity we show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity our results rely on two main assumptions treatment assignment must be a measurable function of threshold crossing rules and enough continuous instruments must be available we illustrate our approach for several classes of models

identification and shape restrictions in nonparametric instrumental variables estimation abstract this paper is concerned with inference about an unidentified linear functional l g where g satisfies y g x u e u w 0 in much applied research x and w are discrete and w has fewer points of support than x consequently l g is not identified nonparametrically and can have any value in this paper uses shape restrictions such as monotonicity or convexity to achieve interval identification of l g the paper shows that under shape restrictions l g is contained in an interval whose bounds can be obtained by solving linear programming problems inference about l g can be carried out by using the bootstrap an empirical application illustrates the usefulness of the method

fiber continuity an anisotropic prior for odf estimation the accurate and reliable estimation of fiber orientation distributions based on diffusion sensitized magnetic resonance images is a major prerequisite for tractography algorithms or any other derived statistical analysis in this work we formulate the principle of fiber continuity fc which is based on the simple observation that the imaging of fibrous tissue implies certain expectations for the measured images from this principle we derive a prior for the estimation of fiber orientation distributions based on high angular resolution diffusion imaging hardi we demonstrate on simulated phantom and in vivo data the superiority of the proposed approach further we propose another application of the fc principle named fc flow a method to resolve complex crossing regions solely based on diffusion tensor imaging dti the idea is to infer directional information in crossing regions from adjacent anisotropic areas

left invariant diffusions on the space of positions and orientations and their application to crossing preserving smoothing of hardi images hardi high angular resolution diffusion imaging is a recent magnetic resonance imaging mri technique for imaging water diffusion processes in fibrous tissues such as brain white matter and muscles in this article we study left invariant diffusion on the group of 3d rigid body movements i e 3d euclidean motion group se 3 and its application to crossing preserving smoothing of hardi images the linear left invariant convection diffusions are forward kolmogorov equations of brownian motions on the space of positions and orientations in 3d embedded in se 3 and can be solved by 3 s 2 convolution with the corresponding green s functions we provide analytic approximation formulas and explicit sharp gaussian estimates for these green s functions in our design and analysis for appropriate nonlinear convection diffusions on hardi data we explain the underlying differential geometry on se 3 we write our left invariant diffusions in covariant derivatives on se 3 using the cartan connection this cartan connection has constant curvature and constant torsion and so have the exponential curves which are the auto parallels along which our left invariant diffusion takes place we provide experiments of our crossing preserving euclidean invariant diffusions on artificial hardi data containing crossing fibers

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

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

generalized method of moments specification testing abstract this paper analyzes the asymptotic power properties of specification tests which are based on a finite set of moment conditions it shows that any such test may fail against general misspecification that causes estimator inconsistency the mutual asymptotic equivalence of maximal degree of freedom tests is shown and the form of optimal tests against specific forms of misspecification is derived applications to testing for exogeneity of a set of instrumental variables are presented

efficient instrumental variables estimation of nonlinear models this paper considers asymptotically efficient instrumental variables estimation of nonlinear models in an i i d environment the class of models includes nonlinear simultaneous equations models and other models of interest a problem in constructing efficient instrumental variables estimators for such models is that the optimal instruments involve a conditional expectation calculation of which can require functional form assumptions for the conditional distribution of endogenous variables as well as integration nonparametric methods provide a way of avoiding this difficulty here it is shown that nonparametric estimates of the optimal instruments can give asymptotically efficient instrumental variables estimators also ways of choosing the nonparametric estimate in applications are discussed two types of nonparametric estimates of the optimal instruments are considered each involves nonparametric regression one by nearest neighbor and the other by series approximation the finite sample properties of the estimators are considered in a small sampling experiment involving an endogenous dummy variable model

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

estimation of fiber orientation probability density functions in high angular resolution diffusion imaging abstract an estimator of the orientation probability density function opdf of fiber tracts in the white matter of the brain from high angular resolution diffusion data is presented unlike q balls which use the funk radon transform to estimate the radial projection of the 3d probability density function the jacobian of the spherical coordinates is included in the funk radon approximation to the radial integral thus true angular marginalizations are computed which allows a strict probabilistic interpretation extensive experiments with both synthetic and real data show the better capability of our method to characterize complex micro architectures compared to other related approaches q balls and diffusion orientation transform especially for low values of the diffusion weighting parameter

improved tractography using asymmetric fibre orientation distributions diffusion mri allows us to make inferences on the structural organisation of the brain by mapping water diffusion to white matter microstructure however such a mapping is generally ill defined for instance diffusion measurements are antipodally symmetric diffusion along x and x are equal whereas the distribution of fibre orientations within a voxel is generally not symmetric therefore different sub voxel patterns such as crossing fanning or sharp bending cannot be distinguished by fitting a voxel wise model to the signal however asymmetric fibre patterns can potentially be distinguished once spatial information from neighbouring voxels is taken into account we propose a neighbourhood constrained spherical deconvolution approach that is capable of inferring asymmetric fibre orientation distributions a fods importantly we further design and implement a tractography algorithm that utilises the estimated a fods since the commonly used streamline tractography paradigm cannot directly take advantage of the new information we assess performance using ultra high resolution histology data where we can compare true orientation distributions against sub voxel fibre patterns estimated from down sampled data finally we explore the benefits of a fods based tractography using in vivo data by evaluating agreement of tractography predictions with connectivity estimates made using different in vivo modalities the proposed approach can reliably estimate complex fibre patterns such as sharp bending and fanning which voxel wise approaches cannot estimate moreover histology based and in vivo results show that the new framework allows more accurate tractography and reconstruction of maps quantifying symmetric and asymmetric fibre complexity

sensitivity analysis for instrumental variables regression with overidentifying restrictions instrumental variables regression iv regression is a method for making causal inferences about the effect of a treatment based on an observational study in which there are unmeasured confounding variables the method requires one or more valid instrumental variables ivs a valid iv is a variable that is associated with the treatment is independent of unmeasured confounding variables and has no direct effect on the outcome often there is uncertainty about the validity of the proposed ivs when a researcher proposes more than one iv the validity of these ivs can be tested through the overidentifying restrictions test although the overidentifying restrictions test does provide some information the test has no power versus certain alternatives and can have low power versus many alternatives due to its omnibus nature to fully address uncertainty about the validity of the proposed ivs we argue that a sensitivity analysis is needed a sensitivity analysis examines the impact of plausible amounts of

impact of mis specification of the treatment model on estimates from a marginal structural model inverse probability of treatment weighted iptw estimation for marginal structural models msms requires the specification of a nuisance model describing the conditional relationship between treatment allocation and confounders however there is still limited information on the best strategy for building these treatment models in practice we developed a series of simulations to systematically determine the effect of including different types of candidate variables in such models we explored the performance of iptw estimators across several scenarios of increasing complexity including one designed to mimic the complexity typically seen in large pharmacoepidemiologic studies our results show that including pure predictors of treatment i e not confounders in treatment models can lead to estimators that are biased and highly variable particularly in the context of small samples the bias and mean squared error of the msm based iptw estimator increase as the complexity of the problem increases the performance of the estimator is improved by either increasing the sample size or using only variables related to the outcome to develop the treatment model estimates of treatment effect based on the true model for the probability of treatment are asymptotically unbiased we recommend including only pure risk factors and confounders in the treatment model when developing an iptw based msm

semiparametric two sample tests in clinical trials with a post randomisation response indicator in many clinical trials involving survival endpoints one has additional data on some binary indicator of response such as initial tumour shrinkage in cancer trials this paper studies the case of randomised clinical trials where the response indicator is available shortly after randomisation and where one can assume that within each stratum defined by the response indicator a two treatment group proportional hazards model holds the same model may also describe some incompletely randomised or observational studies asymptotic relative efficiencies for kaplan meier based estimators versus maximum partial likelihood estimators are examined under this model for estimating either the difference in survival probabilities at a specified time or the parameter estimated by the logrank numerator it is shown that the efficiency gains using the model are more promising when estimating the difference in survival probabilities an example is given comparing the long term survival experience of two groups of patients with advanced hodgkin s disease

clustering method for estimating principal diffusion directions diffusion tensor magnetic resonance imaging dtmri is a non invasive tool for the investigation of white matter structure within the brain however the traditional tensor model is unable to characterize anisotropies of orders higher than two in heterogeneous areas containing more than one fiber population to resolve this issue high angular resolution diffusion imaging hardi with a large number of diffusion encoding gradients is used along with reconstruction methods such as q ball using hardi data the fiber orientation distribution function odf on the unit sphere is calculated and used to extract the principal diffusion directions pdds fast and accurate estimation of pdds is a prerequisite for tracking algorithms that deal with fiber crossings in this paper the pdds are defined as the directions around which the odf data is concentrated estimates of the pdds based on this definition are less sensitive to noise in comparison with the previous approaches a clustering approach to estimate the pdds is proposed which is an extension of fuzzy c means clustering developed for orientation of points on a sphere mdl minimum description length principle is proposed to estimate the number of pdds using both simulated and real diffusion data the proposed method has been evaluated and compared with some previous protocols experimental results show that the proposed clustering algorithm is more accurate more resistant to noise and faster than some of techniques currently being utilized

semiparametric efficient estimation of a conditional density with missing or mismeasured covariates summary pepe and fleming and carroll and wand have recently proposed estimators in a parametric model for the density of a random variable y conditional on a vector of covariates x v when data on one of the regressors x is missing for some study subjects we propose a new class of estimators that remains consistent and asymptotically normal even when the probability that x is missing depends on the observed v and y includes an estimator whose asymptotic variance attains the semiparametric variance bound for the model and when the data are missing completely at random includes an estimator that is asymptotically equivalent to the inefficient estimators proposed by pepe and fleming and by carroll and wand the optimal estimator in our class depends on the unknown probability law generating the data when the vector v of non missing regressors has at most two continuous components we propose an adaptive semiparametric efficient estimator and compare the performance of the proposed semiparametric efficient estimator with the estimators proposed by pepe and fleming and carroll and wand in a small simulation study when v has many continuous components we propose an alternative class of adaptive estimators that should have high efficiency

residual ideals of maclane valuations abstract let k v be a discrete valued field and let x be an indeterminate in 1936 maclane determined all valuations on k x extending v his work has been reviewed and generalized by vaquie by using the graded algebra of a valuation we extend vaquie s approach by studying residual ideals of the graded algebra as an abstract counterpart of certain residual polynomials having a key role in the computational applications of the theory this enables us to determine the structure of the graded algebra of the discrete valuations on k x also let p be the set of monic irreducible polynomials with coefficients in the completion o v of the valuation ring of v the constructive methods of the paper yield a canonical bijection p m between the set of okutsu equivalence classes of prime polynomials and a certain maclane space m whose points may be described in terms of discrete parameters associated with valuations on k x

bayesian nonparametric estimation for dynamic treatment regimes with sequential transition times abstractwe analyze a dataset arising from a clinical trial involving multi stage chemotherapy regimes for acute leukemia the trial design was a 2 2 factorial for frontline therapies only motivated by the idea that subsequent salvage treatments affect survival time we model therapy as a dynamic treatment regime dtr that is an alternating sequence of adaptive treatments or other actions and transition times between disease states these sequences may vary substantially between patients depending on how the regime plays out to evaluate the regimes mean overall survival time is expressed as a weighted average of the means of all possible sums of successive transitions times we assume a bayesian nonparametric survival regression model for each transition time with a dependent dirichlet process prior and gaussian process base measure ddp gp posterior simulation is implemented by markov chain monte carlo mcmc sampling we provide general guidelines for constructing a prior using empirical baye

local computation of differents and discriminants we obtain several results on the computation of different and dis criminant ideals of finite extensions of local fields as an application we deduce routines to compute the p adic valuation of the discriminant disc f and the resultant res f g for polynomials f x g x 2 a x where a is a dedekind domain and p is a non zero prime ideal of a with finite residue field these rou tines do not require the computation of neither disc f nor res f g hence they are useful in cases where this latter computation is inefficient because the polynomials have a large degree or very large coefficients

wanna get away regression discontinuity estimation of exam school effects away from the cutoff in regression discontinuity rd studies exploiting an award or admissions cutoff causal effects are nonparametrically identified for those near the cutoff the effect of treatment on inframarginal applicants is also of interest but identification of such effects requires stronger assumptions than those required for identification at the cutoff this article discusses rd identification and estimation away from the cutoff our identification strategy exploits the availability of dependent variable predictors other than the running variable conditional on these predictors the running variable is assumed to be ignorable this identification strategy is used to study effects of boston exam schools for inframarginal applicants identification based on the conditional independence assumptions imposed in our framework yields reasonably precise and surprisingly robust estimates of the effects of exam school attendance on inframarginal applicants these estimates suggest that the causal effects of exam school

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

double inverse weighted estimation of cumulative treatment effects under nonproportional hazards and dependent censoring in medical studies of time to event data nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect a traditional method for dealing with time dependent treatment effects is to model the time dependence parametrically limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that in the presence of a treatment effect that varies over time investigators are usually interested in the cumulative as opposed to instantaneous treatment effect in many applications censoring time is not independent of event time therefore we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring three measures are proposed including the ratio of cumulative hazards relative risk and difference in restricted mean lifetime for each measure we propose a double inverse weighted estimator constructed by first using inverse probability of treatment weighting iptw to balance the treatment specific covariate distributions then using inverse probability of censoring weighting ipcw to overcome the dependent censoring the proposed estimators are shown to be consistent and asymptotically normal we study their finite sample properties through simulation the proposed methods are used to compare kidney wait list mortality by race

newton polygons of higher order in algebraic number theory we develop a theory of arithmetic newton polygons of higher order that provides the factorization of a separable polynomial over a p adic eld together with relevant arithmetic information about the elds generated by the irreducible factors this carries out a program suggested by ore as an application we obtain fast algorithms to compute discriminants prime ideal decomposition and integral bases of number elds

matching and semi parametric iv estimation a distance based measure of migration and the wages of young men abstract our paper estimates the effect of us internal migration on wage growth for young men between their first and second job our analysis of migration extends previous research by i exploiting the distance based measures of migration in the national longitudinal surveys of youth 1979 nlsy79 ii allowing the effect of migration to differ by schooling level and iii using propensity score matching to estimate the average treatment effect on the treated atet for movers and iv using local average treatment effect late estimators with covariates to estimate the average treatment effect ate and atet for compliers we believe the conditional independence assumption cia is reasonable for our matching estimators since the nlsy79 provides a relatively rich array of variables on which to match our matching methods are based on local linear local cubic and local linear ridge regressions local linear and local ridge regression matching produce relatively similar point estimates and standard errors while local cubic regression matching badly over fits the data and provides very noisy estimates we use the bootstrap to calculate standard errors since the validity of the bootstrap has not been investigated for the matching estimators we use and has been shown to be invalid for nearest neighbor matching estimators we conduct a monte carlo study on the appropriateness of using the bootstrap to calculate standard errors for local linear regression matching the data generating processes in our monte carlo study are relatively rich and calibrated to match our empirical models or to test the sensitivity of our results to the choice of parameter values the estimated standard errors from the bootstrap are very close to those from the monte carlo experiments which lends support to our using the bootstrap to calculate standard errors in our setting from the matching estimators we find a significant positive effect of migration on the wage growth of college graduates and a marginally significant negative effect for high school dropouts we do not find any significant effects for other educational groups or for the overall sample our results are generally robust to changes in the model specification and changes in our distance based measure of migration we find that better data matters if we use a measure of migration based on moving across county lines we overstate the number of moves while if we use a measure based on moving across state lines we understate the number of moves further using either the county or state measures leads to much less precise estimates we also consider semi parametric late estimators with covariates frolich 2007 using two sets of instrumental variables we precisely estimate the proportion of compliers in our data but because we have a small number of compliers we cannot obtain precise late estimates

causal inference by quantile regression kink designs abstract the quantile regression kink design qrkd is proposed by empirical researchers but its causal interpretation remains unknown we show that the qrkd estimand measures a weighted average of heterogeneous marginal effects at respective conditional quantiles of outcome given a designed kink point we also derive limit processes for the qrkd estimator to conduct statistical inference on heterogeneous treatment effects using the qrkd applying our methods to the continuous wage and benefit history project cwbh data we find heterogeneous positive causal effects of unemployment insurance benefits on unemployment durations these effects are larger for individuals with longer unemployment durations

estimation of the time dependent accelerated failure time model in the presence of confounding factors summary cox oakes 1984 p 66 introduced the strong version of the accelerated failure time model with time dependent exposures we provide conditions under which this model could be used to estimate from observational data the causal effect of a time varying exposure or treatment on time to an event of interest in the presence of time dependent confounding variables we propose a class of semiparametric tests and estimators for the model parameters this class contains an estimator that is semipara metric efficient in the sense of begun et al 1983 the purpose of this paper is first to provide conditions under which it would be possible to estimate from observational data the causal effect of a time dependent treatment or exposure on time to an event of interest in the presence of time dependent confounding covariates and then to construct estimators for the treatment effect under these condi tions our approach will be based on the semiparametric estimation of the parameters of the strong version of the accelerated failure time model with time dependent exposures or treatments introduced by cox oakes 1984 p 66 the usual approach to the estimation of the effect of a time varying treatment on survival is to model the hazard of failure at t as a function of past treatment history using a time dependent proportional hazards model we show that the usual approach may be biased whether or not one further adjusts for past confounder history in the analysis when a there exists a time dependent risk factor for or predictor of the event of interest that also predicts subsequent treatment and b past treatment history predicts subsequent risk factor level the following four examples demonstrate conditions a and b will often be true in an observational study in which there is treatment by indication the drug zidovudine formerly azt used in the treatment of the acquired immunodeficiency syndrome is a direct red blood cell toxin that is contra indicated in anaemic subjects i e subjects with depressed red cell counts since the toxic effects of zidovudine can worsen the anaemia further anaemic patients are at increased risk of death thus in an observational study of the effect of zidovudine on survival of patients with the acquired immunodeficiency syndrome anaemia is both a risk factor for death

optimal dynamic treatment regimes summary a dynamic treatment regime is a list of decision rules one per time interval for how the level of treatment will be tailored through time to an individual s changing status the goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response to explicate our objective and to state the assumptions we use the potential outcomes model the method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules we illustrate the methodology proposed via a small simulation