nonparametric estimation of distributional policy effects this paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest in contrast to other methods we do not restrict attention to the effect on the mean in particular our method can be used to conduct inference on the change of the distribution function as a whole its moments and quantiles inequality measures such as the lorenz curve or gini coefficient and to test for stochastic dominance the practical applicability of our procedure is illustrated via a simulation study and an empirical example

adaptive time stepping for incompressible flow part i scalar advection diffusion even the simplest advection diffusion problems can exhibit multiple time scales this means that robust variable step time integrators are a prerequisite if such problems are to be efficiently solved computationally the performance of the second order trapezoid rule using an explicit adams bashforth method for error control is assessed in this work this combination is particularly well suited to long time integration of advection dominated problems herein it is shown that a stabilized implementation of the trapezoid rule leads to a very effective integrator in other situations specifically diffusion problems with rough initial data and general advection diffusion problems with different physical time scales governing the system evolution

conditioning on the propensity score can result in biased estimation of common measures of treatment effect a monte carlo study propensity score methods are increasingly being used to estimate causal treatment effects in the medical literature conditioning on the propensity score results in unbiased estimation of the expected difference in observed responses to two treatments the degree to which conditioning on the propensity score introduces bias into the estimation of the conditional odds ratio or conditional hazard ratio which are frequently used as measures of treatment effect in observational studies has not been extensively studied we conducted monte carlo simulations to determine the degree to which propensity score matching stratification on the quintiles of the propensity score and covariate adjustment using the propensity score result in biased estimation of conditional odds ratios hazard ratios and rate ratios we found that conditioning on the propensity score resulted in biased estimation of the true conditional odds ratio and the true conditional hazard ratio in all scenarios examined treatment effects were biased towards the null treatment effect however conditioning on the propensity score did not result in biased estimation of the true conditional rate ratio in contrast conventional regression methods allowed unbiased estimation of the true conditional treatment effect when all variables associated with the outcome were included in the regression model the observed bias in propensity score methods is due to the fact that regression models allow one to estimate conditional treatment effects whereas propensity score methods allow one to estimate marginal treatment effects in several settings with non linear treatment effects marginal and conditional treatment effects do not coincide

bias reduction in effectiveness analyses of longitudinal ordinal doses with a mixed effects propensity adjustment a mixed effects propensity adjustment is described that can reduce bias in longitudinal studies involving non equivalent comparison groups there are two stages in this data analytic strategy first a model of propensity for treatment intensity examines variables that distinguish among subjects who receive various ordered doses of treatment across time using mixed effects ordinal logistic regression second the effectiveness model examines multiple times until recurrence to compare the ordered doses using a mixed effects grouped time survival model effectiveness analyses are initially stratified by propensity quintile then the quintile specific results are pooled assuming that there is not a propensity x treatment interaction a monte carlo simulation study compares bias reduction in fully specified propensity model relative to misspecified models in addition type i error rate and statistical power are examined the approach is illustrated by applying it to a longitudinal observational study of maintenance treatment of major depression

adaptive time step control for higher order variational time discretizations applied to convection diffusion reaction equations abstract higher order variational time stepping schemes allow an efficient post processing for computing a higher order solution this paper presents an adaptive algorithm whose time step control utilizes the post processed solution the algorithm is applied to convection dominated convection diffusion reaction equations it is shown that the length of the time step properly reflects the dynamics of the solution with respect to the performance accuracy efficiency the variational time stepping schemes are compared with an adaptive crank nicolson scheme whose time step control relies on comparing two solutions computed with schemes of the same order

an adaptive finite element method for evolutionary convection dominated problems abstract we present an adaptive finite element method for evolutionary convection diffusion problems the algorithm is based on an a posteriori indicator of the size of the oscillations displayed by the finite element approximation the procedure is able to refine or coarsen dynamically the mesh adjusting it automatically to evolving layers the method produces nearly non oscillatory approximations in the convection dominated regime we check the performance of the adaptive method with some numerical experiments

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

periodic solutions of a class of singular hamiltonian systems soit r n 0 n n n 3 et soit v c 1 rx r on etudie l existence des solutions periodiques t u t avec une periode prescrite du systeme suivant de n equations differentielles d ordre 2 u v t u

a posteriori error estimates for the crank nicolson method for parabolic equations we derive optimal order a posteriori error estimates for time discretizations by both the crank nicolson and the crank nicolson galerkin methods for linear and nonlinear parabolic equations we examine both smooth and rough initial data our basic tool for deriving a posteriori estimates are second order crank nicolson reconstructions of the piecewise linear approximate solutions these functions satisfy two fundamental properties i they are explicitly computable and thus their difference to the numerical solution is controlled a posteriori and ii they lead to optimal order residuals as well as to appropriate pointwise representations of the error equation of the same form as the underlying evolution equation the resulting estimators are shown to be of optimal order by deriving upper and lower bounds for them depending only on the discretization parameters and the data of our problem as a consequence we provide alternative proofs for known a priori rates of convergence for the crank nicolson method

a new stabilization of adaptive step trapezoid rule based on finite difference interrupts the adaptive step trapezoid rule tr is a generally effective numerical integrator but it is prone to ringing instability and solution stall we introduce a new stabilization algorithm based on finite difference interrupts fdi that reduces ringing and prevents stall unlike previously reported stabilization schemes our algorithm achieves stability and second order accuracy without incurring significant computational cost or spurious diffusion tr with fdi is at least as stable and accurate as existing methods when solving the prototypical scalar problem we demonstrate that it has better stability accuracy and cost when solving the tightly coupled system describing free surface flows of viscoelastic liquids though we demonstrate tr with fdi in the context of a finite element method of lines it is applicable to any tr based algorithm

an adaptive supg method for evolutionary convection diffusion equations abstract an adaptive algorithm for the numerical simulation of time dependent convection diffusion reaction equations will be proposed and studied the algorithm allows the use of the natural extension of any error estimator for the steady state problem for controlling local refinement and coarsening the main idea consists in considering the supg solution of the evolutionary problem as the supg solution of a particular steady state convection diffusion problem with data depending on the computed solution the application of the error estimator is based on a heuristic argument by considering a certain term to be of higher order this argument is supported in the one dimensional case by numerical analysis in the numerical studies particularly the residual based error estimator from 18 will be applied which has proved to be robust in the supg norm the effectivity of this error estimator will be studied and the numerical results accuracy of the solution fineness of the meshes will be compared with results obtained by utilizing the adaptive algorithm proposed in 5

estimation and inference for distribution functions and quantile functions in treatment effect models abstract we propose inverse probability weighted estimators for the distribution functions of the potential outcomes under the unconfoundedness assumption and apply the inverse mapping to obtain the quantile functions we show that these estimators converge weakly to zero mean gaussian processes a simulation method is proposed to approximate these limiting processes based on these results we construct tests for stochastic dominance relations between the potential outcomes monte carlo simulations are conducted to examine the finite sample properties of our tests we apply our test in an empirical example and find that a job training program had a positive effect on incomes

bayesian estimation of the average treatment effect on the treated using inverse weighting we develop a bayesian approach to estimate the average treatment effect on the treated in the presence of confounding the approach builds on developments proposed by saarela et al in the context of marginal structural models using importance sampling weights to adjust for confounding and estimate a causal effect the bayesian bootstrap is adopted to approximate posterior distributions of interest and avoid the issue of feedback that arises in bayesian causal estimation relying on a joint likelihood we present results from simulation studies to estimate the average treatment effect on the treated evaluating the impact of sample size and the strength of confounding on estimation we illustrate our approach using the classic right heart catheterization data set and find a negative causal effect of the exposure on 30 day survival in accordance with previous analyses of these data we also apply our approach to the data set of the national center for health statistics birth data and obtain a negative effect of maternal smoking during pregnancy on birth weight

combining propensity score matching with additional adjustments for prognostic covariates abstract propensity score matching refers to a class of multivariate methods used in comparative studies to construct treated and matched control samples that have similar distributions on many covariates this matching is the observational study analog of randomization in ideal experiments but is far less complete as it can only balance the distribution of observed covariates whereas randomization balances the distribution of all covariates both observed and unobserved an important feature of propensity score matching is that it can be easily combined with model based regression adjustments or with matching on a subset of special prognostic covariates or combinations of prognostic covariates that have been identified as being especially predictive of the outcome variables we extend earlier results by developing approximations for the distributions of covariates in matched samples created with linear propensity score methods for the practically important situation where matching uses both the estimat

variance estimation for stratified propensity score estimators propensity score methods are increasingly used to estimate the effect of a treatment or exposure on an outcome in non randomised studies we focus on one such method stratification on the propensity score comparing it with the method of inverse probability weighting by the propensity score the propensity score the conditional probability of receiving the treatment given observed covariates is usually an unknown probability estimated from the data estimators for the variance of treatment effect estimates typically used in practice however do not take into account that the propensity score itself has been estimated from the data by deriving the asymptotic marginal variance of the stratified estimate of treatment effect correctly taking into account the estimation of the propensity score we show that routinely used variance estimators are likely to produce confidence intervals that are too conservative when the propensity score model includes variables that predict cause the outcome but only weakly predict the treatment in contrast a comparison with the analogous marginal variance for the inverse probability weighted ipw estimator shows that routinely used variance estimators for the ipw estimator are likely to produce confidence intervals that are almost always too conservative because exact calculation of the asymptotic marginal variance is likely to be complex particularly for the stratified estimator we suggest that bootstrap estimates of variance should be used in practice

periodic solutions of a class of hamiltonian systems with singularities this paper deals with a class of time periodic hamiltonian systems obtained by a time dependent perturbation from an autonomous system with a singularity at q 0 in configuration space it is shown that t being the period of the perturbation nondegenerate families of t periodic orbits in the unperturbed problem branch off into a certain number of t periodic orbits for the perturbed problem

estimating and using propensity scores with partially missing data abstract investigators in observational studies have no control over treatment assignment as a result large differences can exist between the treatment and control groups on observed covariates which can lead to badly biased estimates of treatment effects propensity score methods are an increasingly popular method for balancing the distribution of the covariates in the two groups to reduce this bias for example using matching or subclassification sometimes in combination with model based adjustment to estimate propensity scores which are the conditional probabilities of being treated given a vector of observed covariates we must model the distribution of the treatment indicator given these observed covariates much work has been done in the case where covariates are fully observed we address the problem of calculating propensity scores when covariates can have missing values in such cases which commonly arise in practice the pattern of missing covariates can be prognostically important and

fast iterative solvers for buoyancy driven flow problems we outline a new class of robust and efficient methods for solving the navier stokes equations with a boussinesq model for buoyancy driven flow we describe a general solution strategy that has two basic building blocks an implicit time integrator using a stabilized trapezoid rule with an explicit adams bashforth method for error control and a robust krylov subspace solver for the spatially discretized system we present numerical experiments illustrating the efficiency of the chosen preconditioning schemes with respect to the discretization parameters

accelerated staggered coupling schemes for problems of thermoelasticity at finite strains this paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the p version of the finite element method the mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator split numerical relaxation methods have been implemented to accelerate the convergence of the algorithm such methods are well known from coupled fluid structure interaction problems leading to highly efficient algorithms having studied the influence of three different strategies polynomial prediction methods numerical relaxation with constant relaxation coefficients its dynamic variant with a residual based relaxation coefficient and a variant of a reduced order model quasi newton method we present several numerical simulations of quasi static problems investigating the performance of accelerated coupling schemes

perturbation of hamiltonian systems with keplerian potentials on considere l existence des solutions periodiques pour une classe de systemes hamiltoniens obtenus comme des perturbations de l hamiltonien keplerien k p q 1 2 p 2 q 0

the g invariant implicit function theorem in infinite dimensions ii our basic theorem is a version of the implicit function theorem in the case of continuous groups of symmetries the result is sufficiently general to cover a great many applications it generalizes some earlier work of the author and corrects and improves some work of vanderbauwhede we also consider the breaking of symmetries problem and the variational case finally we apply our results to study the periodic solutions of an ordinary differential equation

accurate numerical resolution of transients in initial boundary value problems for the heat equation if the initial and boundary data for a pde do not obey an infinite set of compatibility conditions singularities will arise in the solution at the corners of the initial time space domain for dissipative equations such as the 1 d heat equation or 1 d convection diffusion equations the impacts of these singularities are short lived however they can cause a very severe loss of numerical accuracy if we are interested in transient solutions the phenomenon has been described earlier from a theoretical standpoint here we illustrate it graphically and present a simple remedy which with only little extra cost and effort restores full numerical accuracy

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

estimation of conditional and marginal odds ratios using the prognostic score introduced by hansen in 2008 the prognostic score pgs has been presented as the prognostic analogue of the propensity score pps pps based methods are intended to estimate marginal effects most previous studies evaluated the performance of existing pgs based methods adjustment stratification and matching using the pgs in situations in which the theoretical conditional and marginal effects are equal i e collapsible situations to support the use of pgs framework as an alternative to the pps framework applied researchers must have reliable information about the type of treatment effect estimated by each method we propose four new pgs based methods each developed to estimate a specific type of treatment effect we evaluated the ability of existing and new pgs based methods to estimate the conditional treatment effect cte the marginal average treatment effect on the whole population ate and the marginal average treatment effect on the treated population att when the odds ratio a non collapsible estimator is the measure of interest the performance of pgs based methods was assessed by monte carlo simulations and compared with pps based methods and multivariate regression analysis existing pgs based methods did not allow for estimating the ate and showed unacceptable performance when the proportion of exposed subjects was large when estimating marginal effects pps based methods were too conservative whereas the new pgs based methods performed better with low prevalence of exposure and had coverages closer to the nominal value when estimating cte the new pgs based methods performed as well as traditional multivariate regression copyright 2016 john wiley sons ltd

adaptive time stepping for incompressible flow part ii navier stokes equations we outline a new class of robust and efficient methods for solving the navier stokes equations we describe a general solution strategy that has two basic building blocks an implicit time integrator using a stabilized trapezoid rule with an explicit adams bashforth method for error control and a robust krylov subspace solver for the spatially discretized system we present numerical experiments illustrating the potential of our approach

a minimax method for a class of hamiltonian systems with singular potentials abstract this paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of hamiltonian systems when a singular potential is present the singularity satisfies the strong force condition of gordon when milder singularities are permitted a notion of generalized t periodic solution is introduced and we get existence and multiplicity results for such solutions

aladins an algebraic splitting time adaptive solver for the incompressible navier stokes equations we address a time adaptive solver specifically devised for the incompressible navier stokes ins equations one of the challenging issues in this context is the identification of a reliable a posteriori error estimator typical strategies are based on the combination of the solutions computed either with two different time steps or two schemes with different accuracy in this paper we move from the pressure correction algebraic factorizations formerly proposed by saleri veneziani 2005 these schemes feature an intrinsic hierarchical nature such that an accurate solution for the pressure is obtained by computing intermediate low order guesses the difference between the two estimates provide a natural a posteriori estimator after introducing the incremental formulation of the pressure correction schemes we address the properties of this approach including extensive implementation details numerical results presented refer to 2d and 3d unstructured problems with a particular emphasis on cardiovascular problems which are expected to largely benefit from time adaptive solvers in memory of f saleri 1965 2007

periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials abstract we study the existence of periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials we found periodic solutions lying between two prescribed spheres

the prognostic analogue of the propensity score summary the propensity score collapses the covariates of an observational study into a single measure summarizing their joint association with treatment conditions prognostic scores summarize covariates association with potential responses as with propensity scores stratification on prognostic scores brings to uncontrolled studies a concrete and desirable form of balance a balance that is more familiar as an objective of experimental control like propensity scores prognostic scores can reduce the dimension of the covariate yet causal inferences conditional on them are as valid as are inferences conditional only on the unreduced covariate as a method of adjustment unto itself prognostic scoring has limitations not shared with propensity scoring but it holds promise as a complement to the propensity score particularly in certain designs for which unassisted propensity adjustment is difficult or infeasible

on the smoothing property of the galerkin method for parabolic equations we analyze the galerkin approximation of the general second order parabolic initial boundary value problem for the second order continuous time method with initial data only in l 2 we prove an l 2 error estimate of order o h 2 t analogous results are shown to hold for the error in negative sobolev norms and for the time derivative of the error our analysis uses only elementary energy techniques and the same techniques are shown to give a simple analysis of the backward euler time discretization

a characterization of optimal designs for observational studies summary an empirical investigation of the effects of a treatment is an observational study if it involves the comparison of treated and control groups that were not formed by randomization in such studies treated and control groups may differ systematically with respect to pretreatment measures or covariates and addressing these pre treatment differences is a central concern matching and subclassification are two standard methods of adjusting for observed pretreatment differences they may be used alone e g cochran 1968 or in conjunction with analytical or model based adjustments e g rubin 1973 1979 holford 1978 rosenbaum and rubin 1984 section 3 3 and rosenbaum 1987 1988a in particular rubin s simulation studies suggest that model based adjustments applied to matched or subclassified samples are more robust than model based adjustments applied to unmatched samples the purpose of this paper is to identify the structure of an optimal subclassification i e one in which the treated and control subjects in the same subclass are on average as similar as possible with respect to observed covariates it turns out that this structure is simple and intuitive while adjustments may control imbalances in observed covariates they cannot

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

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

balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity score matched samples the propensity score is a subject s probability of treatment conditional on observed baseline covariates conditional on the true propensity score treated and untreated subjects have similar distributions of observed baseline covariates propensity score matching is a popular method of using the propensity score in the medical literature using this approach matched sets of treated and untreated subjects with similar values of the propensity score are formed inferences about treatment effect made using propensity score matching are valid only if in the matched sample treated and untreated subjects have similar distributions of measured baseline covariates in this paper we discuss the following methods for assessing whether the propensity score model has been correctly specified comparing means and prevalences of baseline characteristics using standardized differences ratios comparing the variance of continuous covariates between treated and untreated subjects comparison of higher order moments and interactions five number summaries and graphical methods such as quantile quantile plots side by side boxplots and non parametric density plots for comparing the distribution of baseline covariates between treatment groups we describe methods to determine the sampling distribution of the standardized difference when the true standardized difference is equal to zero thereby allowing one to determine the range of standardized differences that are plausible with the propensity score model having been correctly specified we highlight the limitations of some previously used methods for assessing the adequacy of the specification of the propensity score model in particular methods based on comparing the distribution of the estimated propensity score between treated and untreated subjects are uninformative

closed orbits of fixed energy for singular hamiltonian systems this paper deals with the existence of periodic solutions of q v q 0 such that 1 2 q 2 v q h where q r n h is a given number v c 2 r n 0 r has a singularity at x 0 and v denotes the gradient of v

joint sufficient dimension reduction and estimation of conditional and average treatment effects the estimation of treatment effects based on observational data usually involves multiple confounders and dimension reduction is often desirable and sometimes inevitable we first clarify the definition of a central subspace that is relevant for the efficient estimation of average treatment effects a criterion is then proposed to simultaneously estimate the structural dimension the basis matrix of the joint central subspace and the optimal bandwidth for estimating the conditional treatment effects the method can easily be implemented by forward selection semiparametric efficient estimation of average treatment effects can be achieved by averaging the conditional treatment effects with a different data adaptive bandwidth to ensure optimal undersmoothing asymptotic properties of the estimated joint central subspace and the corresponding estimator of average treatment effects are studied the proposed methods are applied to a nutritional study where the covariate dimension is reduced from 11 to an effective dimension of one

on the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated a simulation study propensity and prognostic score methods seek to improve the quality of causal inference in non randomized or observational studies by replicating the conditions found in a controlled experiment at least with respect to observed characteristics propensity scores model receipt of the treatment of interest prognostic scores model the potential outcome under a single treatment condition while the popularity of propensity score methods continues to grow prognostic score methods and methods combining propensity and prognostic scores have thus far received little attention to this end we performed a simulation study that compared subclassification and full matching on a single estimated propensity or prognostic score with three approaches combining estimated propensity and prognostic scores full matching on a mahalanobis distance combining the estimated propensity and prognostic scores full mahal full matching on the estimated prognostic propensity score within propensity score calipers full pgppty and subclassification on an estimated propensity and prognostic score grid with 5 5 subclasses subclass 5 5 we considered settings in which one both or neither score model was misspecified the data generating mechanisms varied in the degree of linearity and additivity in the true treatment assignment and outcome models full mahal and full pgppty exhibited strong to superior performance in root mean square error terms across all simulation settings and scenarios methods combining propensity and prognostic scores were no less robust to model misspecification than single score methods even when both score models were incorrectly specified our findings support the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated

assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome this paper proposes a simple technique for assessing the range of plausible causal con clusions from observational studies with a binary outcome and an observed categorical covariate the technique assesses the sensitivity of conclusions to assumptions about an unobserved binary covariate relevant to both treatment assignment and response a medical study of coronary artery disease is used to illustrate the technique inevitably the results of clinical studies are subject to dispute in observational studies one basis for dispute is obvious since patients were not assigned to treatments at random patients at greater risk may be over represented in some treatment groups this paper proposes a method for assess ing the sensitivity of causal conclusions to an unmeasured patient characteristic relevant to both treatment assignment and response despite their limitations observational studies will continue to be a valuable source of information and therefore it is prudent to develop appropriate methods of analysis for them our sensitivity analysis consists of the estimation of the average effect of a treatment on a binary outcome variable after adjustment for observed categorical covariates and an unobserved binary covariate u under several sets of assumptions about u both cornfield et al 1959 and bross 1966 have proposed guidelines for determining whether an unmeasured binary covariate having specified properties could explain all of the apparent effect of a treatment that is whether the treatment effect after adjustment for u could be zero our method has two advantages first cornfield et al 1959 and bross 1966 adjust only for the unmeasured binary covariate u whereas we adjust for measured covariates in addition to the unmeasured covariate u second cornfield et al 1959 and bross 1966 1967 only judge whether the effect of the treatment could be zero having adjusted for u where cornfield et al 1959 employ an implicit yet extreme assumption about u in contrast we provide actual estimates of the treatment effect adjusted for both u and the observed categorical covariates under any assumption about u in principle the ith of the n patients under study has both a binary response r1i that would have resulted if he had received the new treatment and a binary response ro0 that would have resulted if he had received the control treatment in this formulation treatment effects are comparisons of r1i and roi such as r1i roi since each patient receives only one treatment either rli or ro0 is observed but not both and therefore comparisons of rli and roi imply some degree of speculation treatment effects defined as comparisons of the two potential responses r1i and roi of individual patients are implicit in fisher s 1953 randomization test of the sharp null

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

analytical mini max methods for hamiltonian brake orbits of prescribed energy on considere des caracterisations explicites de solutions periodiques de systemes hamiltoniens autonomes d ordre 2 de la forme q v q q t r n ou le potentiel v satisfait les conditions suivantes v c 2 r n v x v o 0 v est strictement convexe sur r n

full matching in an observational study of coaching for the sat among matching techniques for observational studies full matching is in principle the best in the sense that its alignment of comparable treated and control subjects is as good as that of any alternate method and potentially much better this article evaluates the practical performance of full matching for the first time modifying it in order to minimize variance as well as bias and then using it to compare coached and uncoached takers of the sat in this new version with restrictions on the ratio of treated subjects to controls within matched sets full matching makes use of many more observations than does pair matching but achieves far closer matches than does matching with k 2 controls prior to matching the coached and uncoached groups are separated on the propensity score by 1 1 sds full matching reduces this separation to 1 or 2 of an sd in older literature comparing matching and regression cochran expressed doubts that any method of adjustment could substantially reduce observed bias