sensitivity analysis for certain permutation inferences in matched observational studies summary in observational studies treatments are not randomly assigned to experimental units so that randomization tests and their associated interval estimates are not generally applicable in an effort to compensate for the lack of randomization treated and control units are often matched on the basis of observed covariates however the possibility remains of bias due to residual imbalances in unobserved covariates a general though simple method is proposed for displaying the sensitivity of permutation inferences to a range of assumptions about unobserved covariates in matched observational studies the sensitivity analysis is applicable to wilcoxon s signed rank test to the mcnemar cox test for paired binary responses and to some matching problems with a variable number of controls

bayesian sensitivity analysis for unmeasured confounding in observational studies we consider bayesian sensitivity analysis for unmeasured confounding in observational studies where the association between a binary exposure binary response measured confounders and a single binary unmeasured confounder can be formulated using logistic regression models a model for unmeasured confounding is presented along with a family of prior distributions that model beliefs about a possible unknown unmeasured confounder simulation from the posterior distribution is accomplished using markov chain monte carlo because the model for unmeasured confounding is not identifiable standard large sample theory for bayesian analysis is not applicable consequently the impact of different choices of prior distributions on the coverage probability of credible intervals is unknown using simulations we investigate the coverage probability when averaged with respect to various distributions over the parameter space the results indicate that credible intervals will have approximately nominal coverage probability on average when the prior distribution used for sensitivity analysis approximates the sampling distribution of model parameters in a hypothetical sequence of observational studies we motivate the method in a study of the effectiveness of beta blocker therapy for treatment of heart failure

model categories of diagram spectra working in the category mathcal t of based spaces we give the basic theory of diagram spaces and diagram spectra these are functors mathcal d longrightarrow mathcal t for a suitable small topological category mathcal d when mathcal d is symmetric monoidal there is a smash product that gives the category of mathcal d spaces a symmetric monoidal structure examples include begin enumerate item prespectra as defined classically item symmetric spectra as defined by jeff smith item orthogonal spectra a coordinate free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category item gamma spaces as defined by graeme segal item mathcal w spaces an analogue of gamma spaces with finite sets replaced by finite cw complexes in the domain category end enumerate we construct and compare model structures on these categories with the caveat that gamma spaces are always connective these categories and their simplicial analogues are quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category monoids in these categories are strict ring spectra often the subcategories of ring spectra module spectra over a ring spectrum and commutative ring spectra are also model categories when this holds the respective categories of ring and module spectra are quillen equivalent and thus have equivalent homotopy categories this allows interchangeable use of these categories in applications 2000 mathematics subject classification primary 55p42 secondary 18a25 18e30 55u35

the bias due to incomplete matching observational studies comparing groups of treated and control units are often used to estimate the effects caused by treatments matching is a method for sampling a large reservoir of potential controls to produce a control group of modest size that is ostensibly similar to the treated group in practice there is a trade off between the desires to find matches for all treated units and to obtain matched treated control pairs that are extremely similar to each other we derive expressions for the bias in the average matched pair difference due to the failure to match all treated units incomplete matching and the failure to obtain exact matches inexact matching a practical example shows that the bias due to incomplete matching can be severe and moreover can be avoided entirely by using an appropriate multivariate nearest available matching algorithm which in the example leaves only a small residual bias due to inexact matching

receiver operating characteristic analysis under tree orderings of disease classes receiver operating characteristic roc curve and its summary statistics e g the area under curve auc are commonly used to evaluate the diagnostic accuracy for disease processes with binary classification the roc curve has been extended to roc surface for scenarios with three ordinal classes or to hyper surface for scenarios with more than three classes for classifier under tree or umbrella ordering in which the marker measurement for one class is lower or higher than those for the other classes the commonly adopted diagnostic measures are the naive auc nauc based on a pooled class of all the unordered classes and the umbrella volume uv based on the concept of volume under surface however both nauc and uv have some limitations for example nauc depends on the sampling weights for all the classes in population and uv has only been introduced for three class settings in this article we initiate the idea of a new roc framework for tree or umbrella ordering denoted as troc and propose the area under troc curve denoted as tauc as an appropriate diagnostic measure the proposed troc and tauc share many nice features with the traditional roc and auc both parametric and nonparametric approaches are explored to construct the confidence interval estimation of tauc the performances of these methods are compared in simulation studies under a variety settings at the end the proposed methods are applied to a published microarray data set

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

power and sample size for observational studies of point exposure effects inverse probability of treatment weights iptws are commonly used to control for confounding when estimating causal effects of point exposures from observational data when planning a study that will be analyzed with iptws determining the required sample size for a given level of statistical power is challenging because of the effect of weighting on the variance of the estimated causal means this paper considers the utility of the design effect to quantify the effect of weighting on the precision of causal estimates the design effect is defined as the ratio of the variance of the causal mean estimator divided by the variance of a naive estimator if counter to fact no confounding had been present and weights were not needed a simple closed form approximation of the design effect is derived that is outcome invariant and can be estimated during the study design phase once the design effect is approximated for each treatment group sample size calculations are conducted as for a randomized trial but with variances inflated by the design effects to account for weighting simulations demonstrate the accuracy of the design effect approximation and practical considerations are discussed

identification and estimation of causal effects with outcomes truncated by death it is common in medical studies that the outcome of interest is truncated by death meaning that a subject has died before the outcome could be measured in this case restricted analysis among survivors may be subject to selection bias hence it is of interest to estimate the survivor average causal effect defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure in this paper we consider the identification and estimation problems of the survivor average causal effect we propose to use a substitution variable in place of the latent membership in the always survivor group the identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable and may apply to both randomized and observational studies we show that the survivor average causal effect is identifiable with use of such a substitution variable and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions our approaches are illustrated via simulation studies and a data analysis

combining panel data sets with attrition and refreshment samples tistical models that allow for more complex relationships than can be inferred using only cross sectional data panel i e longitudinal data in which the same units are observed repeatedly at different points in time can often provide the richer data needed for such models e g chamberlain 1984 hsiao 1986 baltagi 1995 arellano and honore forthcoming missing data problems however can be more severe in panels because even those units that respond in initial waves of the panel may drop out of the sample in subsequent waves e g hausman and wise 1979 robins and west 1986 ridder 1990 verbeek and nijman 1992 abowd crepon kramarz and trognon 1995 fitzgerald gottschalk and moffitt 1998 and vella 1998 sometimes in the hope of mitigating the effects of such attrition panel data sets are augmented by replacing the units that have dropped out with new units randomly sampled from the original population following ridder 1992 who used such replacement units to test alternative models for attrition we call such additional samples refreshment samples here we explore the benefits of refreshment samples for inference in the presence of attrition two general approaches are often used to deal with attrition in panel data sets when refreshment samples are not available one model based on the missing at random assumption mar rubin 1976 little and rubin 1987 allows the probability of attrition to depend on lagged but not on contemporaneous variables that have missing values the other model denoted by hw in the remainder of the paper given the similarity to a model developed by hausman and wise 1979 allows the probability of attrition to depend on such contemporaneous but not on lagged variables both sets of models have some theoretical plausibility but they rely on fundamentally different restrictions on the

conditional permutation tests and the propensity score in observational studies abstract in observational studies the distribution of treatment assignments is unknown and therefore randomization tests are not generally applicable however permutation tests that condition on sample information about the treatment assignment mechanism can be applicable in observational studies provided treatment assignment is strongly ignorable these tests use the conditional distribution of the treatment assignments given a sufficient statistic for the unknown parameter of the propensity score several tests that are commonly used in observational studies are particular instances of this general procedure moreover conditional permutation tests and covariance adjustment are closely related in the sense that the conditional permutation distribution of the covariance adjusted difference leads to the same inferences as the conditional permutation distribution of the unadjusted difference of sample means a backtrack algorithm is developed to permit efficient calculation of the exact conditional si

sensitivity analyses for unmeasured confounding assuming a marginal structural model for repeated measures robins introduced marginal structural models msms and inverse probability of treatment weighted iptw estimators for the causal effect of a time varying treatment on the mean of repeated measures we investigate the sensitivity of iptw estimators to unmeasured confounding we examine a new framework for sensitivity analyses based on a nonidentifiable model that quantifies unmeasured confounding in terms of a sensitivity parameter and a user specified function we present augmented iptw estimators of msm parameters and prove their consistency for the causal effect of an msm assuming a correct confounding bias function for unmeasured confounding we apply the methods to assess sensitivity of the analysis of hernan et al who used an msm to estimate the causal effect of zidovudine therapy on repeated cd4 counts among hiv infected men in the multicenter aids cohort study under the assumption of no unmeasured confounders a 95 per cent confidence interval for the treatment effect includes zero we show that under the assumption of a moderate amount of unmeasured confounding a 95 per cent confidence interval for the treatment effect no longer includes zero thus the analysis of hernan et al is somewhat sensitive to unmeasured confounding we hope that our research will encourage and facilitate analyses of sensitivity to unmeasured confounding in other applications

on the topological cyclic homology of the integers this article provides a computation of the mod p homotopy groups of the fixed points of the topological hochschild homology of the ring of integers under the action of any finite subgroup of the cirle group whose order is a power of an odd prime p this leads to a computation of the topological cyclic homology groups of the ring of integers and determines also the 7 adic completion of the algebraic at theory of the p adic integers 1 introduction the topological hochschild homology j is a spec trum or infinite loop space associated functorially to each algebraic ring r or more generally to each strictly associative ring spectrum tl it was introduced originally by bokstedt in b the spectrum thh r comes equipped with a natural action of the circle group t the topological cyclic homology of r tc r is the homotopy inverse limit of a diagram of spectra with vertices the fixed point spectra thh r c of thh r under the action of the finite cyclic subgroups c of the circle the maps in this diagram are either inclusions of fixed points or certain frobenius maps particular to the topological hochschild homology construction see g the topological hochschild and cyclic homology of r are both related to the algebraic jt their relation can be depicted by a commutative diagram of spectra

the localization sequence for the algebraic k theory of topological k theory we verify a conjecture of rognes by establishing a localization cofiber sequence of spectra k mathbb z to k ku to k ku to sigma k mathbb z for the algebraic k theory of topological k theory we deduce the existence of this sequence as a consequence of a devissage theorem identifying the k theory of the waldhausen category of finitely generated finite stage postnikov towers of modules over a connective a infty ring spectrum r with the quillen k theory of the abelian category of finitely generated pi 0 r modules

assessing the sensitivity of regression results to unmeasured confounders in observational studies this paper presents a general approach for assessing the sensitivity of the point and interval estimates of the primary exposure effect in an observational study to the residual confounding effects of unmeasured variable after adjusting for measured covariates the proposed method assumes that the true exposure effect can be represented in a regression model that includes the exposure indicator as well as the measured and unmeasured confounders one can use the corresponding reduced model that omits the unmeasured confounder to make statistical inferences about the true exposure effect by specifying the distributions of the unmeasured confounder in the exposed and unexposed groups along with the effects of the unmeasured confounder on the outcome variable under certain conditions there exists a simple algebraic relationship between the true exposure effect in the full model and the apparent exposure effect in the reduced model one can then estimate the true exposure effect by making a simple adjustment to the point and interval estimates of the apparent exposure effect obtained from standard software or published reports the proposed method handles both binary response and censored survival time data accommodates any study design and allows the unmeasured confounder to be discrete or normally distributed we describe applications on two major medical studies

partial identification of functionals of the joint distribution of potential outcomes in this paper we present a systematic study of partial identification of two general classes of functionals of the joint distribution of two potential outcomes when a bivariate sample from the joint distribution is not available to the econometrician assuming the identification of the conditional marginal distributions of potential outcomes and the distribution of the covariate vector we show that the identified sets for functionals in both classes are intervals and provide conditions under which the identified sets point identify the true value of the functionals in addition we establish sufficient and necessary conditions for the covariate information to be informative in the sense of shrinking the identified sets we focus on the application of our general results to evaluating distributional treatment effects of a binary treatment in two commonly used frameworks in the literature for evaluating average treatment effects the selection on observables framework and a latent threshold crossing model we characterize the role of the propensity score in the selection on observables framework and the role of endogenous selection in the latent threshold crossing model examples of policy parameters that our results apply include the correlation coefficient between the potential outcomes many inequality measures of the distribution of treatment effects and median of the distribution of the individual treatment effect

accuracy and cut off point selection in three class classification problems using a generalization of the youden index we study properties of the index j 3 defined as the accuracy or the maximum correct classification for a given three class classification problem specifically using j 3 one can assess the discrimination between the three distributions and obtain an optimal pair of cut off points c 1 c 2 in the sense that the sum of the correct classification proportions will be maximized it also serves as the generalization of the youden index in three class problems parametric and non parametric approaches for estimation and testing are considered and methods are applied to data from an mrs study on human immunodeficiency virus hiv patients

local sensitivity approximations for selectivity bias summary observational data analysis is often based on tacit assumptions of ignorability or randomness the paper develops a general approach to local sensitivity analysis for selectivity bias which aims to study the sensitivity of inference to small departures from such assumptions if m is a model assuming ignorability we surround m by a small neighbourhood at defined in the sense of kullback leibler divergence and then compare the inference for models in iv with that for m interpretable bounds for such differences are developed applications to missing data and to observational comparisons are discussed local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems

causal estimation using semiparametric transformation models under prevalent sampling this paper develops methods and inference for causal estimation in semiparametric transformation models for prevalent survival data through estimation of the transformation models and covariate distribution we propose analytical procedures to estimate the causal survival function as the data are observational the unobserved potential outcome survival time may be associated with the treatment assignment and therefore there may exist a systematic imbalance between the data observed from each treatment arm further due to prevalent sampling subjects are observed only if they have not experienced the failure event when data collection began causing the prevalent sampling bias we propose a unified approach which simultaneously corrects the bias from the prevalent sampling and balances the systematic differences from the observational data we illustrate in the simulation study that standard analysis without proper adjustment would result in biased causal inference large sample properties of the proposed estimation procedures are established by techniques of empirical processes and examined by simulation studies the proposed methods are applied to the surveillance epidemiology and end results seer and medicare linked data for women diagnosed with breast cancer

localization sequences for logarithmic topological hochschild homology we study the logarithmic topological hochschild homology of ring spectra with logarithmic structures and establish localization sequences for this theory our results apply for example to connective covers of periodic ring spectra like real and complex topological k theory mathematics subject classification 14f10 19d55 55p43

valid post selection inference it is common practice in statistical data analysis to perform data driven variable selection and derive statistical inference from the resulting model such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori we propose to produce valid post selection inference by reducing the problem to one of simultaneous inference and hence suitably widening conventional confidence and retention intervals simultaneity is required for all linear functions that arise as coefficient estimates in all submodels by purchasing simultaneity insurance for all possible submodels the resulting post selection inference is rendered universally valid under all possible model selection procedures this inference is therefore generally conservative for particular selection procedures but it is always less conservative than full scheffe protection importantly it does not depend on the truth of the selected submodel and hence it produces valid inference even in wrong models we describe the structure of the simultaneous inference problem and give some asymptotic results

evidence factors in observational studies some experiments involve more than one random assignment of treatments to units an analogous situation arises in certain observational studies although randomization is not used so each assignment may be biased if each assignment is suspect it is natural to ask whether there are separate pieces of information dependent upon different assumptions and perhaps whether conclusions about treatment effects are not critically dependent upon one or another suspect assumption the design of an observational study contains evidence factors if it permits several statistically independent tests of the same null hypothesis about treatment effects where these tests rely on different assumptions about treatment assignments at several levels of assignment two designs and two empirical examples are considered one example of each design in the dose control design there are matched pairs of a treated subject and an untreated control and doses of treatment vary between pairs for treated subjects this yields two evidence factors in the varied intensity design there are matched sets with two treated subjects and one or more untreated controls where the two treated subjects within the same matched set receive different doses of treatment and in a technically different way the design yields two evidence factors

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

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

some approximate evidence factors in observational studies an observational study or nonrandomized experiment has exact evidence factors if it permits several statistically independent tests of the same null hypothesis h0 of no treatment effect where these several tests depend upon different assumptions about bias from nonrandom treatment assignment in an observational study we are typically uncertain about what assumptions truly describe treatment assignment if independent tests each reject h0 and if each of these tests is valid under assumptions about treatment assignment that would invalidate the others then rejection of h0 does not depend upon the truth of any one of these assumptions although exact evidence factors do exist the requirement of exact independence may limit the class of test statistics in ways that reduce pitman efficiency and design sensitivity so one might wish to be free of these limitations a much larger class of statistics permits approximate evidence factors which are not independent but which preserve some of the important con

the assumptions on which causal inferences rest statisticians commonly make causal inferences from the results of randomized experiments but usually question causal inferences from observational studies on the grounds that untestable assumptions are required this paper explains the basis for this situation and examines within quite a general framework various assumptions that appear in the literature it is demonstrated how the role of each assumption is intimately related to the sort of causal inference being considered contrary to general belief it is shown that neither no confounding nor randomization are sufficient assumptions for testing the fundamental causal hypothesis of no causation

a comparison of tests for restricted orderings in the three class case a variety of methods for comparing three distributions have been proposed in the literature these methods assess the same null hypothesis of equal distributions but differ in the alternative hypothesis they consider the alternative hypothesis can be that measurements from the three classes are distributed according to unequal distributions or that measurements between the three classes follow a specific monotone ordering an inverse u shaped umbrella ordering or a u shaped tree ordering this paper compares these tests with respect to power and test size under different simulation scenarios in addition the methods are illustrated in two applications generated by different research questions with data from three classes suggesting monotone and umbrella orders additionally proposals for the appropriate application of these tests are provided

from association to causation in observational studies the role of tests of strongly ignorable treatment assignment abstract if treatment assignment is strongly ignorable then adjustment for observed covariates is sufficient to produce consistent estimates of treatment effects in observational studies a general approach to testing this critical assumption is developed and applied to a study of the effects of nuclear fallout on the risk of childhood leukemia r a fisher s advice on the interpretation of observational studies was make your theories elaborate formally make causal theories sufficiently detailed that under the theory strongly ignorable assignment has testable consequences

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

roc graphs for assessing the ability of a diagnostic marker to detect three disease classes with an umbrella ordering receiver operating characteristic roc curves and the area under these curves are commonly used to assess the ability of a continuous diagnostic marker e g dna methylation markers to correctly classify subjects as having a particular disease or not e g cancer these approaches however are not applicable to settings where the gold standard yields more than two disease states or classes roc surfaces and the volume under the surfaces have been proposed for settings with more than two disease classes these approaches however do not allow one to assess the ability of a marker to differentiate two disease classes from a third disease class without requiring a monotone order for the three disease classes under study that is existing approaches do not accommodate an umbrella ordering of disease classes this article proposes the construction of an roc graph that is applicable for an umbrella ordering furthermore this article proposes that a summary measure for this umbrella roc graph can be used to summarize the classification accuracy and corresponding variance estimates can be obtained using u statistics theory or bootstrap methods the proposed methods are illustrated using data from a study assessing the ability of a dna methylation marker to correctly classify lung specimens into three histologic classes squamous cell carcinoma large cell carcinoma and nontumor lung

causal inference accounting for unobserved confounding after outcome regression and doubly robust estimation causal inference with observational data can be performed under an assumption of no unobserved confounders unconfoundedness assumption there is however seldom clear subject matter or empirical

algebraic k theory of topological k theory we are interested in the arithmetic of ring spectra to make sense of this we must work with structured ring spectra such as s algebras ekmm symmetric ring spectra hss or rings ly we will refer to these as salgebras the commutative objects are then commutative s algebras the category of rings is embedded in the category of s algebras by the eilenberg maclane functor r hr we may therefore view an s algebra as a generalization of a ring in the algebraic sense the added flexibility of s algebras provides room for new examples and constructions which may eventually also shed light upon the category of rings itself in algebraic number theory the arithmetic of the ring of integers in a number field is largely captured by its picard group its unit group and its brauer group these are

sensitivity of two sample permutation inferences in observational studies abstract in observational studies subjects are not randomly assigned to treatment or control so they may differ in their chances of receiving the treatment a simple method is developed and demonstrated for displaying the sensitivity of conventional two group permutation inferences to departures from random assignment of treatments the unmatched case discussed here differs in certain technical and computational details from the matched case discussed previously however the underlying model and the method for quantifying departures from randomization are the same the method may be applied to wilcoxon s rank sum test the gehan and log rank tests for censored outcomes mantel s test for scored categories and fisher s exact test for binary responses the method embeds the usual randomization reference distribution in a one parameter family of departures involving an unobserved covariate that would have been controlled by adjustments had it been observed as this parameter is varied the sensitivity

sensitivity analysis for interactions under unmeasured confounding we develop a sensitivity analysis technique to assess the sensitivity of interaction analyses to unmeasured confounding we give bias formulas for sensitivity analysis for interaction under unmeasured confounding on both additive and multiplicative scales we provide simplified formulas in the case in which either one of the two factors does not interact with the unmeasured confounder in its effects on the outcome an interesting consequence of the results is that if the two exposures of interest are independent e g gene environment independence even under unmeasured confounding if the estimate of the interaction is nonzero then either there is a true interaction between the two factors or there is an interaction between one of the factors and the unmeasured confounder an interaction must be present in either scenario we apply the results to two examples drawn from the literature copyright 2011 john wiley sons ltd

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

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

making sense of sensitivity extending omitted variable bias we extend the omitted variable bias framework with a suite of tools for sensitivity analysis in regression models that does not require assumptions on the functional form of the treatment assignment mechanism nor on the distribution of the unobserved confounders naturally handles multiple confounders possibly acting non linearly exploits expert knowledge to bound sensitivity parameters and can be easily computed by using only standard regression results in particular we introduce two novel sensitivity measures suited for routine reporting the robustness value describes the minimum strength of association that unobserved confounding would need to have both with the treatment and with the outcome to change the research conclusions the partial r2 of the treatment with the outcome shows how strongly confounders explaining all the residual outcome variation would have to be associated with the treatment to eliminate the estimated effect next we offer graphical tools for elaborating on problematic confounders examining the sensitivity of point estimates and t values as well as extreme scenarios finally we describe problems with a common benchmarking practice and introduce a novel procedure to bound the strength of confounders formally on the basis of a comparison with observed covariates we apply these methods to a running example that estimates the effect of exposure to violence on attitudes toward peace

sensitivity of the hazard ratio to nonignorable treatment assignment in an observational study in non randomized studies estimation of treatment effects generally requires adjustment for imbalances in observed covariates one such method based on the propensity score is useful in many applications but may be biased when the assumption of strongly ignorable treatment assignment is violated because it is not possible to evaluate this assumption from the data it is advisable to assess the sensitivity of conclusions to violations of strong ignorability lin et al biomet 1998 54 948 963 have implemented this idea by investigating how an unmeasured covariate may affect the conclusions of an observational study we extend their method to assess sensitivity of the treatment hazard ratio to hidden bias under a range of covariate distributions we derive simple formulas for approximating the true from the apparent treatment hazard ratio estimated under a specific survival model and assess the validity of these formulas in simulation studies we demonstrate the method in an analysis of seer medicare data on the effects of chemotherapy in elderly colon cancer patients

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

design sensitivity in observational studies summary outside the field of statistics the literature on observational studies offers advice about research designs or strategies for judging whether or not an association is causal such as multiple operationalism or a dose response relationship these useful suggestions are typically informal and qualitative a quantitative measure design sensitivity is proposed for measuring the contribution such strategies make in distinguishing causal effects from hidden biases several common strategies are then evaluated in terms of their contribution to design sensitivity a related method for computing the power of a sensitivity analysis is also developed

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

testing one hypothesis twice in observational studies in a matched observational study of treatment effects a sensitivity analysis asks about the magnitude of the departure from random assignment that would need to be present to alter the conclusions of an analysis that assumes that matching for measured covariates removes all bias the reported degree of sensitivity to unmeasured biases depends on both the process that generated the data and the chosen methods of analysis so a poor choice of method may lead to an exaggerated report of sensitivity to bias this suggests the possibility of performing more than one analysis with a correction for multiple inference say testing one null hypothesis using two or three different tests in theory and in an example it is shown that in large samples the gains from testing twice will often be large because testing twice has the larger of the two design sensitivities of the component tests and the losses due to correcting for two tests will often be small because two tests of one hypothesis will typically be highly correlated so a correction for multiple testing that takes this into account will be small an illustration uses data from the u s national health and nutrition examination survey concerning lead in the blood of cigarette smokers copyright 2012 oxford university press

the role of exchangeability in inference abstract this paper is concerned with basic problems of statistical inference the thesis is in three parts 1 that inference is a procedure whereby one passes from a population or sample to a new individual 2 that this connection can be established using de finetti s idea of exchangeability or fisher s concept of a subpopulation and 3 in making the connection use must be made of the appropriate probability these three principles are used in a variety of situations and the topics discussed include analysis of variance and covariance contingency tables and calibration some comments on randomization are also included author

ordered multiple class roc analysis with continuous measurements receiver operating characteristic roc curves have been useful in two group classification problems in three and multiple class diagnostic problems an roc surface or hyper surface can be constructed the volume under these surfaces can be used for inference using bootstrap techniques or u statistics theory in this article roc surfaces and hyper surfaces are defined and their behaviour and utility in multi group classification problems is investigated the formulation of the problem is equivalent to what has previously been proposed in the general multi category classification problem but the definition of roc surfaces here is less complex and addresses directly the narrower problem of ordered categories in the three class and by extension the multi class problem applied to continuous and ordinal data non parametric manipulation of both continuous and discrete test data and comparison between two diagnostic tests applied to the same subjects are considered a three group classification example in the context of hiv neurological disease is presented and the results are discussed

asymptotic separability in sensitivity analysis summary in an observational study in which each treated subject is matched to several untreated controls by using observed pretreatment covariates a sensitivity analysis asks how hidden biases due to unobserved covariates might alter the conclusions the bounds required for a sensitivity analysis are the solution to an optimization problem in general this optimization problem is not separable in the sense that one cannot find the needed optimum by performing a separate optimization in each matched set and combining the results we show however that this optimization problem is asymptotically separable so that when there are many matched sets a separate optimization may be performed in each matched set and the results combined to yield the correct optimum with negligible error this is true when the wilcoxon rank sum test or the hodgeslehmann aligned rank test is applied in matching with multiple controls numerical calculations show that the asymptotic approximation performs well with as few as 10 matched sets in the case of the rank sum test a table is given containing the separable solution with this table only simple arithmetic is required to conduct the sensitivity analysis the method also supplies estimates such as the hodges lehmann estimate and confidence intervals associated with rank tests the method is illustrated in a study of dropping out of us high schools and the effects on cognitive test scores

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

dual and simultaneous sensitivity analysis for matched pairs summary when a study shows an association between a treatment and a response before concluding that there is a causal relationship it is useful to assess whether or not an unobserved variable u might explain the observed association sensitivity analysis clarifies the properties u must have in terms of its relationship to the response and its imbalance in the groups being compared a substantial literature has investigated the imbalance or association between u and group assignment this paper develops a dual sensitivity analysis for matched pairs focusing on the strength of the relationship between u and the response required to reduce an observed association to non significance a third simultaneous form of sensitivity analysis models both relationships between u and treatment assignment and u and response the simultaneous form allows one to compare results from the sensitivity analysis to subject matter knowledge about both relationships the methods are illustrated by several examples

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

topological hochschild homology of connective complex k theory let ku be the connective complex k theory spectrum completed at an odd prime p we present a computation of the mod p 1 homotopy algebra of the topological hochschild homology spectrum of ku

identification of treatment effects under conditional partial independence conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption we derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption these deviations are defined via a conditional treatment assignment probability which makes it straightforward to interpret our results can be used to assess the robustness of empirical conclusions obtained under the baseline conditional independence assumption

causal inference for continuous time processes when covariates are observed only at discrete times most of the work on the structural nested model and g estimation for causal inference in longitudinal data assumes a discrete time underlying data generating process however in some observational studies it is more reasonable to assume that the data are generated from a continuous time process and are only observable at discrete time points when these circumstances arise the sequential randomization assumption in the observed discrete time data which is essential in justifying discrete time g estimation may not be reasonable under a deterministic model we discuss other useful assumptions that guarantee the consistency of discrete time g estimation in more general cases when those assumptions are violated we propose a controlling the future method that performs at least as well as g estimation in most scenarios and which provides consistent estimation in some cases where g estimation is severely inconsistent we apply the methods discussed in this paper to simulated data as well as to a data set collected following a massive flood in bangladesh estimating the effect of diarrhea on children s height results from different methods are compared in both simulation and the real application

bahadur efficiency of sensitivity analyses in observational studies an observational study draws inferences about treatment effects when treatments are not randomly assigned as they would be in a randomized experiment the naive analysis of an observational study assumes that adjustments for measured covariates suffice to remove bias from nonrandom treatment assignment a sensitivity analysis in an observational study determines the magnitude of bias from nonrandom treatment assignment that would need to be present to alter the qualitative conclusions of the naive analysis say leading to the acceptance of a null hypothesis rejected in the naive analysis observational studies vary greatly in their sensitivity to unmeasured biases but a poor choice of test statistic can lead to an exaggerated report of sensitivity to bias the bahadur efficiency of a sensitivity analysis is introduced calculated and connected to established concepts such as the power of a sensitivity analysis and the design sensitivity the bahadur slope equals zero when the sensitivity parameter equ

quantiles in nonrandom samples and observational studies abstract in a nonrandom sample or a nonrandomized comparison of treated and control groups methods are developed for displaying the sensitivity of confidence intervals for population quantiles to the magnitude of the departure from random selection quantiles of a single distribution and for a shift in two distributions are both discussed these confidence intervals are based on a new inequality for the distribution of the number of successes in a nonrandom sample or nonrandomized comparison the inequality has additional applications in particular it greatly accelerates the computations in a sensitivity analysis for the mantel haenszel statistic in a 2 2 s contingency table examples include a nonrandom collection of blood samples from a town with comparatively high levels of radon gas an observational study of chromosome damage from mercury and a study of the drug allopurinol as a cause of skin rash the proof of the inequality makes use of savage s lattice for ranks and holley s inequality wh

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

sensitivity analysis for equivalence and difference in an observational study of neonatal intensive care units in randomized experiments it is sometimes important to demonstrate that two treatments do not differ greatly in their effects or to demonstrate that the treatments have very different effects on one outcome but similar effects on another outcome these demonstrations may take the form of rejecting a null hypothesis of inequivalence in an equivalence test or rejecting a null hypothesis of equal and inequivalent effects on two outcomes the procedures often express a complex hypothesis in terms of component hypotheses and combine the component significance levels to test the complex hypothesis if used in a randomized trial randomization provides valid significance levels for each component test and hence also for the combined procedure in an observational study that is in a study of treatments that were not randomly assigned there is typically concern that significance levels for testing hypotheses about treatment effects may be distorted by failure to control for some unobserved pretreatment cov

the roc manifold for classification systems we define the roc manifold and cc manifold as duals in a given sense their analysis is required to describe the classification system we propose a mathematical definition based on vector space methods to describe both the roc manifolds for n class classification systems fully describe each system in terms of its misclassifications and by conjunction its correct classifications optimal points which minimize misclassifications can be identified even when costs and prior probabilities differ these manifolds can be used to determine the usefulness of a classification system based on a given performance criterion many performance functionals such as summary statistics preferred for cc manifolds can also be evaluated using the roc manifold under certain constraints examples using the roc manifold and performance functionals to compete classification systems are demonstrated with simulated and applied disease detection data

on the k theory of local fields in this paper we establish a connection between the quillen k theory of certain local fields and the de rham witt complex of their rings of integers with logarithmic poles at the maximal ideal the fieldsk we consider are complete discrete valuation fields of characteristic zero with perfect residue field k of characteristic p 2 when k contains the pth roots of unity the relationship between the k theory with z p coefficients and the de rham witt complex can be described by a sequence

bounds on potential risks and causal risk differences under assumptions about confounding parameters nonparametric bounds on causal effects in observational studies are available under deterministic potential outcome models we derive narrower bounds by adding assumptions regarding bias due to confounding this bias is defined as the difference between the expectation of potential outcomes for the exposed group and that for the unexposed group we show that crude effect measures bound causal effects under the given assumptions we then derive bounds for randomized studies with noncompliance which are given by the per protocol effect with perfect compliance in one treatment group the direction of effect becomes identifiable under our assumptions although the assumptions are not themselves identifiable they are nonetheless reasonable in some situations

causal conclusions are most sensitive to unobserved binary covariates there is a rich literature that considers whether an observed relation between treatment and response is due to an unobserved covariate in order to quantify this unmeasured bias an assumption is made about the distribution of this unobserved covariate typically that it is either binary or at least confined to the unit interval in this paper this assumption is relaxed in the context of matched pairs with binary treatment and response one might think that a long tailed unobserved covariate could do more damage remarkably that is not the case the most harm is done by a binary covariate so the case commonly considered in the literature is most conservative this has two practical consequences i it is always safe to assume that an unobserved covariate is binary if one is content to make a conservative statement ii when another assumption seems more appropriate say normal covariate there will be less sensitivity than with a binary covariate this assumption implies that it is possible that a relation between treatment and response that is sensitive to unmeasured bias if the unobserved covariate is dichotomous ceases to be sensitive if the unobserved covariate is normally distributed these ideas are illustrated by three examples it is important to note that the claim in this paper applies to our specific setting of matched pairs with binary treatment and response whether the same conclusion holds in other settings is an open question

sensitivity analysis distributional assumptions and confounding assumptions in a presentation of various methods for assessing the sensitivity of regression results to unmeasured confounding lin psaty and kronmal 1998 biometrics54 948 963 use a conditional independence assumption to derive algebraic relationships between the true exposure effect and the apparent exposure effect in a reduced model that does not control for the unmeasured confounding variable however hernan and robins 1999 biometrics55 1316 1317 have noted that if the measured covariates and the unmeasured confounder both affect the exposure of interest then the principal conditional independence assumption that is used to derive these algebraic relationships cannot hold one particular result of lin et al does not rely on the conditional independence assumption but only on assumptions concerning additivity it can be shown that this assumption is satisfied for an entire family of distributions even if both the measured covariates and the unmeasured confounder affect the exposure of interest these considerations clarify the appropriate contexts in which relevant sensitivity analysis techniques can be applied

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

addressing complications of intention to treat analysis in the combined presence of all or none treatment noncompliance and subsequent missing outcomes summary we study the combined impact that all or none compliance and subsequent missing outcomes can have on the estimation of the intention to treat effect of assignment in randomised studies in this setting a standard analysis which drops subjects with missing outcomes and ignores compliance information can be biased for the intention to treat effect to address all or none compliance that is followed by missing outcomes we construct a new estimation procedure for the intention to treat effect that maintains good randomisation based properties under more plausible nonignorable noncompliance and nonignorable missing outcome conditions the compound exclusion restriction on the effect of assignment and the latent ignorability of the missing data mechanism we present both theoretical results and a simulation study moreover we show how the two key concepts of compound exclusion and latent ignorability are relevant in more complicated settings such as right censoring of a time to event outcome

model based direct adjustment abstract direct adjustment or standardization applies population weights to subclass means in an effort to estimate population quantities from a sample that is not representative of the population direct adjustment has several attractive features but when there are many subclasses it can attach large weights to small quantities of data often in a fairly erratic manner in the extreme direct adjustment can attach infinite weight to nonexistent data a noticeable inconvenience in practice this article proposes a method of model based direct adjustment that preserves the attractive features of conventional direct adjustment while stabilizing the weights attached to small subclasses the sample mean and conventional direct adjustment are both special cases of model based direct adjustment under two different extreme models for the subclass specific selection probabilities the discussion of this method provides some insights into the behavior of true and estimated propensity scores the estimated scores

measuring and estimating diagnostic accuracy when there are three ordinal diagnostic groups this article studies the problem of measuring and estimating the diagnostic accuracy when there are three ordinal diagnostic groups we use a receiver operating characteristic roc surface to describe the probabilities of correct classifications into three diagnostic groups based on various sets of diagnostic thresholds of a test and propose to use the entire and the partial volume under the surface to measure the diagnostic accuracy mathematical properties and probabilistic interpretations of the proposed measure of diagnostic accuracy are discussed under the assumption of normal distributions of the diagnostic test from three diagnostic groups we present the maximum likelihood estimate to the volume under the roc surface and give the asymptotic variance to the estimate we further propose several asymptotic confidence interval estimates to the volume under the roc surface the performance of these confidence interval estimates is evaluated in terms of attaining the nominal coverage probability based on a simulation study in addition we develop a method of sample size determination to achieve an adequate accuracy of the confidence interval estimate finally we demonstrate the proposed methodology by applying it to the clinical diagnosis of early stage alzheimer s disease based on the neuropsychological database of the washington university alzheimer s disease research center

amplification of sensitivity analysis in matched observational studies a sensitivity analysis displays the increase in uncertainty that attends an inference when a key assumption is relaxed in matched observational studies of treatment effects a key assumption in some analyses is that subjects matched for observed covariates are comparable and this assumption is relaxed by positing a relevant covariate that was not observed and not controlled by matching what properties would such an unobserved covariate need to have to materially alter the inference about treatment effects for ease of calculation and reporting it is convenient that the sensitivity analysis be of low dimension perhaps indexed by a scalar sensitivity parameter but for interpretation in specific contexts a higher dimensional analysis may be of greater relevance an amplification of a sensitivity analysis is defined as a map from each point in a low dimensional sensitivity analysis to a set of points perhaps a curve in a higher dimensional sensitivity analysis such that the possible inferences are

stability in the absence of treatment when subjects are measured twice once at each of two symmetrical locations or times stability of responses in the absence of treatment within subjects together with comparability of untreated responses between subjects is often viewed as supporting a conclusion that differences between treated and control responses reflect effects actually caused by the treatment the degree to which this intuitive argument is formally correct is explored in several related models a multivariate normal model a nonparametric model defined by symmetries an analogous randomized experiment and a sensitivity analysis model for observational studies in which treatments are not randomly assigned to subjects nor to locations within subjects card and kreuger s study of the employment effects of the minimum wage is used to illustrate the methods

a cautionary note concerning the use of stabilized weights in marginal structural models marginal structural models are commonly used to estimate the causal effect of a time varying treatment in presence of time dependent confounding when fitting an msm to data the analyst must specify both the structural model for the outcome and the treatment models for the inverse probability of treatment weights the use of stabilized weights is recommended because they are generally less variable than the standard weights in this paper we are concerned with the use of the common stabilized weights when the structural model is specified to only consider partial treatment history such as the current or most recent treatments we present various examples of settings where these stabilized weights yield biased inferences while the standard weights do not these issues are first investigated on the basis of simulated data and subsequently exemplified using data from the honolulu heart program unlike common stabilized weights we find that basic stabilized weights offer some protection against bias in structural models designed to estimate current or most recent treatment effects copyright 2014 john wiley sons ltd

diagram spaces and symmetric spectra abstract we present a general homotopical analysis of structured diagram spaces and discuss the relation to symmetric spectra the main motivating examples are the i spaces which are diagrams indexed by finite sets and injections and j spaces which are diagrams indexed by quillen s localization construction 1 on the category of finite sets and bijections we show that the category of i spaces provides a convenient model for the homotopy category of spaces in which every e space can be rectified to a strictly commutative monoid similarly the commutative monoids in the category of j spaces model graded e spaces using the theory of j spaces we introduce the graded units of a symmetric ring spectrum the graded units detect periodicity phenomena in stable homotopy and we show how this can be applied to the theory of topological logarithmic structures

a propensity score adjustment for multiple group structural equation modeling in the behavioral and social sciences quasi experimental and observational studies are used due to the difficulty achieving a random assignment however the estimation of differences between groups in observational studies frequently suffers from bias due to differences in the distributions of covariates to estimate average treatment effects when the treatment variable is binary rosenbaum and rubin 1983a proposed adjustment methods for pretreatment variables using the propensity score

virtual vector bundles and graded thom spectra we introduce a convenient framework for constructing and analyzing orthogonal thom spectra arising from virtual vector bundles this framework enables us to set up a theory of orientations and graded thom isomorphisms with good multiplicative properties the theory is applied to the analysis of logarithmic structures on commutative ring spectra

pattern mixture and selection models for analysing longitudinal data with monotone missing patterns summary we examine three pattern mixture models for making inference about parameters of the distribution of an outcome of interest y that is to be measured at the end of a longitudinal study when this outcome is missing in some subjects we show that these pattern mixture models also have an interpretation as selection models because these models make unverifiable assumptions we recommend that inference about the distribution of y be repeated under a range of plausible assumptions we argue that of the three models considered only one admits a parameterization that facilitates the examination of departures from the assumption of sequential ignorability the three models are nonparametric in the sense that they do not impose restrictions on the class of observed data distributions owing to the curse of dimensionality the assumptions that are encoded in these models are sufficient for identification but not for inference we describe additional flexible and easily interpretable assumptions under which it is possible to construct estimators that are well behaved with moderate sample sizes these assumptions define semiparametric models for the distribution of the observed data we describe a class of estimators which up to asymptotic equivalence comprise all the consistent and asymptotically normal estimators of the parameters of interest under the postulated semiparametric models we illustrate our methods with the analysis of data from a randomized clinical trial of contracepting women

effect modification and design sensitivity in observational studies in an observational study of treatment effects subjects are not randomly assigned to treatment or control so differing outcomes in treated and control groups may reflect a bias from nonrandom assignment rather than a treatment effect after adjusting for measured pretreatment covariates perhaps by matching a sensitivity analysis determines the magnitude of bias from an unmeasured covariate that would need to be present to alter the conclusions of the naive analysis that presumes adjustments eliminated all bias other things being equal larger effects tend to be less sensitive to bias than smaller effects effect modification is an interaction between a treatment and a pretreatment covariate controlled by matching so that the treatment effect is larger at some values of the covariate than at others in the presence of effect modification it is possible that results are less sensitive to bias in subgroups experiencing larger effects two cases are considered i an a priori grouping into a few categ

a distributional approach for causal inference using propensity scores drawing inferences about the effects of treatments and actions is a common challenge in economics epidemiology and other fields we adopt rubin s potential outcomes framework for causal inference and propose two methods serving complementary purposes one can be used to estimate average causal effects assuming no confounding given measured covariates the other can be used to assess how the estimates might change under various departures from no confounding both methods are developed from a nonparametric likelihood perspective the propensity score plays a central role and is estimated through a parametric model under the assumption of no confounding the joint distribution of covariates and each potential outcome is estimated as a weighted empirical distribution expectations from the joint distribution are estimated as weighted averages or equivalently to first order regression estimates the likelihood estimator is at least as efficient and the regression estimator is at least as efficient and r

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

treatment effect estimation with covariate measurement error this paper investigates the effect that covariate measurement error has on a treatment effect analysis built on an unconfoundedness restriction in which there is conditioning on error free covariates the approach uses small parameter asymptotic methods to obtain the approximate effects of measurement error for estimators of average treatment effects the approximations can be estimated using data on observed outcomes the treatment indicator and error contaminated covariates without employing additional information from validation data or instrumental variables the results can be used in a sensitivity analysis to probe the potential effects of measurement error on the evaluation of treatment effects

cox regression analysis of multivariate failure time data the marginal approach multivariate failure time data are commonly encountered in scientific investigations because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated in this paper i present a general methodology for analysing such data which is analogous to that of liang and zeger for longitudinal data analysis this approach formulates the marginal distributions of multivariate failure times with the familiar cox proportional hazards models while leaving the nature of dependence among related failure times completely unspecified the baseline hazard functions for the marginal models may be identical or different simple estimating equations for the regression parameters are developed which yield consistent and asymptotically normal estimators and robust variance covarinace estimators are constructed to account for the intra class correlation simulation results demonstrate that the large sample approximations are adequate for practical use and that ignoring the intra class correlation could yield rather misleading variance estimators the proposed methodology has been fully implemented in a simple computer program which also incorporates several alternative approaches detailed illustrations with data from four clinical or epidemiologic studies are provided

a comparison of bayesian and monte carlo sensitivity analysis for unmeasured confounding bias from unmeasured confounding is a persistent concern in observational studies and sensitivity analysis has been proposed as a solution in the recent years probabilistic sensitivity analysis using either monte carlo sensitivity analysis mcsa or bayesian sensitivity analysis bsa has emerged as a practical analytic strategy when there are multiple bias parameters inputs bsa uses bayes theorem to formally combine evidence from the prior distribution and the data in contrast mcsa samples bias parameters directly from the prior distribution intuitively one would think that bsa and mcsa ought to give similar results both methods use similar models and the same prior probability distributions for the bias parameters in this paper we illustrate the surprising finding that bsa and mcsa can give very different results specifically we demonstrate that mcsa can give inaccurate uncertainty assessments e g 95 intervals that do not reflect the data s influence on uncertainty about unmeasured confounding using a data example from epidemiology and simulation studies we show that certain combinations of data and prior distributions can result in dramatic prior to posterior changes in uncertainty about the bias parameters this occurs because the application of bayes theorem in a non identifiable model can sometimes rule out certain patterns of unmeasured confounding that are not compatible with the data consequently the mcsa approach may give 95 intervals that are either too wide or too narrow and that do not have 95 frequentist coverage probability based on our findings we recommend that analysts use bsa for probabilistic sensitivity analysis copyright 2017 john wiley sons ltd