testing hypotheses in order in certain circumstances one wishes to test one hypothesis only if certain other hypotheses have been rejected this ordering of hypotheses simplifies the task of controlling the probability of rejecting any true hypothesis in an example from an observational study a treated group is shown to be further from both of two control groups than the two control groups are from each other

superconvergence in finite element methods and meshes that are locally symmetric with respect to a point consider a second order elliptic boundary value problem in any number of space dimensions with locally smooth coefficients and solution consider also its numerical approximation by standard conforming finite element methods with for example fixed degree piecewise polynomials on a quasi uniform mesh family the h method it will be shown that if the finite element function spaces are locally symmetric about a point x 0 with respect to the antipodal map x to x 0 x x 0 then superconvergence ensues at xo under mild conditions on what happens outside a neighborhood of x 0 for piecewise polynomials of even degree superconvergence occurs in function values for piecewise polynomials of odd degree it occurs in derivatives

asymptotic error expansions for the finite element method for second order elliptic problems in r n n geq2 i local interior expansions our aim here is to give sufficient conditions on the finite element spaces near a point so that the error in the finite element method for the function and its derivatives at the point have exact asymptotic expansions in terms of the mesh parameter h valid for h sufficiently small such expansions are obtained from the so called asymptotic expansion inequalities valid in mathbf r n for n geq2 studies by schatz in math comp 67 1998 pp 877 899 and siam j numer anal 38 2000 pp 1269 1293

sensitivity analysis for m estimates tests and confidence intervals in matched observational studies huber s m estimates use an estimating equation in which observations are permitted a controlled level of influence the family of m estimates includes least squares and maximum likelihood but typical applications give extreme observations limited weight maritz proposed methods of exact and approximate permutation inference for m tests confidence intervals and estimators which can be derived from random assignment of paired subjects to treatment or control in contrast in observational studies where treatments are not randomly assigned subjects matched for observed covariates may differ in terms of unobserved covariates so differing outcomes may not be treatment effects in observational studies a method of sensitivity analysis is developed for m tests m intervals and m estimates it shows the extent to which inferences would be altered by biases of various magnitudes due to nonrandom treatment assignment the method is developed for both matched pairs with one treated subject matched to one control and for matched sets with one treated subject matched to one or more controls the method is illustrated using two studies i a paired study of damage to dna from exposure to chromium and nickel and ii a study with one or two matched controls comparing side effects of two drug regimes to treat tuberculosis the approach yields sensitivity analyses for i m tests with huber s weight function and other robust weight functions ii the permutational t test which uses the observations directly and iii various other procedures such as the sign test noether s test and the permutation distribution of the efficient score test for a location family of distributions permutation inference with covariance adjustment is briefly discussed

on construction of the smallest one sided confidence interval for the difference of two proportions for any class of one sided 1 confidence intervals with a certain monotonicity ordering on the random confidence limit the smallest interval in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables is constructed based on a direct analysis of coverage probability function a special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived this interval is then applied to identify the minimum effective dose med for binary data in dose response studies and a multiple test procedure that controls the familywise error rate at level is obtained a generalization of constructing the smallest one sided confidence interval to other discrete sample spaces is discussed in the presence of nuisance parameters

a new criterion for confounder selection we propose a new criterion for confounder selection when the underlying causal structure is unknown and only limited knowledge is available we assume all covariates being considered are pretreatment variables and that for each covariate it is known i whether the covariate is a cause of treatment and ii whether the covariate is a cause of the outcome the causal relationships the covariates have with one another is assumed unknown we propose that control be made for any covariate that is either a cause of treatment or of the outcome or both we show that irrespective of the actual underlying causal structure if any subset of the observed covariates suffices to control for confounding then the set of covariates chosen by our criterion will also suffice we show that other commonly used criteria for confounding control do not have this property we use formal theory concerning causal diagrams to prove our result but the application of the result does not rely on familiarity with causal diagrams an investigator simply need ask is the covariate a cause of the treatment and is the covariate a cause of the outcome if the answer to either question is yes then the covariate is included for confounder control we discuss some additional covariate selection results that preserve unconfoundedness and that may be of interest when used with our criterion

constructing multiple test procedures for partially ordered hypothesis sets a popular method to control multiplicity in confirmatory clinical trials is to use a so called hierarchical or fixed sequence test procedure this requires that the null hypotheses are ordered a priori for example in order of clinical importance the procedure tests the hypotheses in this order using level tests until one is not rejected it then stops so that no subsequent hypotheses are eligible for rejection this procedure strongly controls the familywise error rate fwe that is to say the probability that any true hypotheses are rejected this paper describes a simple generalization of this approach in which the null hypotheses are partially ordered it is convenient to display the partial ordering in a directed acyclic graph dag we consider sequentially rejective procedures based on the partial ordering in which a hypothesis is tested only when all preceding hypotheses have been tested and rejected in general such procedures do not control the fwe but it is shown that when certain intersection hypotheses are added strong control of the fwe is obtained the purpose of the method is to construct inference strategies for confirmatory clinical trials that better reflect the trial objectives copyright 2007 john wiley sons ltd

multiple test procedures for identifying the maximum safe dose we consider dose response studies for safety assessment of crop protection compounds and drugs and we offer a hypothesis testing approach for identifying the maximum dose level that is guaranteed to be safe with preassigned confidence the focus is on step down sd multiple test procedures for identifying the maximum safe dose we propose two classes of contrasts among the dose means as test statistics for these procedures pairwise contrasts pc and helmert contrasts hc the first procedure sd2pc consists of a sequence of ordinary t tests and is thus easy to apply but it can have very low power for certain step response functions the second procedure sd1hc does not suffer from this drawback but it requires a weak monotonicity assumption for its mathematical validity the powers of sd2pc and sd1hc are studied via monte carlo simulation we recommend sd2pc for linear response functions and sd1hc for step response functions the procedures are illustrated by applying them to data from an aquatic

a new finite element gradient recovery method superconvergence property this is the first in a series of papers in which a new gradient recovery method is introduced and analyzed it is proved that the method is superconvergent for translation invariant finite element spaces of any order the method maintains the simplicity efficiency and superconvergence properties of the zienkiewicz zhu patch recovery method in addition for uniform triangular meshes the method is superconvergent for the linear element under the chevron pattern and ultraconvergent at element edge centers for the quadratic element under the regular pattern applications of this new gradient recovery technique will be discussed in forthcoming papers

ultraconvergence of the patch recovery technique ii the ultraconvergence property of a gradient recovery technique proposed by zienkiewicz and zhu is analyzed for the laplace equation in the two dimensional setting under the assumption that the pollution effect is not present or is properly controlled it is shown that the convergence rate of the recovered gradient at an interior node is two orders higher than the optimal global convergence rate when even order finite element spaces and local uniform rectangular meshes are used

spr technique and finite element correction this paper considers the finite element method for two point boundary value problems using projection interpolation some correction results for the derivative and displacement are proved directly computational results demonstrate the theoretical findings

superconvergence in high order galerkin finite element methods in this paper we shall use local estimates to give the superconvergence of high order galerkin finite element method for the elliptic equation of second order with constant coefficients by using the symmetric technique and integral identity we get improved superconvergence on the inner locally symmetric mesh with respect to a point x0 for rectangular and triangular meshes

weighted m statistics with superior design sensitivity in matched observational studies with multiple controls in a nonrandomized or observational study a weak association between receipt of the treatment and an outcome may be explained not as effects caused by the treatment but rather by a small bias in the assignment of individuals to treatment or control however a strong association may be explained as noncausal only by a large bias the strength of the association between treatment and outcome is not uniform across the data from a study and this motivates giving greater weight where the association is stronger in an observational study with treated control matched pairs it is known that results are less sensitive to unmeasured biases if pairs with small absolute differences in outcomes are given little weight in the analysis more precisely such a test statistic has superior design sensitivity how should outcomes be weighted if an observational study is matched in sets with one treated subject and several controls an m statistic is the quantity equated to zero in defining huber s m estimates includin

substantial gains in bias reduction from matching with a variable number of controls summary in observational studies that match several controls to each treated subject substantially greater bias reduction is possible if the number of controls is not fixed but rather is allowed to vary from one matched set to another in certain cases matching with a fixed number of controls may remove only 50 of the bias in a covariate whereas matching with a variable number of controls may remove 90 of the bias even though both control groups have the same number of controls in total an example of matching in a study of surgical mortality is discussed in detail

small bound for birational automorphism groups of algebraic varieties with an appendix by yujiro kawamata we give an effective upper bound of bir x for the birational automorphism group of an irregular n fold with n 3 of general type in terms of the volume v v x under an albanese smoothness and simplicity condition to be precise rm bir x leq d 3 v 10 an optimum linear bound rm bir x leq frac 1 3 times 42 3 v is obtained for those threefolds with non maximal albanese dimension for all n 3 a bound rm bir x leq d n v 10 is obtained when albx is generically finite alb x is smooth and alb x is simple

assessment of the extent of corroboration of an elaborate theory of a causal hypothesis using partial conjunctions of evidence factors an elaborate theory of predictions of a causal hypothesis consists of several falsifiable statements derived from the causal hypothesis statistical tests for the various pieces of the elaborate theory help to clarify how much the causal hypothesis is corroborated in practice the degree of corroboration of the causal hypothesis has been assessed by a verbal description of which of the several tests provides evidence for which of the several predictions this verbal approach can miss quantitative patterns in this paper we develop a quantitative approach we first decompose these various tests of the predictions into independent factors with different sources of potential biases support for the causal hypothesis is enhanced when many of these evidence factors support the predictions a sensitivity analysis is used to assess the potential bias that could make the finding of the tests spurious along with this multiparameter sensitivity analysis we consider the partial conjunctions of the tests these partial conjunctions quantify the evidence supporting various fractions of the collection of predictions a partial conjunction test involves combining tests of the components in the partial conjunction we find the asymptotically optimal combination of tests in the context of a sensitivity analysis our analysis of an elaborate theory of a causal hypothesis controls for the familywise error rate

sensitivity analysis for multiple comparisons in matched observational studies through quadratically constrained linear programming abstracta sensitivity analysis in an observational study assesses the robustness of significant findings to unmeasured confounding while sensitivity analyses in matched observational studies have been well addressed when there is a single outcome variable accounting for multiple comparisons through the existing methods yields overly conservative results when there are multiple outcome variables of interest this stems from the fact that unmeasured confounding cannot affect the probability of assignment to treatment differently depending on the outcome being analyzed existing methods allow this to occur by combining the results of individual sensitivity analyses to assess whether at least one hypothesis is significant which in turn results in an overly pessimistic assessment of a study s sensitivity to unobserved biases by solving a quadratically constrained linear program we are able to perform a sensitivity analysis while enforcing that unmeasured confounding must have the same impact on the treatm

superconvergence and a posteriori error estimation in triangular mixed finite elements in this paper we prove superconvergence results for the vector variable when lowest order triangular mixed finite elements of raviart thomas type 17 on uniform triangulations are used i e that the h mbox div omega distance between the approximate solution and a suitable projection of the real solution is of higher order than the h mbox div omega error we prove results for both dirichlet and neumann boundary conditions recently duran 9 proved similar results for rectangular mixed finite elements and superconvergence along the gauss lines for rectangular mixed finite elements was considered by douglas ewing lazarov and wang in 11 8 and 18 the triangular case however needs some extra effort using the superconvergence results a simple postprocessing of the approximate solution will give an asymptotically exact a posteriori error estimator for the l 2 omega error in the approximation of the vector variable

a note on multiple testing procedures in dose finding it is shown that in some recently proposed multiple test procedures for dose finding tamhane hochberg and dunnett 1996 biometrics 52 21 37 strong control of the familywise error is only guaranteed if order relations are assumed to hold among the means procedures that can be applied safely without assuming any restrictions on the means can be based on the classical many one comparisons of doses with the zero dose

the local superconvergence of the trilinear element for the three dimensional poisson problem abstract in this paper we shall combine the finite element theory of green s function presented in this paper the extrapolation technique and the local symmetric technique to investigate the local superconvergence of the trilinear element for the three dimensional poisson equation

discovering findings that replicate from a primary study of high dimension to a follow up study we consider the problem of identifying whether findings replicate from one study of high dimension to another when the primary study guides the selection of hypotheses to be examined in the follow up study as well as when there is no division of roles into the primary and the follow up study we show that existing meta analysis methods are not appropriate for this problem and suggest novel methods instead we prove that our multiple testing procedures control for appropriate error rates the suggested family wise error rate controlling procedure is valid for arbitrary dependence among the test statistics within each study a more powerful procedure is suggested for false discovery rate fdr control we prove that this procedure controls the fdr if the test statistics are independent within the primary study and independent or have positive dependence in the follow up study for arbitrary dependence within the primary study and either arbitrary dependence or positive dependence in the follow up study

stepwise confidence intervals without multiplicity adjustment for dose response and toxicity studies abstract not all simultaneous inferences need multiplicity adjustment if the sequence of individual inferences is predefined and failure to achieve the desired inference at any step renders subsequent inferences unnecessary then multiplicity adjustment is not needed this can be justified using the closed testing principle to test appropriate hypotheses that are nested in sequence starting with the most restrictive one but what hypotheses are appropriate may not be obvious in some problems we give a fundamentally different confidence set based justification by partitioning the parameter space naturally and using the principle that exactly one member of the partition contains the true parameter in dose response studies designed to show superiority of treatments over a placebo negative control or a drug known to be efficacious active control the confidence set approach generates methods with meaningful guarantee against incorrect decision whereas previous applications of the closed testing app

a new approach to richardson extrapolation in the finite element method for second order elliptic problems this paper presents a nonstandard local approach to richardson extrapolation when it is used to increase the accuracy of the standard finite element approximation of solutions of second order elliptic boundary value problems in mathbb r n n ge 2 the main feature of the approach is that it does not rely on a traditional asymptotic error expansion but rather depends on a more easily proved weaker a priori estimate derived in 19 called an asymptotic error expansion inequality in order to use this inequality to verify that the richardson procedure works at a point we require a local condition which links the different subspaces used for extrapolation roughly speaking this condition says that the subspaces are similar about a point i e any one of them can be made to locally coincide with another by a simple scaling of the independent variable about that point examples of finite element subspaces that occur in practice and satisfy this condition are given

a recycling framework for the construction of bonferroni based multiple tests in this paper we describe bonferroni based multiple testing procedures mtps as strategies to split and recycle test mass here test mass refers to parts of the nominal level alpha at which the family wise error rate is controlled briefly test mass is split between different null hypotheses and whenever a null hypothesis is rejected the part of alpha allocated to it may be recycled to the testing of other hypotheses these recycling mtps are closed testing procedures based on raw p values associated with testing the individual null hypotheses and the class of such mtps includes for example serial and parallel gatekeeping fallback and holm procedures graphical displays and a concise algebraic notation are provided for such mtps this recycling approach has pedagogical advantages and may facilitate the tailoring of mtps for different purposes

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

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part 1 a smooth problem and globally quasi uniform meshes a class of a posteriori estimators is studied for the error in the maximum norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems the meshes are unstructured and in particular it is not assumed that there are any known superconvergent points the estimators are based on averaging operators which are approximate gradients recovered gradients which are then compared to the actual gradient of the approximation on each element conditions are given under which they are asympotically exact or equivalent estimators on each single element of the underlying meshes asymptotic exactness is accomplished by letting the approximate gradient operator average over domains that are large in a controlled fashion to be detailed below compared to the size of the elements

fdr control with pseudo gatekeeping based on a possibly data driven order of the hypotheses we propose a multiple testing procedure controlling the false discovery rate the procedure is based on a possibly data driven ordering of the hypotheses which are tested at the uncorrected level q until a suitable number is not rejected when the order is data driven larger effect sizes are considered first therefore selecting more interesting hypotheses with larger probability the proposed procedure is valid under independence for the test statistics we also propose a modification which makes our procedure valid under arbitrary dependence it is shown in simulation that we compare particularly well when the sample size is small we conclude with an application to identification of molecular signatures of intracranial ependymoma the methods are implemented in an r package somemtp freely available on cran

hierarchical testing of variable importance a frequently encountered challenge in high dimensional regression is the detection of relevant variables variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated when taking the multiplicity of the testing problem into account the power diminishes even further to gain power and insight it can be advantageous to look for influence not at the level of individual variables but rather at the level of clusters of highly correlated variables we propose a hierarchical approach variable importance is first tested at the coarsest level corresponding to the global null hypothesis the method then tries to attribute any effect to smaller subclusters or even individual variables the smallest possible clusters which still exhibit a significant influence on the response variable are retained it is shown that the proposed testing procedure controls the familywise error rate at a prespecified level simultaneously over all resolution levels the method has power comparable to the bonferroni holm procedure on the level of individual variables and dramatically larger power for coarser resolution levels the best resolution level is selected adaptively

sequential implementation of stepwise procedures for identifying the maximum tolerated dose this article considers the problem of finding the maximum tolerated dose mtd of a drug in human trials the mtd is defined as the maximum test dose with toxicity probability less than or equal to a target toxicity rate we adopt the multiple test framework with step down tests used in an escalation stage and step up tests used in a deescalation stage to allow sequential dose assignments for ethical purposes by formulating the estimation problem as a testing problem the proposed procedures formally control the error probability of selecting an unsafe dose in addition we can control the probability of correctly selecting the mtd under a parameter subspace where no toxicity probability lies in an interval bracketed by the target toxicity rate and an unacceptably high toxicity rate the so called indifference zone this frequentist property which is currently lacking in the conduct of dose finding trials in humans is appealing from a regulatory standpoint we give the general expressions of the se

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

impact of multiple matched controls on design sensitivity in observational studies summary in an observational study one treated subject may be matched for observed covariates to either one or several untreated controls the common motivation for using several controls rather than one is to increase the power of a test of no effect under the doubtful assumption that matching for observed covariates suffices to remove bias from nonrandom treatment assignment does the choice between one or several matched controls affect the sensitivity of conclusions to violations of this doubtful assumption with continuous responses it is known that reducing the heterogeneity of matched pair differences reduces sensitivity to unmeasured biases but increasing the sample size has a highly circumscribed effect on sensitivity to bias is the use of several controls rather than one analogous to a reduction in heterogeneity or to an increase in sample size the issue is examined for huber s m statistics including the t test the examination having three components an example asymptotic calculations using design sensitivity and a simulation use of multiple controls with continuous responses yields a nontrivial reduction in sensitivity to unmeasured biases an example looks at lead and cadmium in the blood of smokers from the 2008 national health and nutrition examination survey a by product of the discussion is a new result giving the design sensitivity for the permutation distribution of m statistics

a powerful approach to the study of moderate effect modification in observational studies effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate generally larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates so a causal conclusion may be considerably firmer if this pattern is noted if it occurs we propose a new strategy called the submax method that combines exploratory and confirmatory efforts to determine whether there is stronger evidence of causality that is greater insensitivity to unmeasured confounding in some subgroups of individuals it uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates for l binary covariates the method splits the population l times into two subpopulations perhaps first men and women perhaps then smokers and nonsmokers computing a test statistic from each subpopulation and appends the test statistic for the whole population making 2 l 1 test statistics in total although l binary covariates define 2 l interaction groups only 2 l 1 tests are performed and at least l 1 of these tests use at least half of the data the submax method achieves the highest design sensitivity and the highest bahadur efficiency of its component tests moreover the form of the test is sufficiently tractable that its large sample power may be studied analytically the simulation suggests that the submax method exhibits superior performance in comparison with an approach using cart when there is effect modification of moderate size using data from the nhanes i epidemiologic follow up survey an observational study of the effects of physical activity on survival is used to illustrate the method the method is implemented in the r package submax which contains the nhanes example an online appendix provides simulation results and further analysis of the example

on δ equivalence with the best in k sample models in recent work we introduced a general a weak and a strong partitioning principles for the construction of multiple decision procedures as multiple testing or selection procedures partitioning principles can be viewed as natural extensions of the closure principle and sometimes yield more powerful decision procedures in this article we consider the problem of establishing equivalence with the best with respect to k treatment means where equivalence is defined in terms of a threshold value 0 we reformulate the original selection problem as a multiple testing problem and develop various step down and step up procedures by applying the closure principle and partitioning principles the new step down procedure is shown to provide a uniform improvement over procedures currently in use moreover we propose some projection methods that yield confidence intervals being compatible with stepwise tests and selection procedures

the partitioning principle a powerful tool in multiple decision theory a first general principle and nowadays state of the art for the construction of powerful multiple test procedures controlling a multiple level a is the so called closure principle in this article we introduce another powerful tool for the construction of multiple decision procedures especially for the construction of multiple test procedures and selection procedures this tool is based on a partition of the parameter space and will be called partitioning principle pp in the first part of the paper we review basic concepts of multiple hypotheses testing and discuss a slight generalization of the current theory in the second part we present various variants of the pp for the construction of multiple test procedures these are a general pp gpp a weak pp wpp and a strong pp spp it will be shown that depending on the underlying decision problem a pp may lead to more powerful test procedures than a formal application of the closure principle fcp moreover the more complex spp may be more powerful than the wpp based on a duality between testing and selecting pps can also be applied for the construction of more powerful selection procedures in the third part of the paper fcp wpp and spp are applied and compared in some examples

detecting dose response with contrasts analyses of dose response studies should separate the question of the existence of a dose response relationship from questions of functional form and finding the optimal dose a well chosen contrast among the estimated effects of the studied doses can make a powerful test for detecting the existence of a dose response relationship a contrast based test attains its greatest power when the pattern of the coefficients has the same shape as the true dose response relationship however it loses power when the contrast shape and the true dose response shape are not similar thus a primary test based on a single contrast is often risky two or more appropriately chosen contrasts can assure sufficient power to justify the cost of a multiplicity adjustment an example shows the success of a two contrast procedure in detecting dose response which had frustrated several standard procedures

the sequential rejection principle of familywise error control closed testing and partitioning are recognized as fundamental principles of familywise error control in this paper we argue that sequential rejection can be considered equally fundamental as a general principle of multiple testing we present a general sequentially rejective multiple testing procedure and show that many well known familywise error controlling methods can be constructed as special cases of this procedure among which are the procedures of holm shaffer and hochberg parallel and serial gatekeeping procedures modern procedures for multiple testing in graphs resampling based multiple testing procedures and even the closed testing and partitioning procedures themselves we also give a general proof that sequentially rejective multiple testing procedures strongly control the familywise error if they fulfill simple criteria of monotonicity of the critical values and a limited form of weak familywise error control in each single step the sequential rejection principle gives a novel theoretical perspective on many well known multiple testing procedures emphasizing the sequential aspect its main practical usefulness is for the development of multiple testing procedures for null hypotheses possibly logically related that are structured in a graph we illustrate this by presenting a uniform improvement of a recently published procedure

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

bounds on orders of finite subgroups ofpgln k abstract we characterize the pairs k n k a field n a positive integer for which there is a bound on the orders of finite subgroups of pgl n k explicit bounds are given in important cases an application is made to the analogous problem for central simple k algebras of degree n

ultraconvergence of zz patch recovery at mesh symmetry points the ultraconvergence property of the zienkiewicz zhu gradient patch recovery technique based on local discrete least squares fitting is established for a large class of even order finite elements the result is valid at all rectangular mesh symmetry points different smoothing strategies are discussed and numerical examples are demonstrated

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

generalized cornfield conditions for the risk difference a central question in causal inference with observational studies is the sensitivity of conclusions to unmeasured confounding the classical cornfield condition allows us to assess whether an unmeasured binary confounder can explain away the observed relative risk of the exposure on the outcome it states that for an unmeasured confounder to explain away an observed relative risk the association between the unmeasured confounder and the exposure and the association between the unmeasured confounder and the outcome must both be larger than the observed relative risk in this paper we extend the classical cornfield condition in three directions first we consider analogous conditions for the risk difference and allow for a categorical not just a binary unmeasured confounder second we provide more stringent thresholds that the maximum of the above mentioned associations must satisfy rather than weaker conditions that both must satisfy third we show that all the earlier results on cornfield conditions hold under weaker assumptions than previously used we illustrate the potential applications by real examples where our new conditions give more information than the classical ones

a two stage stepwise estimation procedure this article proposes a two stage simultaneous confidence procedure for the comparisons of k pairs of population means without using multiplicity adjustment of more than two populations the proposed procedure can be broadly applied to parametric or nonparametric models it is robust and versatile because its derivation only utilizes a partitioning approach in conjunction with a bivariate adjustment without any assumption on the underlying distribution to elucidate the application the proposed procedure is intertwined with the estimation of the therapeutic window of a drug it provides confidence limits for the efficacy and the toxicity of the effective doses highest ineffective dose safe doses and lowest unsafe dose simultaneously such estimation information facilitates follow up studies in clinical trials as an illustrative example the new procedure is applied to analyze a data set on molecular cancer therapeutics regarding the apoptotic killing effects of different chemical compounds on two leukemia cell lines

a new superconvergence and extrapolation for second order triangular element in this paper we find a new superconvergence and extrapolation for second order triangular element based on w m he j z cui q d zhu an improved method on superconvergence and extrapolation math numer sinica 24 2002 3 in chinese of course some numerical examples are given to investigate those estimates

asymptotically exact a posteriori estimators for the pointwise gradient error on each element in irregular meshes part ii the piecewise linear case we extend results from part i about estimating gradient errors elementwise a posteriori given there for quadratic and higher elements to the piecewise linear case the key to our new result is to consider certain technical estimates for differences in the error e x 1 e x 2 rather than for e x itself we also give a posteriori estimators for second derivatives on each element

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

multiple test procedures for dose finding the problem of identifying the lowest dose level for which the mean response differs from that at the zero dose level is considered a general framework for stepwise testing procedures that use contrasts among the dose level means is proposed using this framework several new procedures are derived these and some existing procedures including that of williams 1971 biometrics 27 103 117 1972 biometrics 28 519 531 are compared analytically and by an extensive simulation study for the normal theory balanced one way layout case it is pointed out that the procedures based on the so called step and basin contrasts proposed by ruberg 1989 journal of american statistical association 84 816 822 have excessively high type i familywise error rates fwes and hence they should not be used some findings of the simulation study are as follows for monotone dose mean configurations williams procedure and two step down test procedures based on helmert and linear contrasts offer the best performance for nonmonotone dose mean configurations the performance of williams procedure does degrade somewhat but the other two procedures are still the best for more complex designs a simple step down test procedure that uses any alpha level tests not necessarily t tests to compare each dose level with the zero dose level controls the fwe and is the only alternative available but its power is rather low especially under nonmonotone configurations step up procedures are generally dominated by step down procedures when the same contrasts are used although the differences are not great

ultraconvergence of high order fems for elliptic problems with variable coefficients in this paper we investigate local ultraconvergence properties of the high order finite element method fem for second order elliptic problems with variable coefficients under suitable regularity and mesh conditions we show that at an interior vertex which is away from the boundary with a fixed distance the gradient of the post precessed kth k ge 2 k 2 order finite element solution converges to the gradient of the exact solution with order mathcal o h k 2 mathrm ln h 3 o hk 2 lnh 3 the proof of this ultraconvergence property depends on a new interpolating operator some new estimates for the discrete green s function a symmetry theory derived in 26 and the richardson extrapolation technique in 20 numerical experiments are performed to demonstrate our theoretical findings

the ultraconvergence of derivative for bicubic finite element abstract it is for the first time that we obtained the o h 6 convergence of the derivatives for bicubic finite element by a new recovery technique proposed in meng and zhu l x meng q d zhu the ultraconvergence derivative recovery technique for odd degree elements a computer based test result natur sci j 25 2 2003 117 121 this numerical postprocessing result is theoretically justified by using projection interpolant and the theory of discrete green s function in this paper

traditional multiplicity adjustment methods in clinical trials this tutorial discusses important statistical problems arising in clinical trials with multiple clinical objectives based on different clinical variables evaluation of several doses or regiments of a new treatment analysis of multiple patient subgroups etc simultaneous assessment of several objectives in a single trial gives rise to multiplicity if unaddressed problems of multiplicity can undermine integrity of statistical inferences the tutorial reviews key concepts in multiple hypothesis testing and introduces main classes of methods for addressing multiplicity in a clinical trial setting general guidelines for the development of relevant and efficient multiple testing procedures are presented on the basis of application specific clinical and statistical information case studies with common multiplicity problems are used to motivate and illustrate the statistical methods presented in the tutorial and software implementation of the multiplicity adjustment methods is discussed copyright 2013 john wiley sons ltd

a general class of one sample nonparametric test statistics based on subsamples abstract a general class of nonparametric test statistics is constructed by considering the sign of the most extreme value in subsamples of size m taken from n independent observations the test statistics can be expressed as linear rank statistics and reduce to the sign test statistic for m 1 and a modified wilcoxon signed rank test statistic for m 2 asymptotic normality of properly standardized versions of our statistics is established under general conditions small sample power simulations as well as pitman and bahadur efficiencies indicate that members of our class do well in comparison with already existing test statistics

a new u statistic with superior design sensitivity in matched observational studies summary in an observational or nonrandomized study of treatment effects a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for observed covariates suffice to remove all bias the power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude in particular if this specified magnitude is no departure then this is the same as the power of a randomization test in a randomized experiment a new family of u statistics is proposed that includes wilcoxon s signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study wilcoxon s statistic has high power to detect small effects in large randomized experiments that is it often has good pitman efficiency but small effects are invariably sensitive to small unobserved biases members of this family of u statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis for example in one situation with 250 pair differences that are normal with expectation 1 2 and variance 1 the power of a sensitivity analysis that uses wilcoxon s statistic is 0 08 while the power of another member of the family of u statistics is 0 66 the topic is examined by performing a sensitivity analysis in three observational studies using an asymptotic measure called the design sensitivity and by simulating power in finite samples the three examples are drawn from epidemiology clinical medicine and genetic toxicology

multiplicity adjustment for multiple endpoints in clinical trials with multiple doses of an active treatment frequently multiple doses of an active treatment and multiple endpoints are simultaneously considered in the designs of clinical trials for these trials traditional multiplicity adjustment procedures such as bonferroni hochberg and hommel procedures can be applied when treating the comparisons of different doses to the control on all endpoints at the same level however these approaches will not take into account the possible dose response relationship on each endpoint and therefore are less specific and may have lower power to gain power in this paper we consider the problem as a two dimensional multiplicity problem one dimension concerns the multiple doses and the other dimension concerns the multiple endpoints we propose procedures which consider the dose order to form the closure of the procedures and control the family wise type i error rate in a strong sense for this two dimensional problem numerical examples show that procedures proposed in this paper in general have higher power than the commonly used procedures e g the regular hochberg procedure especially for comparing the higher dose to the control

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

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

an exact test with high power and robustness to unmeasured confounding effects in observational studies it is agreed that the sensitivity of the findings to unmeasured confounders needs to be assessed the issue is that a poor choice of test statistic can result in overstated sensitivity to hidden bias of this kind in this article a new adaptive test is proposed guided by considerations of low sensitivity to hidden bias it is tailored so that its power is greater than other leading tests both in finite and infinite samples one way of defining power in case of possible confounders is as the probability of reporting robustness ie insensitivity of a true discovery to potential bias in case of finite samples we compute the power by simulations when sample size approaches infinity a meaningful indicator of the power is the design sensitivity which is computed analytically and found to be better in the new test than in existing tests another asymptotic criterion for comparing tests when there is concern for confounders is bahadur efficiency the proposed test outperforms commonly used tests in terms of bahadur efficiency in most sampling situations the advantages of the new test mainly stem from its adaptivity it combines two test statistics and consequently achieves the best design sensitivity and the best bahadur efficiency of the two as a real world examination we compare 441 daily smokers to 441 nonsmokers to test the effect of smoking on periodontal disease the new test is more robust to unmeasured confounders than both the wilcoxon signed rank test and the paired t test

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

compatible simultaneous lower confidence bounds for the holm procedure and other bonferroni based closed tests we consider the problem of simultaneously testing multiple one sided null hypotheses single step procedures such as the bonferroni test are characterized by the fact that the rejection or non rejection of a null hypothesis does not take the decision for any other hypothesis into account for stepwise test procedures such as the holm procedure the rejection or non rejection of a null hypothesis may depend on the decision of other hypotheses it is well known that stepwise test procedures are by construction more powerful than their single step counterparts this power advantage however comes only at the cost of increased difficulties in constructing compatible simultaneous confidence intervals for the parameters of interest for example such simultaneous confidence intervals are easily obtained for the bonferroni method but surprisingly hard to derive for the holm procedure in this paper we discuss the inherent problems and show that ad hoc solutions used in practice typically do not control the pre specified simultaneous confidence level instead we derive simultaneous confidence intervals that are compatible with a certain class of closed test procedures using weighted bonferroni tests for each intersection hypothesis the class of multiple test procedures covered in this paper includes gatekeeping procedures based on bonferroni adjustments fixed sequence procedures the simple weighted or unweighted bonferroni procedure by holm and the fallback procedure we illustrate the results with a numerical example

identifying effective and or safe doses by stepwise confidence intervals for ratios typical randomized clinical dose finding studies consist of the comparison of several doses of a drug versus a placebo interest lies in estimating relevant doses among those under investigation for efficacy and safety variables such as the minimum effective dose or the maximum safe dose or estimating both doses simultaneously step down procedures have been proposed for comparing the standardized differences of the dose groups against placebo in this paper we consider the ratio of population means and propose stepwise confidence intervals for these ratios these confidence intervals do not require multiplicity adjustments and yield the same decisions as the associated test procedures in addition several power concepts are investigated within the present framework the results allow sample size determination in the design phase of a study for the probability of estimating correctly the dose of interest auxiliary results of a numerical study show the range of application of these methods

equivalence with respect to a control stepwise tests summary the problem of selecting those treatments which are equivalent or bioequivalent to a control treatment is investigated by using single step step down and step up multipletesting procedures for each of the tests considered the null hypothesis is that of nonequivalence and the hypotheses are rejected in either a single step or a stepwise fashion while controlling the familywise error rate the single step procedure is based on expanded confidence intervals as discussed by bofinger the step down procedure is based on the method of naik and the step up procedure on the method of dunnett and tamhane almost all the critical constants used in the procedures are based on tables already published

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

on the projective schur group of a field abstract if k is a field the projective schur group ps k of k is the subgroup of the brauer group br k consisting of those classes which contain a projective schur algebra i e a homomorphic image of a twisted group algebra k g with g finite h 2 g k it has been conjectured by nelis and van oystaeyen j algebra 137 1991 501 518 that ps k br k for all fields k we disprove this conjecture by showing that ps k br k for rational function fields k 0 x where k 0 is any infinite field which is finitely generated over its prime field

the local ultraconvergence for high degree galerkin finite element methods abstract in this paper we investigate the local ultraconvergence of k degree k 3 finite element methods for the second order elliptic boundary value problem with constant coefficients over a family of uniform rectangular triangular meshes t h on a bounded rectangular domain d the k degree finite element estimates are developed for the green s function and its derivatives they are employed to explore the relationship among d i s t x d d i s t x m and the ultraconvergence of k degree finite element methods at vertex x where m is the set of corners of d numerical examples are conducted to demonstrate our theoretical results

global and local refinement techniques yielding nonobtuse tetrahedral partitions preservation of basic qualitative properties for example the maximum principle ofthe solution of partial differential equations by its finite element approximations is an important goal in mathematical modelling and simulation nonobtuse tetrahedral partitions and linear finite elements guarantee the validity of the discrete analogues of the maximum principle for a wide class of parabolic and elliptic problems in order to get more accurate approximation we often need to refine the used partitions globally or locally in this paper we first propose two variants of global refinement techniques which produce nonobtuse face to face tetrahedral partitions second we present a new local refinement technique which generates nonobtuse face to face tetrahedral partitions in a neighbourhood of a given vertex

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

cross screening in observational studies that test many hypotheses abstractwe discuss observational studies that test many causal hypotheses either hypotheses about many outcomes or many treatments to be credible an observational study that tests many causal hypotheses must demonstrate that its conclusions are neither artifacts of multiple testing nor of small biases from nonrandom treatment assignment in a sense that needs to be defined carefully hidden within a sensitivity analysis for nonrandom assignment is an enormous correction for multiple testing in the absence of bias it is extremely improbable that multiple testing alone would create an association insensitive to moderate biases we propose a new strategy called cross screening different from but motivated by recent work of bogomolov and heller on replicability cross screening splits the data in half at random uses the first half to plan a study carried out on the second half then uses the second half to plan a study carried out on the first half and reports the more favorable conclusions of the tw