a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

causal inference probability theory and graphical insights causal inference from observational studies is a fundamental topic in biostatistics the causal graph literature typically views probability theory as insufficient to express causal concepts in observational studies in contrast the view here is that probability theory is a desirable and sufficient basis for many topics in causal inference for the following two reasons first probability theory is generally more flexible than causal graphs besides explaining such causal graph topics as m bias adjusting for a collider and bias amplification and attenuation when adjusting for instrumental variable probability theory is also the foundation of the paired availability design for historical controls which does not fit into a causal graph framework second probability theory is the basis for insightful graphical displays including the bk plot for understanding simpson s paradox with a binary confounder the bk2 plot for understanding bias amplification and attenuation in the presence of an unobserved binary confounder and the pad plot for understanding the principal stratification component of the paired availability design

a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media abstract we develop a probabilistic collocation eulerian lagrangian localized adjoint method on sparse grids for assessing co2 leakage through wells in randomly heterogeneous porous media by utilizing the intrinsic mathematical numerical and physical properties of the mathematical model we model the process in which co2 is injected into a deep aquifer spreads within the aquifer and upon reaching a leaky well rises up to a shallower aquifer to quantify the leakage rate which depends on the pressure build up in the aquifer due to injection and the buoyancy of co2 the underlying eulerian lagrangian framework has high potential to improve the efficiency and accuracy for the numerical simulation of complex flow and transport processes in co2 sequestration the sparse grid probabilistic collocation framework adds computationally efficient uncertainty quantification functionality onto pre existing eulerian lagrangian methods in a nonintrusive manner it also provides a scalable framework to consider uncertainty in a straightforward parallel manner preliminary numerical experiments show the feasibility and potential of the method

non parametric analysis of covariance for confirmatory randomized clinical trials to evaluate dose response relationships in confirmatory randomized clinical trials that are designed to compare multiple doses of a test treatment with a control group and with one another there are often statistical issues regarding compound hypotheses and multiple comparisons which need to be considered in most cases the analysis plan needs a clear specification for the proposed order for conducting statistical tests or for managing the overall significance level which statistical methods will be used and whether adjustment for covariates will be performed there are several benefits of specifying non parametric analysis of covariance ancova for performing the primary confirmatory analyses only minimal assumptions are needed beyond randomization in the study design whereas regression model based methods have assumptions about model fit for which departures may require modifications that are incompatible with a fully prespecified analysis plan non parametric methods provide traditionally expected results of ancova namely a typically small adjustment to the estimate for a treatment comparison so as to account for random imbalance of covariates between treatment groups and variance reduction for this estimate when covariates are strongly correlated with the response of interest the application of non parametric ancova is illustrated for two randomized clinical trials the first has a 3 x 4 factorial response surface design for the comparison of 12 treatments that is combinations of three doses of one drug and four doses of a second drug for change in blood pressure and the second example addresses the comparison of three doses of test treatment and placebo for time to disease progression this clinical trial has comparisons among treatments made for a dichotomous criterion wilcoxon rank scores and averages of cumulative survival rates in each example the non parametric covariance method provides variance reduction relative to its unadjusted counterpart

an optimal order error estimate for the mass conservative characteristic finite element scheme abstract the mass conservative characteristic mcc finite element scheme preserves the mass balance which is an important property in the numerical simulation of the convection diffusion problems in this paper an optimal order error estimate is obtained for the model problem in one space dimension the convergence rate is o h 2 t in the l l 2 norm for the linear finite element some numerical examples are given to confirm the conclusion

finite deformation plasticity based on the additive split of the rate of deformation and hyperelasticity abstract finite deformation plasticity formulation based on additive split of rate of deformation and hyperelasticity is presented this approach is valid for finite elastic and plastic strains while rendering the choice and numerical integration of objective stress rates superfluous as the results are automatically objective for small elastic strains our method reduces to the classical hypoelastic corotational formulation provided that the dienes objective stress rate is employed while in the absence of inelastic deformation it coincides with the hyper elastic formulation the validity of the model has been examined on four test problems and the numerical results were found to be in good agreement with either the exact solution or experimental data

frailty models for pneumonia to death with a left censored covariate frailty models are multiplicative hazard models for studying association between survival time and important clinical covariates when some values of a clinical covariate are unobserved but known to be below a threshold called the limit of detection lod naive approaches ignoring this problem such as replacing the undetected value by the lod or half of the lod often produce biased parameter estimate with larger mean squared error of the estimate to address the lod problem in a frailty model we propose a flexible smooth nonparametric density estimator along with simpson s numerical integration technique this is an extension of an existing method in the likelihood framework for the estimation and inference of the model parameters the proposed new method shows the estimators are asymptotically unbiased and gives smaller mean squared error of the estimates compared with the existing method the proposed new method does not require distributional assumptions for the underlying covariates simulation studies were conducted to evaluate the performance of the new method in realistic scenarios we illustrate the use of the proposed method with a data set from genetic and inflammatory markers of sepsis study in which interlekuin 10 was subject to lod copyright 2015 john wiley sons ltd

incorporating prognostic factors into causal estimators a comparison of methods for randomised controlled trials with a time to event outcome in randomised controlled trials the effect of treatment on those who comply with allocation to active treatment can be estimated by comparing their outcome to those in the comparison group who would have complied with active treatment had they been allocated to it we compare three estimators of the causal effect of treatment on compliers when this is a parameter in a proportional hazards model and quantify the bias due to omitting baseline prognostic factors causal estimates are found directly by maximising a novel partial likelihood based on a structural proportional hazards model and based on a corrected dataset derived after fitting a rank preserving structural failure time model where necessary we extend these methods to incorporate baseline covariates comparisons use simulated data and a real data example analysing the simulated data we found that all three methods are accurate when an important covariate was included in the proportional hazards model maximum bias 5 4 however failure to adjust for this prognostic factor meant that causal treatment effects were underestimated maximum bias 11 4 because estimators were based on a misspecified marginal proportional hazards model analysing the real data example we found that adjusting causal estimators is important to correct for residual imbalances in prognostic factors present between trial arms after randomisation our results show that methods of estimating causal treatment effects for time to event outcomes should be extended to incorporate covariates thus providing an informative compliment to the corresponding intention to treat analysis copyright 2012 john wiley sons ltd

inconsistent treatment estimates from mis specified logistic regression analyses of randomized trials when the difference between treatments in a clinical trial is estimated by a difference in means then it is well known that randomization ensures unbiassed estimation even if no account is taken of important baseline covariates however when the treatment effect is assessed by other summaries for example by an odds ratio if the outcome is binary then bias can arise if some covariates are omitted regardless of the use of randomization for treatment allocation or the size of the trial we present accurate closed form approximations for this asymptotic bias when important normally distributed covariates are omitted from a logistic regression we compare this approximation with ones in the literature and derive more convenient forms for some of these existing results the expressions give insight into the form of the bias which simulations show is usable for distributions other than the normal the key result applies even when there are additional binary covariates in the model

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

time stepping along characteristics with incomplete iteration for a galerkin approximation of miscible displacement in porous media miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations the pressure equation is elliptic while the concentration equation is parabolic but normally convection dominated a sequential backward difference time stepping scheme is defined it approximates the pressure by a standard galerkin procedure and the concentration by a combination of a galerkin method and the method of characteristics optimal convergence rates in l 2 and h 1 are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time truncation errors than those of standard methods numerical results published elsewhere have confirmed that larger time steps are appropriate

unobserved covariates in the two sample comparison of survival times a maximin efficiency robust test in analysing a clinical trial with the logrank test the hazards between the two groups are usually assumed to be proportional nevertheless this hypothesis is no longer valid with unobserved covariates as a consequence there is a loss of power of the logrank test for testing the null hypothesis h 0 of no treatment effect we propose a test suited for taking into account unobserved covariates the proposed approach is based on a proportional hazard frailty model whereby the omitted covariates are considered as an unobserved frailty variable the procedure is as follows in a first step the weighted logrank test optimal for testing h 0 against a general proportional hazard frailty model is obtained and its specialization for a gamma frailty variable is derived in a second step the proposed test is obtained by combining the maximin efficiency robustness principle and the gamma frailty distribution properties simulation studies investigate the power properties of the test for different frailty distributions a breast cancer clinical trial is analysed as an example the proposed test might be recommended rather than the logrank for practical situations in which one expects heterogeneity related to omitted covariates

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

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

a discussion of stress rates in finite deformation problems abstract it has recently been shown that the finite elastic plastic solution of the simple shear problem exhibits an oscillatory stress response when kinematic hardening is employed while the solution for isotropic hardening gives a monotonically increasing stress this paper analyzes this response on the basis of continuum mechanical descriptions of the problem three objective stress rates are recalled and spatial descriptions of plasticity at finite deformation are reviewed for the usual generalization of the infinitesimal theory as well as a theory based on an invariant measure of true stress in light of the equations for the evolution of the yield surface the hypoelastic solution to the simple shear problem for each of the three stress rates is presented it is shown that the use of the jaumann rate in the generalization of the infinitesimal theory leads to an oscillation in the evolution of the yield surface in simple shear which is explained on the basis of the hypoelastic solution an alternative theory which makes use of the polar decomposition predicts a monotonically increasing shear stress

a nonparametric method for dealing with mismeasured covariate data abstract mismeasurement of covariate data is a frequent problem in statistical data analysis however when true and mismeasured data are obtained for a subsample of the observations it is possible to estimate the parameters relating the outcome to the covariate of interest maximum likelihood methods that rely on parametric models for the mismeasurement have not met with much success realistic models for the mismeasurement process are difficult to construct the form of the likelihood is often intractable and more important such methods are not robust to model misspecification we propose an easily implemented method that is nonparametric with respect to the mismeasurement process and that is applicable when mismeasurement is due to the problem of missing data errors in variables or use of imperfect surrogate covariates specifically denote the outcome variable by y the covariate data subject to mismeasurement by x and the remaining covariates including perhaps surrogates or mismeasured values

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

two stress update algorithms for large strains accuracy analysis and numerical implementation two algorithms for the stress update i e time integration of the constitutive equation in large strain solid mechanics are compared from an analytical point of view the order of the truncation error associated to the numerical integration is deduced for each algorithm a priori using standard numerical analysis this accuracy analysis has been performed by means of a convected frame formalism which also allows a unied derivation of both algorithms in spite of their inherent dierences then the two algorithms are adapted from convected frames to a xed cartesian frame and implemented in a small strain nite element code the implementation is validated by means of a set of simple deformation paths simple shear extension extension and compression extension and rotation and two benchmark tests in non linear mechanics the necking of a circular bar and a shell under ring loads in these numerical tests the observed order of convergence is in very good agreement with the theoretical order of convergence thus corroborating the accuracy analysis 1997 john wiley sons ltd

convergence of a fully conservative volume corrected characteristic method for transport problems we consider the convergence of a volume corrected characteristics mixed method vccmm for advection diffusion systems it is known that without volume correction the method is first order convergent provided there is a nondegenerate diffusion term we consider the advective part of the system and give some properties of the weak solution with these properties we prove that the volume corrected method with no diffusion term gives a lower order l 1 convergence rate of mathcal o h sqrt delta t h delta t r where r is related to the accuracy of the characteristic tracing this result compares favorably to godunov s method but avoids the cfl constraint so large time steps can be taken in practice in fact godunov s method converges at mathcal o h 1 2 which is our result for delta t ch where now c is not limited however the optimal choice delta t ch 2 2r 1 gives a better rate mathcal o h 2r 2r 1 than godunov s method e g mathcal o h 2 3 if r 1 with a nondegenerate diffusion term we obtain an l 2 error estimate for the problem we also prove the existence of and give an error estimate for a perturbed velocity field for which the volume is locally conserved finally some convergence tests are given to verify the optimal convergence rate for r 1

semiparametric regression models for repeated events with random effects and measurement error abstract statistical methodology is presented for the regression analysis of multiple events in the presence of random effects and measurement error omitted covariates are modeled as random effects our approach to parameter estimation and significance testing is to start with a naive model of semiparametric poisson process regression and then to adjust for random effects and any possible covariate measurement error we illustrate the techniques with data from a randomized clinical trial for the prevention of recurrent skin tumors

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

estimators and confidence intervals for the marginal odds ratio using logistic regression and propensity score stratification propensity score methods are widely used to estimate treatment or exposure effects in observational studies in studies with binary response the effect can be described as an odds ratio and the mantel haenszel estimator is traditionally used for stratified data although propensity score methods are designed for marginal treatment effects it has been shown that the mantel haenszel estimator stratified for propensity score is a questionable estimator for the marginal odds ratio which describes the change in odds of response if everybody versus nobody were treated we studied recently proposed alternative estimators for the marginal odds ratio one stratified for propensity score the other derived from logistic regression additionally we adapted the methodology of the logistic regression based estimator for the derivation of a marginal odds ratio estimator to covariate adjustment by the propensity score we also derived corresponding variance estimators using the delta method the estimators were illustrated and compared to the inverse probability weighted estimator and the stratified mantel haenszel estimator in a study dealing with respiratory tract infections in children in germany furthermore simulation studies that were carried out to investigate relative bias variance and coverage probability showed reasonable performance of marginal odds ratio estimators if response rates or regression based approaches were used their variances were accurately estimated in contrast the stratified mantel haenszel estimator was substantially biased in some situations due to problems of non collapsibility and thus it is generally inappropriate for a reliable estimation of the marginal odds ratio

numerical analysis of a second order pure lagrange galerkin method for convection diffusion problems part ii fully discretized scheme and numerical results we analyze a second order pure lagrange galerkin method for variable coefficient convection diffusion possibly degenerate diffusion equations with mixed dirichlet robin boundary conditions in a previous paper the proposed second order pure lagrangian time discretization scheme was introduced and analyzed for the same problem more precisely the l infty h 1 stability and l infty h 1 error estimates of order o delta t 2 had been obtained moreover for the particular case of incompressible flows stability inequalities with constants independent of the final time have been stated in the present paper l infty h 1 error estimates of order o delta t 2 o h k are obtained for the fully discretized pure lagrange galerkin method to prove these results we use some properties obtained in the previous paper finally numerical tests are presented that confirm the theoretical results

a second order characteristics finite element scheme for natural convection problems in this paper a second order characteristics finite element scheme is applied to the numerical solution of natural convection problems firstly after recalling the mathematical model a second order time discretization of the material time derivative is introduced next fully discretized schemes are proposed by using finite element methods numerical results for the two dimensional problem of buoyancy driven flow in a square cavity with differentially heated side walls are given and compared with a reference solution

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

a geometric approach to assess bias due to omitted covariates in generalized linear models summary misspecifying generalized linear models by omitting covariates associated with the response can result in seriously biased estimates of the effects of the included covariates for certain models such bias can occur even when the omitted covariate is independent of the included covariates as in studies with randomized treatment assignment this paper presents a geometric approach to assess the direction of the bias resulting from omitted covariates and develop intuition about the effects of omitted covariates we show that the direction of the bias depends simply on geometric properties of the link function we present an expression for the magnitude of the bias and the results of simulations which corroborate these findings we also consider an extension of the methods to assess the effects of omitted covariates which are correlated with those included generalized linear models are frequently used in situations where the model has been incompletely specified due to the omission of important covariates for example in observational studies important covariates may be omitted from the regression model due to either an incorrect conceptual understanding of the phenomenon under study or an inability to collect data on all the relevant factors related to the outcome under study in experimental studies involving randomization covariates may also be omitted in the latter situation one may feel that model misspecification due to omitted covariates should not alter estimates of treatment effect since the omitted covariates are independent of treatment assignment although this is true for the linear regression model the classic example of collapsing 2 x 2 tables shows that incorrectly specifying logistic regression models by omitting covariates associated with the binary response can result in seriously attenuated estimates of the regression coefficients even when the omitted covariate is independent of the included covariates suppose that y is a binary outcome x and z are binary covariates and that the true model for the probability of response is given by

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

numerical methods for convection dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures finite element and finite difference methods are combined with the method of characteristics to treat a parabolic problem of the form cu t bu x au x x f optimal order error estimates in l 2 and w 1 2 are derived for the finite element procedure various error estimates are presented for a variety of finite difference methods the estimates show that for convection dominated problems b gg a these schemes have much smaller time truncation errors than those of standard methods extensions to n space variables and time dependent or nonlinear coefficients are indicated along with applications of the concepts to certain problems described by systems of differential equations

algorithmic tangent matrix approach for mixed hardening model of endochronic plasticity abstract a three dimensional 3 d algorithmic tangent matrix approach is developed for elastoplastic finite element fe analysis using the mixed hardening model of the endochronic plasticity the simple radial return algorithm is implemented in the development of the underlying strain controlled integration algorithm which is unconditionally stable precise implementation of the radial return is due to the use of the exponential algorithm the 3 d formulation is applied to fe micromechanics modeling of a undirectional metal matrix composite subjected to non proportional transverse normal longitudinal shear cyclic loading the predicted macroscopic and microscopic responses consistently demonstrate the computational advantages of the present approach

a fully mass and volume conserving implementation of a characteristic method for transport problems the characteristics mixed method considers the transport not of a single point or fluid particle but rather the mass in an entire region of fluid this mass is transported along the characteristic curves of the hyperbolic part of the transport equation and the scheme thereby produces very little numerical dispersion conserves mass locally and can use long time steps however since the shape of a characteristic trace back region must be approximated in numerical implementation its volume may be incorrect resulting in inaccurate concentration densities and further inaccurate reaction dynamics we present a simple modification to the characteristics mixed method that conserves both mass and volume of the transported fluid regions our algorithm also handles boundary conditions through a space time change of variables in the trace back routines which allows the boundary to be treated as if it were interior to the domain nearly point sources such as wells present special difficulties since characteristic trace back curves converge in their vicinity we also present techniques that allow one to conservatively implement wells the techniques are illustrated in five numerical examples

the lowest order characteristic mixed finite element scheme for convection dominated diffusion problem a new characteristic mixed finite element method mfem is proposed by combining the method of characteristics with the new mixed variational formulation for the convection dominated diffusion problem the error estimates for both the original variable u and auxiliary variable p are derived via the properties of the integral identity and mean value techniques at the same time some numerical experiments are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

average effects based on regressions with a logarithmic link function a new approach with stochastic covariates researchers often use regressions with a logarithmic link function to evaluate the effects of a treatment on a count variable in order to judge the average effectiveness of the treatment on the original count scale they compute average treatment effects which are defined as the average difference between the expected outcomes under treatment and under control current practice is to evaluate the expected differences at every observation and use the sample mean of these differences as a point estimate of the average effect the standard error for this average effect estimate is based on the implicit assumption that covariate values are fixed i e do not vary across different samples in this paper we present a new way of analytically computing average effects based on regressions with log link using stochastic covariates and develop new formulas to obtain standard errors for the average effect in a simulation study we evaluate the statistical performance of our new estimator and compare it with the traditional approach our findings suggest that the new approach gives unbiased effect estimates and standard errors and outperforms the traditional approach when strong interaction and or a skewed covariate is present

a finite element semi lagrangian method with l2 interpolation summary high order accurate methods for convection dominated problems have the potential to reduce the computational effort required for a given order of solution accuracy the state of the art in this field is more advanced for eulerian methods than for semi lagrangian slag methods in this paper we introduce a new slag method that is based on combining the modified method of characteristics with a high order interpolating procedure the method employs the finite element method on triangular meshes for the spatial discretization an l2 interpolation procedure is developed by tracking the feet of the characteristic lines from the integration nodes numerical results are illustrated for a linear advection diffusion equation with known analytical solution and for the viscous burgers equation the computed results support our expectations for a robust and highly accurate finite element slag method copyright 2012 john wiley sons ltd

a mass conservative characteristic fe scheme for optimal control problems governed by convection diffusion equations abstract in this paper we develop a mass conservative characteristic finite element scheme for optimal control problems governed by linear singularly perturbed convection diffusion equations we discuss the case that the velocity fields are non divergence free the space discretization of the state variable is done by piecewise linear continuous functions whereas the control variable is approximated by piecewise constant functions due to the limitation of the regularity the scheme preserves the mass balance for the original state equation we derive a priori error estimates for both the control and state approximations some numerical examples are presented to show the efficiency of the proposed scheme

uniform error analysis for lagrange galerkin approximations of convection dominated problems in this paper we present a rigorous error analysis for the lagrange galerkin method applied to convection dominated diffusion problems we prove new error estimates in which the constants depend on norms of the data and not of the solution and do not tend to infinity in the hyperbolic limit this is in contrast to other results in this field for the time discretization uniform convergence with respect to the diffusion parameter of order o k tn is shown for initial values in l2 and o k for initial values in h2 for the spatial discretization with linear finite elements we verify uniform convergence of order o h2 min h h2 k for data in h2 by interpolation of banach spaces suboptimal convergence rates are derived under less restrictive assumptions the analysis is heavily based on a priori estimates uniform in the diffusion parameter for the solution of the continuous and the semidiscrete problem they are derived in a lagrangian framework by transforming the eulerian coordinates completely into subcharacteristic coordinates finally we illustrate the error estimates by some numerical results

the modified method of characteristics with adjusted advection the mmoc procedure for approximating the solutions of transport dominated diffusion problems does not automatically preserve integral conservation laws leading to mass balance errors in many kinds of flow problems the variant called the mmocaa discussed herein preserves the conservation law at a minor additional computational cost it is shown that its solution in either galerkin or finite difference form converges at the same rates as were proved earlier by dougl as and russell for the standard mmoc procedure

yule s association paradox and ignored stratum heterogeneity in capture recapture studies abstract this article explores a reparameterization of a 2 2 table this reparameterization turns out to be useful in considering the consequences of amalgamating several 2 2 tables a formal theorem is derived that permits characterization of yule s association paradox the same theorem also permits discussion of the likely direction of error incurred when using capture recapture methods to estimate the size of a population this has implications for the wily trout argument in the census correction controversy

uniform estimates for eulerian lagrangian methods for singularly perturbed time dependent problems we prove a priori optimal order error estimates in a weighted energy norm for several eulerian lagrangian methods for singularly perturbed time dependent convection diffusion equations with full regularity the estimates depend only on certain sobolev norms of the initial and right hand side data but not on varepsilon or any norm of the true solution and so hold uniformly with respect to varepsilon we use the interpolation of spaces and stability estimates to derive an varepsilon uniform estimate for problems with minimal or intermediate regularity where the convergence rates are proportional to certain besov norms of the initial and right hand side data

two grid methods for characteristic finite volume element solution of semilinear convection diffusion equations abstract two grid methods for characteristic finite volume element solutions are presented for a kind of semilinear convection dominated diffusion equations the methods are based on the method of characteristics two grid method and the finite volume element method the nonsymmetric and nonlinear iterations are only executed on the coarse grid with grid size h and the fine grid solution with grid size h can be obtained by a single symmetric and linear step it is proved that the coarse grid can be much coarser than the fine grid the two grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy h o h 1 3

inference for covariates that accounts for ascertainment and random genetic effects in family studies summary family studies to identify disease related genes often collect families with multiple cases if environmental exposures or other measured covariates are also important they should be incorporated into these genetic analyses to control for confounding and increase statistical power we propose a two level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment by conditioning on the number of cases in the family we describe a conditional maximum likelihood analysis based on this model when genetic effects are negligible this conditional likelihood reduces to standard conditional logistic regression we show that the simpler conditional logistic regression typically yields biased estimators of exposure effects and we describe conditions under which the conditional logistic approach has little or no bias

optimization based mesh correction with volume and convexity constraints we consider the problem of finding a mesh such that 1 it is the closest with respect to a suitable metric to a given source mesh having the same connectivity and 2 the volumes of its cells match a set of prescribed positive values that are not necessarily equal to the cell volumes in the source mesh this volume correction problem arises in important simulation contexts such as satisfying a discrete geometric conservation law and solving transport equations by incremental remapping or similar semi lagrangian transport schemes in this paper we formulate volume correction as a constrained optimization problem in which the distance to the source mesh defines an optimization objective while the prescribed cell volumes mesh validity and or cell convexity specify the constraints we solve this problem numerically using a sequential quadratic programming sqp method whose performance scales with the mesh size to achieve scalable performance we develop a specialized multigrid based preconditioner for optimality systems that arise in the application of the sqp method to the volume correction problem numerical examples illustrate the importance of volume correction and showcase the accuracy robustness and scalability of our approach

viscoplasticity for instabilities due to strain softening and strain rate softening three viscoplastic approaches are examined in this paper first the overstress viscoplastic models i e the perzyna model and the duvaut lions model are outlined next a consistency viscoplastic approach is presented in the consistency model a rate dependent yield surface is employed while the standard kuhn tucker conditions for loading and unloading remain valid for this reason the yield surface can expand and shrink not only by softening or hardening e ects but also by softening hardening rate e ects a full algorithmic treatment is presented for each of the three models including the derivation of a consistent tangential sti ness matrix based on a limited numerical experience it seems that the consistency model shows a faster global convergence than the overstress approaches for softening problems all three approaches have a regularising e ect in the sense that the initial value problem remains well posed the width of the shear band is determined by the material parameters and if present by the size of an imperfection a relation between the length scales of the three models is given furthermore it is shown that the consistency model can properly simulate the so called s type instabilities which are associated with the occurrence of travelling portevin le chatelier bands 1997 john wiley sons ltd

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

effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable we consider three commonly used statistical tests for assessing the association between an explanatory variable and a measured binary or survival time response variable and investigate the loss in efficiency from mismodelling or mismeasuring the explanatory variable with respect to mismodelling we examine the consequences of using an incorrect dose metameter in a test for trend of mismodelling a continuous explanatory variable and of discretizing a continuous explanatory variable we also examine the consequences of classification errors for a discrete explanatory variable and of measurement errors for a continuous explanatory variable for all three statistical tests the asymptotic relative efficiency are corresponding to each type of mis specification equals the square of the correlation between the correct and fitted form of the explanatory variable this result is evaluated numerically for the different types of mis specification to provide insight into the selection of tests the interpretation of results and the design of studies where the correct explanatory variable cannot be measured exactly

regression analysis with clustered data clustered data are found in many different types of studies for example studies involving repeated measures inter rater agreement studies household surveys crossover designs and community randomized trials analyses based on population average and cluster specific models are commonly used for estimating treatment exposure effects with clustered data this paper discusses conditions when one or both types of models are appropriate for estimating causal effects and when there is agreement between population average and cluster specific analyses applications of survey sampling methods to the robust estimation of standard errors of estimated treatment parameters are discussed

solution of nonlinear convection diffusion problems by a conservative galerkin characteristics method we consider a scheme for nonlinear degenerate convection dominant diffusion problems that arise in contaminant transport in porous media with equilibrium adsorption isotherm this scheme is based on a regularization relaxation scheme that has been introduced by jager and kacur numer math 60 407 427 1991 m2an math model numer anal 29 n5 605 627 1995 with a type of numerical integration by bermejo siam j numer anal 32 425 455 1995 to the modified method of characteristics with adjusted advection mmocaa that was recently developed by douglas et al numer math 83 3 353 369 1999 comput geosci 1 155 190 1997 we present another variant of adjusting advection method the convergence of the scheme is proved an error estimate of the approximated scheme is derived computational experiments are carried out to illustrate the capability of the scheme to conserve the mass

error analysis for characteristics based methods for degenerate parabolic problems we consider characteristics based finite element methods for solving nonlinear degenerate advection diffusion equations these equations have applications in the simulation of petroleum reservoirs and groundwater aquifers and in the modeling of free boundary problems standard finite element galerkin methods have been studied for these equations in this paper we analyze the characteristics based finite element methods for them the main difficulty in the analysis is that the equations are degenerate and the solution lacks regularity here we develop a technique that respects the degeneracy and the known minimal regularity this technique is based on the green operator for standard elliptic equations and is developed directly for the degenerate advection diffusion equations we concentrate our analysis on the modified method of characteristics mmoc and one of its variants the modified method of characteristics with adjusted advection mmocaa which conserves mass we derive error estimates in various norms the extension to other variants is discussed the present technique is also applied to nondegenerate problems error estimates previously obtained for the mmoc are derived under much weaker regularity assumptions on the solution and the error estimates for the mmocaa appear new even in the nondegenerate case finally numerical results are presented to show the sharpness of the error estimates derived

the variational formulation and solution of problems of finite strain elastoplasticity based on the use of a dissipation function the solution of initial boundary value problems involving finite elastoplastic deformations is discussed the formulation considered differs from conventional formulations in that the evolution law is expressed in terms of the dissipation function a generalized midpoint rule is used to obtain an incremental problem a variational form of which is derived the finite element method is used for spatial discretization and an algorithm to solve the resulting discrete problem is developed this algorithm has the predictor corrector structure common to most solution procedures for problems in plasticity methods for imposing the plastic incompressibility constraint are investigated solutions to two axisymmetric examples obtained using the proposed algorithm are presented and compared with those obtained by other authors

covariance analysis in generalized linear measurement error models we summarize some of the recent work on the errors in variables problem in generalized linear models the focus is on covariance analysis and in particular testing for and estimation of treatment effects there is a considerable difference between the randomized and non randomized models when testing for an effect in randomized studies simple techniques exist for testing for a treatment effect in some instances such as linear and multiplicative regression simple methods exist for estimating the treatment effect in other examples such as logistic regression estimating a treatment effect requires careful attention to measurement error in non randomized studies there is no recourse to understanding and modelling measurement error in particular ignoring measurement error can lead to the wrong conclusions for example the true but unobserved data may indicate a positive effect for treatment while the observed data indicate the opposite some of the possible methods are outlined and compared

analysing the relationship between change in a risk factor and risk of disease there are numerous examples in the epidemiologic literature of analyses that relate the change in a risk factor such as serum cholesterol to the risk of an adverse outcome such as heart disease many of these analyses fit some type of regression model such as logistic regression or the cox model for survival time data that includes both the change in the risk factor and the baseline value as covariates we show that this method of adjusting for the baseline level can produce misleading results the problem occurs when the true value of the risk factor relates to the outcome and the measured value differs from the true value due to measurement error we may find the observed change in the risk factor significantly related to the outcome when there is in fact no relationship between the true change and the outcome if the question of interest is whether a person who lowers his level of the risk factor by means of drugs or lifestyle changes will thereby reduce his risk of disease then we should consider an association due solely to measurement error as spurious we present a method that adjusts for the measurement error in a linear regression analysis and show that an analogous adjustment applies asymptotically to logistic regression as in other errors in variables problems this analysis depends on knowledge of the relative variances of the random variation the true baseline value and the true change since the magnitudes of these variances are usually unknown and sometimes unknowable the distinction between true change and measurement error being ambiguous we recommend a sensitivity analysis that examines how the analysis results depend on the assumptions concerning the variances the commonly used analysis method corresponds to the extreme case in which there is no measurement error we use data from the framingham study and simulations to illustrate these points

an efficient characteristic finite difference s ddm scheme for convection diffusion equations abstract in this paper an efficient splitting domain decomposition method scheme for solving time dependent convection diffusion reaction equations is analyzed a three step method along each direction is used to solve the solution over each block divided sub domain at every time interval the new solutions are firstly solved by the quadratic interpolation then the intermediate fluxes on the interfaces of sub domains are computed by local multi point weighted average from the new solutions lastly the solutions and fluxes in the interiors of sub domains are computed by the splitting implicit characteristic difference method by some auxiliary lemmas and the defined intermediate exact solution the stability and error estimate are given in discrete l 2 norm we further prove that our scheme is of second order convergence in space and of first order convergence in time numerical experiments are presented to validate theoretical result

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

an optimal order error estimate to ellam schemes for transient advection diffusion equations on unstructured meshes the eulerian lagrangian localized adjoint method ellam provides a general characteristic procedure for solving transient advection diffusion equations with general boundary conditions in a mass conservative manner in this paper we prove an optimal order error estimate in the l 2 norm and a superconvergence estimate in the energy norm for the ellam scheme to d dimensional transient advection diffusion equations with general flux boundary conditions on unstructured meshes

an implicit algorithm for hypoelasto plastic and hypoelasto viscoplastic endochronic theory in finite strain isotropic kinematic hardening model this paper is concerned with objective stress update algorithm for elasto plastic and elasto viscoplastic endochronic theory within the framework of additive plasticity the elastic response is stated in terms of hypoelastic model and endochronic constitutive equations are stated in unrotated frame of reference a trivially incrementally objective integration scheme for rate constitutive equations is established algorithmic modulus consistent with numerical integration algorithm of constitutive equations is extracted the implementation is validated by means of a set of simple deformation paths simple shear extension and rotation two benchmark test in nonlinear mechanics the necking of a circular bar and expansion of a thick walled cylinder a test which demonstrates the capabilities of the proposed model in simulation of cyclic loading and ratcheting in finite strain case cyclically loaded notched bar and finally the analysis of a tensile test which presents a shear band with a finite thickness independent of the finite element mesh using endochronic viscoplastic constitutive model

two stage residual inclusion for survival data and competing risks an instrumental variable approach with application to seer medicare linked data instrumental variable is an essential tool for addressing unmeasured confounding in observational studies two stage predictor substitution 2sps estimator and two stage residual inclusion 2sri are two commonly used approaches in applying instrumental variables recently 2sps was studied under the additive hazards model in the presence of competing risks of time to events data where linearity was assumed for the relationship between the treatment and the instrument variable this assumption may not be the most appropriate when we have binary treatments in this paper we consider the 2sri estimator under the additive hazards model for general survival data and in the presence of competing risks which allows generalized linear models for the relation between the treatment and the instrumental variable we derive the asymptotic properties including a closed form asymptotic variance estimate for the 2sri estimator we carry out numerical studies in finite samples and apply our methodology to the linked surveillance epidemiology and end results seer medicare database comparing radical prostatectomy versus conservative treatment in early stage prostate cancer patients

uniform estimates of an eulerian lagrangian method for time dependent convection diffusion equations in multiple space dimensions we prove a priori error estimates for a family of eulerian lagrangian methods for time dependent convection diffusion equations in multiple space dimensions which hold uniformly with respect to the vanishing parameter varepsilon we use the interpolation of spaces and stability estimates to derive an varepsilon uniform estimate for problems with minimal or intermediate regularity where the convergence rates are proportional to certain besov norms of the initial and right hand side data these estimates theoretically justify the strength of eulerian lagrangian methods

incremental kinematics for finite element applications a kinematical algorithm is proposed in which the input is the incremental deformation gradient corresponding to an increment in motion for a time step and the output is a constant rate of stretching tensor and a rotation tensor the concept of algorithmic objectivity is discussed with a stronger statement of objectivity than those advanced in previous works being set forth the importance of strong objectivity is illustrated for applications in which moderately large rotation increments are to be expected accuracy of the proposed algorithm is discussed and illustrated with example calculations and it is shown that the accuracy of the algorithm may be extended to arbitrary order also the computational effort associated with the proposed algorithm is seen to compare favourably to that of other algorithms

a characteristics mixed covolume method for a convection dominated transport problem in this paper we propose a characteristics mixed covolume method for approximating the solution to a convection dominated transport problem the method is a combination of characteristic approximation to handle the convection term in time and mixed covolume method spatial approximation to deal with the diffusion term the velocity and press are approximated by the lowest order raviart thomas mixed finite element space on rectangles the projection of a mixed covolume element is introduced we prove its first order optimal rate of convergence for the approximate velocities in the l 2 norm as well as for the approximate pressures in the l 2 norm

robust alternatives to ancova for estimating the treatment effect via a randomized comparative study in comparing two treatments via a randomized clinical trial the analysis of covariance ancova technique is often utilized to estimate an overall treatment effect the ancova is generally perceiv

a new mcc mfe method for compressible miscible displacement in porous media this paper presents a new mass conservative finite element method for solving the compressible miscible displacement problem in porous media this new method combines characteristic tracking with the mixed finite element method specifically the mass conservative characteristic finite element method is applied to the concentration equation whereas the mixed finite element method with continuous flux approximation is used for the flow equation this procedure conserves mass globally convergence of the fully discrete scheme is analyzed and optimal l 2 norm and h 1 norm error estimates for the concentration are obtained numerical experiments are presented to illustrate the theoretical analysis

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

analysis of failure time data with multilevel clustering with application to the child vitamin a intervention trial in nepal we consider the problem of estimating covariate effects in the marginal cox proportional hazard model and multilevel associations for child mortality data collected from a vitamin a supplementation trial in nepal where the data are clustered within households and villages for this purpose a class of multivariate survival models that can be represented by a functional of marginal survival functions and accounts for hierarchical structure of clustering is exploited based on this class of models an estimation strategy involving a within cluster resampling procedure is proposed and a model assessment approach is presented the asymptotic theory for the proposed estimators and lack of fit test is established the simulation study shows that the estimates are approximately unbiased and the proposed test statistic is conservative under extremely heavy censoring but approaches the size otherwise the analysis of the nepal study data shows that the association of mortality is much greater within households than within villages

using follow up data to avoid omitted variable bias an application to cardiovascular epidemiology omitted variable bias is discussed in the context of linear models it is shown that the effect of omitted variables can be controlled in linear models for metric dependent variables by using data from follow up studies two different models for analysing such data are proposed in the first model the omitted variables are assumed to be uncorrelated with the explanatory variables in the model and to be constant over time these assumptions lead to a special structure of the covariance matrix of the errors over time efficient estimation of the parameters in the linear model has to take this special covariance matrix of the errors into account by using appropriate generalized least squares or maximum likelihood methods in the second model the omitted variables are assumed to be time constant additionally they are allowed to be correlated with the explanatory variables that is these variables are omitted confounders in the usual epidemiological sense it is shown that even in this case the parameters of the linear model can be estimated consistently with ordinary least squares if a follow up study is available the differences between the parameter estimates under the first and the second model may be used to construct a hausman test for misspecification the models the estimation methods and the hausman test are illustrated by the example that explores the determinants of serum cholesterol in german adoloscents of both sexes

a two grid mmoc finite element method for nonlinear variable order time fractional mobile immobile advection diffusion equations abstract a fully discrete two grid modified method of characteristics mmoc scheme is proposed for nonlinear variable order time fractional advection diffusion equations in two space dimensions the mmoc is used to handle the advection dominated transport and the two grid method is designed for efficiently solving the resulting nonlinear system optimal l 2 error estimates are derived for both the mmoc scheme and the corresponding two grid mmoc scheme numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed method

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

estimation efficiency with omitted covariates in generalized linear models abstract although omitting covariates associated with the response in generalized linear models can yield seriously biased estimates of the effects of the included covariates in certain settings there is no bias this article considers the effect of omitted covariates on the efficiency of the estimated effects of the included covariates in these cases i consider the case where the omitted covariate is independent of the included covariates as in studies with randomized treatment assignment as well as the case where the omitted covariate is correlated with the included but not a confounder i present expressions to show that omitting covariates associated with the response and independent of the included covariate can result in serious efficiency losses for estimates of the effects of the included covariates i also present expressions to show that omitting nonconfounding covariates can lead to efficiency gains these expressions also quantify the magnitude of estimation efficiency with omitted covaria

the mmoc and mmocaa schemes for the finite volume element method of convection diffusion problems we present and analyze the modified method of characteristics mmoc and the modified method of characteristics with adjusted advection mmocaa for the finite volume element fve method of convection diffusion problems these two schemes maintain the advantages of both the mmoc and the fve method and the mmocaa scheme discussed herein conserves the conservation law globally at a minor additional computational cost optimal order error estimates in the h 1 norm are proved for these schemes a numerical example is presented to confirm the estimates