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

exact nonparametric inference when doses are measured with random errors studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose if the doses are measured with error then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response if one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0 that is the dose errors are pure errors and not say systematic underreporting of exposure then the presence of zero dose controls is all that is needed to obtain exact distribution free confidence intervals and tests and consistent point estimates the method is simpler for matched pairs than for matched sets with two or more matched subjects and it is illustrated using two studies one of each kind with matched pairs as in this first example the method uses wilcoxon s signed rank test as the basis for inference when there are several zero dos

the asymptotic properties of nonparametric tests for comparing survival distributions the asymptotic distribution under alternative hypotheses is derived for a class of statistics used to test the equality of two survival distributions in the presence of arbitrary and possibly unequal right censoring the test statistics include equivalents to the log rank statistic the modified wilcoxon statistic and the class of rank invariant test procedures introduced by peto peto when there are equal censoring distributions and the hazard functions are proportional the sample size formula for the f test used to compare exponential samples is shown to be valid for the log rank test in certain situations the power of the log rank test falls as the amount of censoring decreases

estimating the reliability of an exposure variable in the presence of confounders in this paper we discuss estimation of the reliability of an exposure variable in the presence of confounders measured without error we give an explicit formula that shows how the exposure becomes less reliable as the degree of correlation between the exposure and confounders increases we also discuss biases in the corresponding logistic regression estimates and methods for correction data from a matched case control study of hormone levels and risk of breast cancer are used to illustrate the methods

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

score tests in generalized linear measurement error models summary hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x the efficient score test for the hypothesis of no association depends on the conditional expectation e xi w which is generally unknown the usual test substitutes w for e xi w and is asymptotically valid but not efficient we investigate two new test statistics appropriate when w x z where z is an independent measurement error the first is a wald test based on estimators corrected for measurement error despite the correction for attenuation in the estimator this test has the same local power as the usual test the second test employs an estimator of e x i w and is both asymptotically efficient for normal errors and approximately efficient when the measurement error variance is small

a simple sequential stopping rule for monte carlo simulation in this paper a sequential stopping rule for the estimation of a probability p by means of monte carlo simulation is analyzed it is shown that the proposed estimator is almost unbiased and guarantees a given relative precision irrespective of p under very mild conditions the method also guarantees a certain confidence level for a given relative estimation error provided that p does not exceed a maximum value an extension to importance sampling is discussed

a preconditioner with inexact element face solver for three dimensional p version finite element methods in this paper we propose to modify a preconditioner developed in pavarino and widlund comput math appl 33 1997 193 for three dimensional p version finite element or spectral element approximations by solving the sub problems on element faces with an inexact element face solver such a modification reduces the cost to evaluate the action of the preconditioner from o p4 to o p3 per element face where p is the polynomial degree used for approximation furthermore it is shown that the coefficient matrix of the inexact solver is spectrally equivalent to the original stiffness matrix on element faces therefore such a change will not affect the polylogarithmic estimate given in pavarino and widlund for the condition number of the preconditioned system numerical results are also given to confirm the theoretical analysis

tests for no treatment effect in randomized clinical trials summary we propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals these residuals result from regressing the response on covariates but not treatment in contrast to model based score tests this procedure maintains nominal size when the model is misspecified and in particular when relevant covariates are omitted from the regression the efficiency of the procedure is evaluated for regressions with some but not all required covariates for many generalized linear models and survival models conventional model based score tests are shown to have supranominal size when relevant covariates are omitted but logistic regression and the proportional hazards model are robust

iterative substructuring methods for spectral element discretizations of elliptic systems ii mixed methods for linear elasticity and stokes flow iterative substructuring methods are introduced and analyzed for saddle point problems with a penalty term two examples of saddle point problems are considered the mixed formulation of the linear elasticity system and the generalized stokes system in three dimensions these problems are discretized with mixed spectral element methods the resulting stiffness matrices are symmetric and indefinite the interior unknowns of each element are first implicitly eliminated by using exact local solvers the resulting saddle point schur complement is solved with a krylov space method with block preconditioners the velocity block can be approximated by a domain decomposition method e g of wire basket type which is constructed from a local solver for each face of the elements and a coarse solver related to the wire basket of the elements the condition number of the preconditioned operator is independent of the number of spectral elements and is bounded from above by the product of the square of the logarithm of the spectral degree and the inverse of the discrete inf sup constant of the problem

comparing the effects of continuous and discrete covariate mismeasurement with emphasis on the dichotomization of mismeasured predictors it is well known that imprecision in the measurement of predictor variables typically leads to bias in estimated regression coefficients we compare the bias induced by measurement error in a continuous predictor with that induced by misclassification of a binary predictor in the contexts of linear and logistic regression to make the comparison fair we consider misclassification probabilities for a binary predictor that correspond to dichotomizing an imprecise continuous predictor in lieu of its precise counterpart on this basis nondifferential binary misclassification is seen to yield more bias than nondifferential continuous measurement error however it is known that differential misclassification results if a binary predictor is actually formed by dichotomizing a continuous predictor subject to nondifferential measurement error when the postulated model linking the response and precise continuous predictor is correct this differential misclassification is found to yield less bias than continuous measurement error in contrast with nondifferential misclassification i e dichotomization reduces the bias due to mismeasurement this finding however is sensitive to the form of the underlying relationship between the response and the continuous predictor in particular we give a scenario where dichotomization involves a trade off between model fit and misclassification bias we also examine how the bias depends on the choice of threshold in the dichotomization process and on the correlation between the imprecise predictor and a second precise predictor

using regression models to analyze randomized trials asymptotically valid hypothesis tests despite incorrectly specified models regression models are often used to test for cause effect relationships from data collected in randomized trials or experiments this practice has deservedly come under heavy scrutiny because commonly used models such as linear and logistic regression will often not capture the actual relationships between variables and incorrectly specified models potentially lead to incorrect conclusions in this article we focus on hypothesis tests of whether the treatment given in a randomized trial has any effect on the mean of the primary outcome within strata of baseline variables such as age sex and health status our primary concern is ensuring that such hypothesis tests have correct type i error for large samples our main result is that for a surprisingly large class of commonly used regression models standard regression based hypothesis tests but using robust variance estimators are guaranteed to have correct type i error for large samples even when the models are incorrectly specified to the best of our knowledge this robustness of such model based hypothesis tests to incorrectly specified models was previously unknown for poisson regression models and for other commonly used models we consider our results have practical implications for understanding the reliability of commonly used model based tests for analyzing randomized trials

the use of maximin efficiency robust tests in combining contingency tables and survival analysis abstract a test is the maximin efficiency robust test for a family of possible models underlying the data if no other test has higher minimum efficiency relative to the asymptotically optimum test for each model methods used to examine the efficiency robustness of rank tests for the two sample problem are adapted to obtain maximin efficiency robust procedures for testing the equality of proportions across several 2 2 tables for combining the results of tests for trend in several 2 x j tables in which the dose response function is one of a set of possible monotone functions and to analyze censored survival data when either the wilcoxon or log rank may be appropriate in the survival setting the robust test has maximin efficiency 93 3 relative to the wilcoxon or long rank when each is optimum in contrast to the 75 relative efficiency each statistic has when the other is optimum

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

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

coalescence of low viscosity fluids in air an electrical method is used to study the early stages of coalescence of two low viscosity drops a drop of aqueous nacl solution is suspended in air above a second drop of the same solution which is grown until the drops touch at that point a rapidly widening bridge forms between them by measuring the resistance and capacitance of the system during this coalescence event one can obtain information about the time dependence of the characteristic bridge radius and its characteristic height at early times a new asymptotic regime is observed that is inconsistent with previous theoretical predictions the measurements at several drop radii and approach velocities are consistent with a model in which the two liquids coalesce with a slightly deformed interface

inexact solvers on element interfaces for the p and h p finite element method parallel and iterative solvers for large scale linear system arising from finite element discretization based on domain decomposition decompose the approximation spaces into a number of subspaces the corresponding subproblems are solved in these subspaces and the solutions are corrected in an iterative process the subproblems are much smaller in size and much easier to be solved one of these subspaces is spanned by high order element side modes in two dimensions and high order element face modes in three dimensions solving the subproblems on the element interfaces is a major cost in each step of iteration to reduce computational cost various inexact solvers on element interfaces are proposed in this paper with theoretical analysis and numerical illustrations

balancing domain decomposition for mixed finite elements the rate of convergence of the balancing domain decomposition method applied to the mixed finite element discretization of second order elliptic equations is analyzed the balancing domain decomposition method introduced by mandel in 24 is a substructuring method that involves at each iteration the solution of a local problem with dirichlet data a local problem with neumann data and a coarse grid problem to propagate information globally and to insure the consistency of the neumann problems it is shown that the condition number grows at worst like the logarithm squared of the ratio of the subdomain size to the element size in both two and three dimensions and for elements of arbitrary order the bounds are uniform with respect to coefficient jumps of arbitrary size between subdomains the key component of our analysis is the demonstration of an equivalence between the norm induced by the bilinear form on the interface and the h 1 2 norm of an interplant of the boundary data computational results from a message passing parallel implementation on an intel delta machine demonstrate the scalability properties of the method and show almost optimal linear observed speed up for up to 64 processors

flexible regression models with cubic splines we describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates this simple method can help prevent the problems that result from inappropriate linearity assumptions we compare restricted cubic spline regression to non parametric procedures for characterizing the relationship between age and survival in the stanford heart transplant data we also provide an illustrative example in cancer therapeutics

inflation of the type i error rate when a continuous confounding variable is categorized in logistic regression analyses this paper demonstrates an inflation of the type i error rate that occurs when testing the statistical significance of a continuous risk factor after adjusting for a correlated continuous confounding variable that has been divided into a categorical variable we used monte carlo simulation methods to assess the inflation of the type i error rate when testing the statistical significance of a risk factor after adjusting for a continuous confounding variable that has been divided into categories we found that the inflation of the type i error rate increases with increasing sample size as the correlation between the risk factor and the confounding variable increases and with a decrease in the number of categories into which the confounder is divided even when the confounder is divided in a five level categorical variable the inflation of the type i error rate remained high when both the sample size and the correlation between the risk factor and the confounder were high

power and sample size calculations for generalized regression models with covariate measurement error covariate measurement error is often a feature of scientific data used for regression modelling the consequences of such errors include a loss of power of tests of significance for the regression parameters corresponding to the true covariates power and sample size calculations that ignore covariate measurement error tend to overestimate power and underestimate the actual sample size required to achieve a desired power in this paper we derive a novel measurement error corrected power function for generalized linear models using a generalized score test based on quasi likelihood methods our power function is flexible in that it is adaptable to designs with a discrete or continuous scalar covariate exposure that can be measured with or without error allows for additional confounding variables and applies to a broad class of generalized regression and measurement error models a program is described that provides sample size or power for a continuous exposure with a normal measurement error model and a single normal confounder variable in logistic regression we demonstrate the improved properties of our power calculations with simulations and numerical studies an example is given from an ongoing study of cancer and exposure to arsenic as measured by toenail concentrations and tap water samples

schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions domain decomposition methods provide powerful preconditioners for the iterative solution of the large systems of algebraic equations that arise in finite element or finite difference approximations

a polylogarithmic bound for an iterative substructuring method for spectral elements in three dimensions iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems a p version finite element method based on continuous piecewise q p functions is considered for second order elliptic problems in three dimensions this special method can also be viewed as a conforming spectral element method an iterative method is designed for which the condition number of the relevant operator grows only in proportion to 1 log p 2 this bound is independent of jumps in the coefficient of the elliptic problem across the interfaces between the subregions numerical results are also reported which support the theory

effects of treatment induced mortality and tumor induced mortality on tests for carcinogenicity in small samples statistical tests of carcinogenicity are shown to have varying degrees of robustness to the effects of mortality mortality induced by two different mechanisms is studied mortality due to the tumor of interest and mortality due to treatment independent of the tumor the two most commonly used tests the life table test and the cochran armitage linear trend test are seen to be highly sensitive to increases in treatment lethality using small sample simulations increases in tumor lethality are seen to affect the performance of commonly used prevalence tests such as logistic regression a simple survival adjusted quantal response test appears to be the most robust of all the procedures considered

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

a parallel implementation of an iterative substructuring algorithm for problems in three dimensions numerical results from a parallel implementation of a class of iterative substructuring algorithms are reported the algorithms are for solving self adjoint elliptic partial differential equations in three dimensions results are given for several variants of the algorithm in the first variant exact interior solvers are used in the second one multigrid v cycle is used to solve the interior problems approximately the results are compared with theoretical behavior of the algorithm reported in previous work a numerical experiment involving the equations of linear elasticity is also included

preconditioning on element interfaces for the p version finite element method and spectral element method in the preconditioned iterative method based on nonoverlapping domain decompositions the preconditioner is usually of block diagonal type to calculate its action on a residual vector it is required to solve a linear system of algebraic equations with the coefficient matrix being the schur complement block corresponding to the interface to reduce the computational cost the schur complement blocks in the preconditioners can be replaced with other simpler matrices which are called the interface preconditioners in this paper we discuss various interface preconditioners for the p version finite element method and spectral element method in r2 and r3 emphases are placed on 1 the lower and upper bounds of the condition numbers for the preconditioned schur complement blocks using the interface preconditioners which characterize the enlargement of the overall condition numbers and 2 the algorithms to efficiently implement the interface preconditioners numerical results are presented for the condition numbers using various interface preconditioners

testing hypotheses with binary data subject to misclassification errors analysis and experimental design summary consider a binary random variable having outcomes subject to misclassification errors where the probabilities of misclassification errors depend on outcome the asymptotic relative efficiencies are derived for comparing two binomial populations comparing stratified binomial populations and for paired comparisons the probabilities of misclassification can vary with strata or be different for each pair the criterion for optimum experimental designs is shown to be the ratio of the asymptotic relative efficiency to expected cost per observation this criterion implies that mixtures of different experiments can never be optimal a number of experimental strategies is discussed

analysis of iterative methods for the steady and unsteady stokes problem application to spectral element discretizations a new and detailed analysis of the basic uzawa algorithm for decoupling of the pressure and the velocity in the steady and unsteady stokes operator is presented the paper focuses on the following new aspects explicit construction of the uzawa pressure operator spectrum for a semiperiodic model problem general relationship of the convergence rate of the uzawa procedure to classical inf sup discretization analysis and application of the method to high order variational discretization

an iterative and parallel solver based on domain decomposition for the h p version of the finite element method in this paper we propose a new interative and parallel solver based on domain decomposition for the h p version of the finite element method in two dimensions it improves our previous work in two aspects 1 a subdomain may contain several super elements of the coarse mesh thus can be of arbitrary shape and size this makes the solver more efficient and more flexible in computational practice 2 the p version components i e the high order side and internal modes in every element are treated separately which results in better parallelism

recursive nonparametric testing for dose response relaflonships subject to downturns at high doses summary a general recursive strategy is introduced to test nonparametrically for an increasing dose response relationship when a downturn in response at high doses is possible a specific implementation involving a test of jonckheere 1954 and terpstra 1952 is considered and its size and power properties are investigated via monte carlo methods data from mutation research illustrate the phenomenon of concern

prediction in censored survival data a comparison of the proportional hazards and linear regression models although the analysis of censored survival data using the proportional hazards and linear regression models is common there has been little work examining the ability of these estimators to predict time to failure this is unfortunate since a predictive plot illustrating the relationship between time to failure and a continuous covariate can be far more informative regarding the risk associated with the covariate than a kaplan meier plot obtained by discretizing the variable in this paper the predictive power of the cox 1972 journal of the royal statistical society series b 34 187 202 proportional hazards estimator and the buckley james 1979 biometrika 66 429 436 censored regression estimator are compared using computer simulations and heuristic arguments it is shown that the choice of method depends on the censoring proportion strength of the regression the form of the censoring distribution and the form of the failure distribution several examples are provided to illustrate the usefulness of the methods

covariate measurement errors and parameter estimation in a failure time regression model summary estimation in cox s failure time regression model is considered when the regression vector is subject to measurement error a hazard function model is induced for the failure rate given the measured covariate and a partial likelihood function is derived for the relative risk parameters this partial likelihood function may involve the baseline hazard function as well as the regression parameter but useful inference techniques arise for testing whether the regression parameter equals zero and for more general inferences in important special cases explicit consideration is given to testing equality of survival curves when group membership is subject to misclassification and to relative risk estimation with normally distributed covariates approaches to regression estimation using the overall likelihood function and a marginal likelihood function based on failure time ranks are also indicated illustration of the possible effect of covariate errors on relative risk estimation is provided

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

improved sequential stopping rule for monte carlo simulation this letter presents an improved result on the negative binomial monte carlo technique analyzed in a previous paper see ieee trans commun vol 54 no 2 pp 231 41 feb 2006 for the estimation of an unknown probability p specifically the confidence level associated to a relative interval p mu 2 pmu 1 with mu 1 mu 2 1 is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper and for any value of p this extends the applicability of the estimator relaxing the conditions that guarantee a given confidence level

multilevel methods for the h p and hp versions of the boundary element method in this paper we give an overview on the definition of finite element spaces for the h p and hp version of the bem along with preconditioners of additive schwarz type we consider screen problems with a hypersingular or a weakly singular integral equation of first kind on an open surface as model problems for the hypersingular integral equation and the h version with piecewise bilinear functions on a coarse and a fine grid we analyze a preconditioner by iterative substructuring based on a non overlapping decomposition of we prove that the condition number of the preconditioned linear system behaves polylogarithmically in h h here h is the size of the subdomains and h is the size of the elements for the hp version and the hypersingular integral equation we comment in detail on an additive schwarz preconditioner which uses piecewise polynomials of high degree on the fine grid and yields also a polylogarithmically growing condition number for the weakly singular integral equation where no continuity of test and trial functions across the element boundaries has to been enforced the method works for nonuniform degree distributions as well numerical results supporting our theory are reported

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

domain decomposition method for the h p version finite element method domain decomposition method for the h p version of the finite element method in two and three dimensions are discussed using the framework of additive schwarz method various iterative methods are described with their condition numbers estimated further to reduce the cost for solving the sub problems on element interfaces different inexact interface solvers are proposed the effects on the overall condition number as well as their efficient implementation are analyzed

the schwarz algorithm for spectral methods recently the schwarz alternating method has been successfully coupled to spatial discretizations of spectral type in order to solve boundary value problems in complex geometries with infinite order accuracy in this paper a simple version of the method is considered a proof of its convergence is given in the energy norm exploiting the properties of discrete harmonic polynomials and a discrete maximum principle for spectral methods more general situations can be handled theoretically in one space dimension

the problem of selecting the shape functions for a p type finite element abstract the paper addresses the question of the optimal selection of the shape functions for p type finite elements and discusses the effectivity of the conjugate gradient and multilevel iteration method for solving the corresponding linear system the selection of the shape functions is of major importance for the performance of the solver based on iterative methods neither the theory nor practice of the optimal selection of the shape functions is available yet we have seen that the condensation approach which has obvious advantages from the point of parallel computations is a very effective tool for keeping the condition number under the control and is especially advantageous for the conjugate gradient method

the asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates summary in many epidemiological studies the exposure variable of interest cannot be measured directly the classical approaches to errors in variables in regression do not extend easily to the nonlinear models commonly used in epidemiologic al research furthermore the traditional additive measurement error model cannot adequately represent many surrogate relationships by considering the effect of using surrogate independent variables on the efficient score statistic some of the difficulties inherent in the estimation problem may be avoided for the null hypothesis of no association a simple and flexible procedure can be used to calculate the optimal score test the asymptotic relative efficiency of this test to the test based upon the true exposures is derived the optimal test is also compared to the naive procedure of substituting the surrogate into the score test for the true exposure

the effect of pooling across strata in perfectly balanced studies pair matching frequency matching and stratification are used to obtain perfect exposure balance within strata defined by levels of confounders we consider the consequences of pooling such balanced data across strata in the analysis we examine model based inference for a variety of response variables and generalized linear regressions as well as for the cox 1972 journal of the royal statistical society series b 34 187 220 model if the data are pooled so that stratum effects are omitted from the regression certain models retain nominal size including all poisson models and all normal models with known variance the model based tests have supranominal size for all exponential models and subnominal size for all bernoulli models and for the cox model these results contrast with a previous analysis of simple randomization which only ensures exposure balance on average with simple randomization omission of stratum effects from these models leads to model based significance tests with supranominal size except for the cox and bernoulli models which retain nominal size just as for simple randomization however it is wise to include stratum effects in the analysis of perfectly balanced data to avoid biased estimation of exposure effects and to increase the efficiency of the comparison though motivated by cohort data these results also apply to balanced case control data under the logistic model

robust estimation of causal effects of binary treatments in unconfounded studies with dichotomous outcomes the estimation of causal effects has been the subject of extensive research in unconfounded studies with a dichotomous outcome y cangul chretien gutman and rubin 2009 demonstrated that logistic regression for a scalar continuous covariate x is generally statistically invalid for testing null treatment effects when the distributions of x in the treated and control populations differ and the logistic model for y given x is misspecified in addition they showed that an approximately valid statistical test can be generally obtained by discretizing x followed by regression adjustment within each interval defined by the discretized x this paper extends the work of cangul et al 2009 in three major directions first we consider additional estimation procedures including a new one that is based on two independent splines and multiple imputation second we consider additional distributional factors and third we examine the performance of the procedures when the treatment effect is non null of all the methods considered and in most of the experimental conditions that were examined our proposed new methodology appears to work best in terms of point and interval estimation copyright 2012 john wiley sons ltd

multiply robust inference for statistical interactions a primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures when the main interest lies in the interaction this approach is not entirely satisfactory because it is prone to possibly severe bias when the main exposure effects or the associations between outcome and extraneous factors are misspecified in this article we consider conditional mean models with identity or log link that postulate the statistical interaction in terms of a finite dimensional parameter but are otherwise unspecified we show that estimation of the interaction parameter often is not feasible in this model because it requires nonparametric estimation of auxiliary conditional expectations given high dimensional variables we thus consider multiply robust estimation under a union model th

testing in semiparametric models with interaction with applications to gene environment interactions motivated from the problem of testing for genetic effects on complex traits in the presence of gene environment interaction we develop score tests in general semiparametric regression problems that involves tukey style 1 degree of freedom form of interaction between parametrically and non parametrically modelled covariates we find that the score test in this type of model as recently developed by chatterjee and co workers in the fully parametric setting is biased and requires undersmoothing to be valid in the presence of non parametric components moreover in the presence of repeated outcomes the asymptotic distribution of the score test depends on the estimation of functions which are defined as solutions of integral equations making implementation difficult and computationally taxing we develop profiled score statistics which are unbiased and asymptotically efficient and can be performed by using standard bandwidth selection methods in addition to overcome the difficulty of solving functional equations we give easy interpretations of the target functions which in turn allow us to develop estimation procedures that can be easily implemented by using standard computational methods we present simulation studies to evaluate type i error and power of the method proposed compared with a naive test that does not consider interaction finally we illustrate our methodology by analysing data from a case control study of colorectal adenoma that was designed to investigate the association between colorectal adenoma and the candidate gene nat2 in relation to smoking history

a note on the efficiency of sandwich covariance matrix estimation the sandwich estimator also known as robust covariance matrix estimator heteroscedasticity consistent covariance matrix estimate or empirical covariance matrix estimator has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified surprisingly though there has been little discussion of properties of the sandwich method other than consistency we investigate the sandwich estimator in quasi likelihood models asymptotically and in the linear case analytically we show that under certain circumstances when the quasi likelihood model is correct the sandwich estimate is often far more variable than the usual parametric variance estimate the increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the p

deconvolution based score tests in measurement error models consider a generalized linear model with response y and scalar predictor x instead of observing x a surrogate w x z is observed where z represents measurement error and is independent of x and y the efficient score test for the absence of association depends on m w e x mid w w which is generally unknown assuming that the distribution of z is known asymptotically efficient tests are constructed using nonparametric estimators of m w rates of convergence for the estimator of m w are established in the course of proving efficiency of the proposed test

a domain decomposition algorithm for elliptic problems in three dimensions most domain decomposition algorithms have been developed for problems in two dimensions one reason for this is the difficulty in devising a satisfactory easy to implement robust method of providing global communication of information for problems in three dimensions several methods that work well in two dimension do not perform satisfactorily in three dimensions a new iterative substructuring algorithm for three dimensions is proposed it is shown that the condition number of the resulting preconditioned problem is bounded independently of the number of subdomains and that the growth is quadratic in the logarithm of the number of degrees of freedom associated with a subdomain the condition number is also bounded independently of the jumps in the coefficients of the differential equation between subdomains the new algorithm also has more potential parallelism than the iterative substructuring methods previously proposed for problems in three dimensions

estimation of the quadratic errors in variables model summary an estimator is presented for the coefficients of the quadratic functional relationship the estimator is shown to be asymptotically normally distributed as the sample size increases in deriving this result it is not assumed that replication occurs a monte carlo study is presented agreeing well with the asymptotic results an example from the earth sciences is analysed

the loss in efficiency from misspecifying covariates in proportional hazards regression models summary this note considers partial likelihood score tests for association between a covariate process and survival time based on a proportional hazards regression model we derive the asymptotic efficiency of the test based on a misspecified form of the covariate process relative to the test based on the correct form the results can be used to assess the consequences of various types of misspecification

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

testing for gene environment interaction under exposure misspecification complex interplay between genetic and environmental factors characterizes the etiology of many diseases modeling gene environment gxe interactions is often challenged by the unknown functional form of the environment term in the true data generating mechanism we study the impact of misspecification of the environmental exposure effect on inference for the gxe interaction term in linear and logistic regression models we first examine the asymptotic bias of the gxe interaction regression coefficient allowing for confounders as well as arbitrary misspecification of the exposure and confounder effects for linear regression we show that under gene environment independence and some confounder dependent conditions when the environment effect is misspecified the regression coefficient of the gxe interaction can be unbiased however inference on the gxe interaction is still often incorrect in logistic regression we show that the regression coefficient is generally biased if the genetic factor is associated with the outcome directly or indirectly further we show that the standard robust sandwich variance estimator for the gxe interaction does not perform well in practical gxe studies and we provide an alternative testing procedure that has better finite sample properties

schwarz methods of neumann neumann type for three dimensional elliptic finite element problems several domain decomposition methods of neumann neumann type are considered for solving the large linear systems of algebraic equations that arise from discretizations of elliptic problems by finite elements we will only consider problems in three dimensions several new variants of the basic algorithm are introduced in a schwarz method framework that provides tools which have already proven very useful in the design and analysis of other domain decomposition and multi level methods the neumann neumann algorithms have several advantages over other domain decomposition methods the subregions which define the subproblems only share the boundary degrees of freedom with their neighbors the subregions can also be of quite arbitrary shape and many of the major components of the preconditioner can be constructed from subprograms available in standard finite element program libraries in its original form however the algorithm lacks a mechanism for global transportation of information and its performance therefore suffers when the number of subregions increases in the new variants of the algorithms considered in this paper the preconditioners include global components of low rank to overcome this difficulty bounds are established for the condition number of the iteration operator which are independent of the number of subregions and depend only polylogarithmically on the number of degrees of freedom of individual local subproblems results are also given for problems with arbitrarily large jumps in the coefficients across the interfaces separating the subregions 1995 john wiley sons inc

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

loss in efficiency caused by omitting covariates and misspecifying exposure in logistic regression models we examine the effects of omitting covariates and misspecifying the explanatory variable of interest on tests of association between the explanatory variable and response based on logistic regression models we assume throughout that the covariates are statistically independent of the explanatory variable as under simple randomization a general expression for the asymptotic loss in efficiency from omitting covariates and misspecifying the explanatory variable is derived the expression for the asymptotic efficiency of the misspecified test statistic relative to the correctly specified test can be factored into two parts each of which is less than or equal to 1 the first part reflects the consequences of misspecifying exposure whereas the other part captures the effect of omitting needed covariates this result permits numerical evaluation of the approximate loss in efficiency and can be useful in developing guidelines for study design and model fitting procedures we discuss applications of the resul

an additive schwarz preconditioner for p version boundary element approximation of the hypersingular operator in three dimensions additive schwarz preconditioners are developed for the p version of the boundary element method for the hypersingular integral equation on surfaces in three dimensions the principal preconditioner consists of decomposing the subspace into local spaces associated with the element interiors supplemented with a wirebasket space associated with the the element interfaces the wirebasket correction involves inverting a diagonal matrix if exact solvers are used on the element interiors then theoretical analysis shows that growth of the condition number of the preconditioned system is bounded by 1 log p 2 for an open surface and 1 log p for a closed surface a modified form of the preconditioner only requires the inversion of a diagonal matrix but results in a further degradation of the condition number by a factor p 1 log p

multilevel schwarz methods for elliptic problems with discontinuous coefficients in three dimensions multilevel schwarz methods are developed for a conforming finite element approximation of second order elliptic problems we focus on problems in three dimensions with possibly large jumps in the coefficients across the interface separating the subregions we establish a condition number estimate for the iterative operator which is independent of the coefficients and grows at most as the square of the number of levels we also characterize a class of distributions of the coefficients called quasi monotone for which the weighted l 2 projection is stable and for which we can use the standard piecewise linear functions as a coarse space in this case we obtain optimal methods i e bounds which are independent of the number of levels and subregions we also design and analyze multilevel methods with new coarse spaces given by simple explicit formulas we consider nonuniform meshes and conclude by an analysis of multilevel iterative substructuring methods

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

on errors in variables in binary regression berkson case abstract in binary regression the predictor variables may be measured with error the berkson case of the errors in variables problem is considered under which the values of the predictor variables are set by the experimenter but not achieved exactly a particular model for this case is considered with probit regression and normally distributed errors of observation the regression parameters for intercept and slope are to be estimated two estimators are studied the maximum likelihood estimator mle and a modification of it in a simulation study the modified mle is shown to improve on the mle in a situation with substantial measurement error quantal bioassay is an important field of application of the berkson case of the binary regression model in quantal bioassay there is a stimulus perhaps a carcinogen or poison with doses x to be determined by the experimenter to address questions on carcinogenicity or toxicity of the stimulus each experimental animal is assigned a dose of the stimulus

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

iterative substructuring methods for spectral element discretizations of elliptic systems i compressible linear elasticity an iterative substructuring method for the system of linear elasticity in three dimensions is introduced and analyzed the pure displacement formulation for compressible materials is discretized with the spectral element method the resulting stiffness matrix is symmetric and positive definite the proposed method provides a domain decomposition preconditioner constructed from local solvers for the interior of each element and for each face of the elements and a coarse global solver related to the wire basket of the elements as in the scalar case the condition number of the preconditioned operator is independent of the number of spectral elements and grows as the square of the logarithm of the spectral degree

spectral element methods for large scale parallel navier stokes calculations abstract we analyze the computational complexity of a recently developed two level iteration scheme for spectral element solution of the time dependent incompressible navier stokes equations in complex domains we present several algorithmic advances which significantly enhance the scalability of this approach including implementation of an advanced combine operation for degrees of freedom on subdomain edges parallel solution of the fine grained coarse grid problem and implementation of local low order finite element preconditioners for the find grid problem timings on the 512 node intel delta machine show that the combined improvements lead to a fourfold reduction in navier stokes solution time for the particular case of a three dimensional boundary layer calculation consisting of one million degrees of freedom

testing treatment effects in unconfounded studies under model misspecification logistic regression discretization and their combination logistic regression is commonly used to test for treatment effects in observational studies if the distribution of a continuous covariate differs between treated and control populations logistic regression yields an invalid hypothesis test even in an uncounfounded study if the link is not logistic this flaw is not corrected by the commonly used technique of discretizing the covariate into intervals a valid test can be obtained by discretization followed by regression adjustment within each interval

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

iterative substructuring methods for spectral elements problems in three dimensions based on numerical quadrature abstract iterative substructuring methods form an important family of domain decomposition algorithms for elliptic finite element problems two preconditioners for p version finite element methods based on continuous piecewise qp functions are considered for second order elliptic problems in three dimensions these special methods can also be viewed as spectral element methods the first iterative method is designed for the galerkin formulation of the problem the second applies to linear systems for a discrete model derived by using gauss lobatto legendre quadrature for both methods it is established that the condition number of the relevant operator grows only in proportion to 1 log p 2 these bounds are independent of the number of elements into which the given region has been divided their diameters as well as the jumps in the coefficients of the elliptic equation between elements results of numerical computations are also given which provide upper bounds on the condition numbers as functions of p and which confirms the correctness of our theory

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

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

regression dilution in the proportional hazards model the problem of regression dilution arising from covariate measurement error is investigated for survival data using the proportional hazards model the naive approach to parameter estimation is considered whereby observed covariate values are used inappropriately in the usual analysis instead of the underlying covariate values a relationship between the estimated parameter in large samples and the true parameter is obtained showing that the bias does not depend on the form of the baseline hazard function when the errors are normally distributed with high censorship adjustment of the naive estimate by the factor 1 lambda where lambda is the ratio of within person variability about an underlying mean level to the variability of these levels in the population sampled removes the bias as censorship increases the adjustment required increases and when there is no censorship is markedly higher than 1 lambda and depends also on the true risk relationship

effects of mismodeling on tests of association based on logistic regression models we consider the effects of misspecifying the covariate vector on tests of association between a particular covariate and the response variable in logistic regression models misspecification can include random measurement error discretizing a continuous explanatory variable and mismodeling the functional form of an explanatory variable the effects of misspecification are examined by deriving the asymptotic distribution of the test statistic under a sequence of models applications of this result are discussed