interim analysis on survival data its potential bias and how to repair it we consider interim analyses in clinical trials or observational studies with a time to event outcome variable where the survival curves are compared using the hazard ratio resulting from a proportional hazards ph model or tested with the logrank test or another two sample test we show and illustrate with an example that if the ph assumption is violated the results of interim analyses can be heavily biased this is due to the fact that the censoring pattern in interim analyses can be completely different from the final analysis we argue that when the ph assumption is violated interim analyses are only sensible if a fixed time horizon for the final analysis is specified and at the time of the interim analysis sufficient information is available over the whole time interval up to the horizon we show how the bias can then be remedied by introducing in the estimation and testing procedures an appropriate weighting that reflects the weights to be expected in the final analysis the consequences for design and analysis are discussed and some practical recommendations are given copyright 2005 john wiley sons ltd

on hamiltonian stationary lagrangian spheres in non einstein kahler surfaces hamiltonian stationary lagrangian spheres in kahler einstein surfaces are minimal we prove that in the family of non einstein kahler surfaces given by the product 1 2 of two complete orientable riemannian surfaces of different constant gauss curvatures there is only a non minimal hamiltonian stationary lagrangian sphere this example defined when the surfaces 1 and 2 are spheres is unstable

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

the codazzi equation for surfaces abstract in this paper we study the classical codazzi equation in space forms from an abstract point of view and use it as an analytic tool to derive global results for surfaces in different ambient spaces in particular we study the existence of holomorphic quadratic differentials the uniqueness of immersed spheres in geometric problems height estimates and the geometry and uniqueness of complete or properly embedded weingarten surfaces

correction to the application of the conjugate gradient method for the solution of electromagnetic scattering from arbitrarily oriented wire antennas the method of conjugate gradients is applied to the analysis of radiation from thin wire antennas with this iterative technique it is possible to solve electrically large arbitrarily oriented wire structures without storing any matrices as is conventionally done in the method of moments the basic difference between the proposed method and galerkin s method for the same expansion functions is that for the iterative technique we are solving a least squares problem hence as the order of the approximation is increased the proposed technique guarantees a monotonic decrease of the least squared error parallel ai y parallel 2 whereas galerkin s method does not even though the method converges for any initial guess a good one may significantly reduce the time of computation also explicit error formulas are given for the rate of convergence of this method hence any problem can be solved to a prespecified degree of accuracy it is shown that the method has the advantage of a direct solution as the final solution is obtained in a finite number of steps the method is also suitable for solving singular operator equations in which case the method monotonically converges to the least squares solution with minimum norm numerical results are presented for the thin wire antennas and are compared with the solution obtained by the method of moments

an iterative method for solving electrostatic problems the method of steepest descent is applied to the solution of electrostatic problems the relation between this method and the rayleigh ritz galerkin s and the method of least squares is outlined also explicit error formulas are given for the rate of convergence for this method it is shown that this method is also suitable for solving singular operator equations in that case this method monotonically converges to the solution with minimum norm finally it is shown that the technique yields as a by product the smallest eigenvalue of the operator in the finite dimensional space in which the problem is solved numerical results are presented only for the electrostatic case to illustrate the validity of this procedure which show excellent agreement with other available data

isometric immersions into ⁿ ℝ and ℍⁿ ℝ and applications to minimal surfaces we give a necessary and sufficient condition for an n dimensional riemannian manifold to be isometrically immersed in s n x or n in terms of its first and second fundamental forms and of the projection of the vertical vector field on its tangent plane we deduce the existence of a one parameter family of isometric minimal deformations of a given minimal surface in s 2 or 2 x r obtained by rotating the shape operator

harmonic maps and constant mean curvature surfaces in h 2 x r we introduce a it hyperbolic gauss map into the poincar e disk for any surface in bbb h 2 times bbb r with regular vertical projection and prove that if the surface has constant mean curvature h 1 2 this hyperbolic gauss map is harmonic conversely we show that every nowhere conformal harmonic map from an open simply connected riemann surface sigma into the poincar e disk is the hyperbolic gauss map of a two parameter family of such surfaces as an application we obtain that any holomorphic quadratic differential on sigma can be realized as the abresch rosenberg holomorphic differential of some and generically infinitely many complete surfaces with h 1 2 in bbb h 2 times bbb r a similar result applies to minimal surfaces in the heisenberg group rm nil 3 finally we classify all complete minimal vertical graphs in bbb h 2 times bbb r

improved impedance matrix localization method em problems moment method calculations have the well known limitations of requiring excessive storage and execution times for even modestly large electromagnetics problems the impedance matrix localization iml method was introduced as a modification to standard moment method calculations to ease these limitations it utilizes a matrix transformation which effectively changes the basis testing functions into ones resembling traveling waves an improved method that uses an orthogonal transformation to generate standing wave like basis functions is presented here remarkable improvements are achieved in the numerical stability of the method and in its compatibility with iterative solvers furthermore the correspondence of the large elements in this matrix to geometrical theory of diffraction gtd terms is strengthened as is the possibility of further increasing the speed of iterative solutions by constructing preconditioners based on the pattern of nonzero matrix elements

comments on application of fft and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies in the original paper ibid vol ap 34 no 5 p 635 40 1986 t k sarkar et al describe how the fast fourier transform fft and the conjugate gradient method cgm can be used to efficiently make use of the convolutional form of the electric field integral equation for straight wire antennas the commentators agree that the cgm converges more rapidly than the previously used method of steepest descent and the spectral iteration technique they also point out that experience with the dyadic green s function encountered in the two dimensional transverse electric te and three dimensional equations for dielectric bodies is not so encouraging it is found that for these cases the cgm convergence can be quite slow degrading the efficiency of the algorithm in addition the solution obtained using the pulse basis point matching method to discretize the integral equation are very inaccurate for the two dimensional te and three dimensional cases a reply to these comments from the authors of the original paper is included

uniqueness of minimal surfaces whose boundary is a horizontal graph and some bernstein problems in mathbb h 2 times mathbb r we deduce that a connected compact immersed minimal surface in mathbb h 2 times mathbb r whose boundary has an injective horizontal projection on an admissible convex curve in partial infty mathbb h 2 times mathbb r and satisfies an admissible bounded slope condition is the morrey s solution of the plateau problem and is a horizontal minimal graph we prove that there is no entire horizontal minimal graph in mathbb h 2 times mathbb r

equivariant willmore surfaces in conformal homogeneous three spaces abstract the complete classification of homogeneous three spaces is well known for some time of special interest are those with rigidity four which appear as riemannian submersions with geodesic fibres over surfaces with constant curvature consequently their geometries are completely encoded in two values the constant curvature c of the base space and the so called bundle curvature r in this paper we obtain the complete classification of equivariant willmore surfaces in homogeneous three spaces with rigidity four all these surfaces appear by lifting elastic curves of the base space once more the qualitative behaviour of these surfaces is encoded in the above mentioned parameters c r the case where the fibres are compact is obtained as a special case of a more general result that works via the principle of symmetric criticality for bundle like conformal structures in circle bundles however if the fibres are not compact a different approach is necessary we compute the differential equation satisfied by the equivariant willmore surfaces in conformal homogeneous spaces with rigidity of order four and then we reduce directly the symmetry to obtain the euler lagrange equation of 4 r 2 elasticae in surfaces with constant curvature c we also work out the solving natural equations and the closed curve problem for elasticae in surfaces with constant curvature it allows us to give explicit parametrizations of willmore surfaces and willmore tori in those conformal homogeneous 3 spaces

characterization of f extremal disks abstract we show uniqueness for overdetermined elliptic problems defined on topological disks with c 2 boundary i e positive solutions u to u f u 0 in m 2 g so that u 0 and u c t e along the unit outward normal along under the assumption of the existence of a candidate family to do so we adapt the galvez mira generalized hopf type theorem 19 to the realm of overdetermined elliptic problem when m 2 g is the standard sphere s 2 and f is a c 1 function so that f x 0 and f x x f x for any x r we construct such candidate family considering rotationally symmetric solutions this proves the berestycki caffarelli nirenberg conjecture in s 2 for this choice of f more precisely this shows that if u is a positive solution to u f u 0 on a topological disk s 2 with c 2 boundary so that u 0 and u c t e along then must be a geodesic disk and u is rotationally symmetric in particular this gives a positive answer to the schiffer conjecture d cf 33 35 for the first dirichlet eigenvalue and classifies simply connected harmonic domains cf 28 also called serrin problem in s 2

a hopf differential for constant mean curvature surfaces in s2 r and h2 r a basic tool in the theory of constant mean curvature cmc surfaces in space forms is the holomorphic quadratic differential discovered by h hopf in this paper we generalize this differential to immersed cmc surfaces in the product spaces s r and h r and prove a corresponding result about the geometry of immersed cmc spheres s in these target spaces

regularization of the moment matrix solution by a nonquadratic conjugate gradient method inspired by tikhonov regularization a nonlinear conjugate gradient method is proposed with the purpose of simultaneously regularizing and solving the moment matrix equation the procedure is based on a nonquadratic conjugate gradient algorithm with exact line search restart and rescale applied to the problem of tm scattering by perfectly conducting rectangular cylinders the method is shown to exhibit a fast convergence rate

notes on submanifolds in warped products in this paper we study submanifolds in the warped product m fr where m is a riemannian manifold f is the warping function we investigate the graphs with positive gaussian curvature in m2 r the minimal graphs in m fr and the totally geodesic submanifolds in m fr

a hopf theorem for ambient spaces of dimensions higher than three we consider surfaces m 2 immersed in e c n times mathbb r where e c n is a simply connected n dimensional complete riemannian manifold with constant sectional curvature e c n and assume that the mean curvature vector of the immersion is parallel in the normal bundle we consider further a hopf type complex quadratic form q on m 2 where the complex structure of m 2 is compatible with the induced metric it is not hard to check that q is holomorphic see 3 p 289 we will use this fact to give a reasonable description of immersed surfaces in e c n times mathbb r that have parallel mean curvature vector

application of the singular function expansion to an integral equation for scattering the dirichlet scattering problem is solved exactly for a surface of arbitrary smooth shape the solution is given in terms of the complete orthonormal set of functions defined on the surface and arising as singular functions of the integral operator since the singular values do not have a point of accumulation at zero the method is of much greater practical value than the eigenmode expansion method eem since the terms in the infinite series are naturally ordered by size of singular value the dominance of one or several terms in the series may be established without explicit evaluation of the coupling coefficients extentions of the method to other boundary value problems and applications to the singularity expansion method sem are described

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

covariate adjustment using propensity scores for dependent censoring problems in the accelerated failure time model in many medical studies estimation of the association between treatment and outcome of interest is often of primary scientific interest standard methods for its evaluation in survival analysis typically require the assumption of independent censoring this assumption might be invalid in many medical studies where the presence of dependent censoring leads to difficulties in analyzing covariate effects on disease outcomes this data structure is called semicompeting risks data for which many authors have proposed an artificial censoring technique however confounders with large variability may lead to excessive artificial censoring which subsequently results in numerically unstable estimation in this paper we propose a strategy for weighted estimation of the associations in the accelerated failure time model weights are based on propensity score modeling of the treatment conditional on confounder variables this novel application of propensity scores avoids excess artificial censoring caused by the confounders and simplifies computation monte carlo simulation studies and application to aids and cancer research are used to illustrate the methodology

analysis of cylindrical antennas a spectral iteration technique the cylindrical antenna problem has been tackled using the spectral iteration technique an iterative scheme is employed for improving on an initially assumed form of the current distribution use is made of the fast fourier transform fft algorithm and the cumbersome process of matrix inversion is circumvented consequently this method is capable of handling a larger number of unknown coefficients in the expansion of the current distribution furthermore it provides a convenient means of testing for the satisfaction of the boundary conditions on the surface of the antenna convergence criteria for the iteration process have been established and the use of an acceleration procedure is illustrated different types of source models have been investigated and the convergence of both local and nonlocal parameters is also discussed

a note on the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator the relationship between the conjugate gradient method and polynomials orthogonal over the spectrum of a linear operator is discussed it is shown that as a byproduct of the conjugate gradient construction two sets of polynomials are generated which are orthogonal with respect to a positive real measure over the spectrum of a self adjoint operator the roots of these polynomials can under certain circumstances be used to track the eigenvalues or singular values of the relevant operator

adaptive spectral estimation by the conjugate gradient method this paper proposes an alternative technique for adaptive spectral estimation the new technique applies the method of conjugate gradient which is used for iteratively finding the generalized eigenvector corresponding to the minimum generalized eigenvalue of a semidefinite hermitian matrix to the adaptive spectral analysis problem computer simulations have been performed to compare the new method to existing ones from the limited examples presented it is seen that the new method is computationally more efficient at the expense of more core storage also this method is effective for small data records and can implement noise correction to yield unbiased spectral estimates if an estimate of the noise covariance matrix is available the technique performs well for both narrow band and wide band signals

estimation of treatment effect under non proportional hazards and conditionally independent censoring in clinical trials with time to event outcomes it is common to estimate the marginal hazard ratio from the proportional hazards model even when the proportional hazards assumption is not valid this is unavoidable from the perspective that the estimator must be specified a priori if probability statements about treatment effect estimates are desired marginal hazard ratio estimates under non proportional hazards are still useful as they can be considered to be average treatment effect estimates over the support of the data however as many have shown under non proportional hazard the usual unweighted marginal hazard ratio estimate is a function of the censoring distribution which is not normally considered to be scientifically relevant when describing the treatment effect in addition in many practical settings the censoring distribution is only conditionally independent e g differing across treatment arms which further complicates the interpretation in this paper we investigate an estimator of the hazard ratio that removes the influence of censoring and propose a consistent robust variance estimator we compare the coverage probability of the estimator to both the usual cox model estimator and an estimator proposed by xu and o quigley 2000 when censoring is independent of the covariate the new estimator should be used for inference that does not depend on the censoring distribution it is particularly relevant to adaptive clinical trials where by design censoring distributions differ across treatment arms copyright 2012 john wiley sons ltd

generalized martingale residual processes for goodness of fit inference in cox s type regression models in the paper a general class of stochastic processes based on the sums of weighted martingale transform residuals for goodness of fit inference in general cox s type regression models is studied their form makes the inference robust to covariate outliers a weak convergence result for such processes is obtained giving the possibility of establishing the randomness of their graphs together with the construction of the formal x 2 type goodness of fit tests by using the khmaladze innovation approach a modified version of the initial class of processes is also defined weak convergence results for the processes are derived this leads to the main application which concerns the formal construction of the kolmogorov smirnov and cramer von mises type goodness of fit tests this is done within the general situation considered

a schoen theorem for minimal surfaces in h 2 r abstract in this paper we prove that a complete minimal surface immersed in h 2 r with finite total curvature and two ends each one asymptotic to a vertical geodesic plane must be a horizontal catenoid moreover we give a geometric description of minimal ends of finite total curvature in h 2 r we also prove that a minimal complete end e with finite total curvature is properly immersed and that the gaussian curvature of e is locally bounded in terms of the geodesic distance to its boundary

existence of barriers for surfaces with prescribed curvatures in m2 r abstract we present a deformation process of surfaces from a product space m 1 r into another product space m 2 r such that the relation of the principal curvatures of the deformed surfaces can be controlled in terms of the curvatures of m 1 and m 2 thus we obtain subsolutions for the existence or barriers for the non existence of surfaces with prescribed curvatures in a general product space m r

bias correction for score tests arising from misspecified proportional hazards regression models when censoring depends on both treatment group and covariates tests for a randomised treatment effect arising from cox s proportional hazards model are not in general centred at zero under the null and can be seriously distorted we propose a corrected test that modifies the at risk indicator in a way that corrects for this bias the resulting test is asymptotically valid regardless of whether or not the fitted model is correctly specified implementation of the corrected test requires that the dependence of censoring on treatment group and covariates be modelled simulations indicate that the bias corrected test performs well even when the dependence of censoring on treatment group and covariates is not modelled exactly and maintains high efficiency relative to the uncorrected test when the latter is valid

scattering from planar structures containing small features using the adaptive integral method aim fast integral equation algorithms such as the adaptive integral method aim have been demonstrated to reduce memory and execution time associated with moment method solutions for arbitrarily shaped three dimensional 3 d geometries in this paper we examine the efficiency of aim in modeling planar structures that contain small and intricate details as is the case with spirals and slot antennas such geometries require high tessellation due to the inclusion of very small features resulting in a large number of unknowns aim with its capability to translate the original grid to an equivalent sparser uniform grid is uniquely suited for the analysis of such geometries in the latter part of the paper we demonstrate the application of aim in connection with a finite element boundary integral formulation for cavity backed antennas

the geometry of finite topology bryant surfaces we prove that in the three dimensional hyperbolic space h 3 the properly embedded constant mean curvature one surfaces with finite topology are of finite total curvature and each ends are regular this imply in particular that the hrosphere is the only properly embedded simply connected constant mean curvature one surface in h 3

holomorphic quadratic differentials and the bernstein problem in heisenberg space we classify the entire minimal vertical graphs in the heisenberg group nil 3 endowed with a riemannian left invariant metric this classification which provides a solution to the bernstein problem in nil 3 is given in terms of the abresch rosenberg holomorphic differential for minimal surfaces in nil 3

warping functions of some warped products abstract in this paper we study the warping functions of some warped products let h n be the n dimensional hyperbolic space with sectional curvature 1 we prove that if the warping function f of the warped product h n f r has a critical point then h n f r h n 1 if and only if f x k cosh r x where k is a positive constant r x denotes the hyperbolic distance from x to a fixed point we also prove that if the sectional curvature of the warped product m f r is nonnegative then f is constant providing that the riemannian manifold m is complete and connected

a hopf theorem for non constant mean curvature and a conjecture of a d alexandrov we prove a uniqueness theorem for immersed spheres of prescribed non constant mean curvature in homogeneous three manifolds in particular this uniqueness theorem proves a conjecture by a d alexandrov about immersed spheres of prescribed weingarten curvature in mathbb r 3 for the special but important case of prescribed mean curvature as a consequence we extend the classical hopf uniqueness theorem for constant mean curvature spheres to the case of immersed spheres of prescribed antipodally symmetric mean curvature in mathbb r 3

surfaces with parallel mean curvature in ℂℙⁿ ℝ and ℂℍⁿ ℝ we consider surfaces with parallel mean curvature vector pmc surfaces in cp r and ch r and more generally in cosymplectic space forms we introduce a holomorphic quadratic differential on such surfaces this is then used in order to show that the anti invariant pmc 2 spheres of a 5 dimensional non flat cosymplectic space form of product type are actually the embedded rotational spheres s h m r of hsiang and pedrosa where m is a complete simply connected surface with constant curvature when the ambient space is a cosymplectic space form of product type and its dimension is greater than 5 we prove that an immersed non minimal non pseudo umbilical anti invariant 2sphere lies in a product space m r where m is a space form we also provide a reduction of codimension theorem for the pmc surfaces of a non flat cosymplectic space form

on the existence of branch points in the eigenvalues of the electric field integral equation operator in the complex frequency plane it is demonstrated by specific examples that eigenvalues of the electric field integral equation efie operator for finite extent objects in lossless media can have branch points in the complex frequency s plane specifically it is shown from the analysis of the spheroidal wave equation in the s plane that branch points are present in the eigenvalues of the integral operator associated with the scalar scattering problem from a perfectly conducting spheroid similarly it is concluded from the analysis of the mathieu s differential equation that branch points besides that associated with the infinite extent of the object exist in the s plane behavior of the eigenvalues of the efie operator for a perfectly conducting infinite elliptic cylinder a proof is given that branch point singularities cannot occur in the eigenvalues of efie operators for structures in which geometrical symmetry completely determines the eigenfunctions and hence they are frequency independent it is conjectured that branch points may always be present when sufficient object symmetry is lacking this conjecture is supported by the fact that branch points appear when a sphere is deformed into a spheroid or when a circular cylinder is deformed into an elliptic one an analogous phenomenon has been observed in circuit and transmission line problems for example it is shown that when the taper parameter of an exponential transmission line goes to zero the line becomes uniform and thus a symmetrical structure the branch points in the eigenvalues of the impedance matrix move away to infinity

a scheme to analyze conducting plates of resonant size using the conjugate gradient method and the fast fourier transform a scheme for analyzing electrodynamic problems involving conducting plates of resonant size using the conjugate gradient cg method and the fast fourier transform fft is presented in detail the problems are analyzed by solving their corresponding electric field integral equation the procedure is made easy and systematic by using a sampling process with rooftop functions to represent the induced current and pulses to average the fields these functions have been widely used in moment method mm applications the scheme is an efficient numerical tool benefiting from the good convergence and low memory requirements of the cg and the low cpu time consumed in performing convolutions with the fft in comparison with the mm the scheme avoids the storage of large matrices and reduces the computer time by an order of magnitude several results are presented and compared with analytical numerical or measured values that appear in the literature