from taubes currents to almost kahler forms the taubes current is introduced by taubes in j symplectic geom 9 161 250 2011 as an intermediate step to construct almost kahler forms in this paper we prove that an almost complex structures being almost kahler structure in dimension four is the equivalent of the existence of taubes currents precisely we show that taubes currents could be regularized to almost kahler forms up to small perturbations of cohomology classes on any 4 dimensional almost complex manifold m j a similar result is established for higher dimensions under the assumption of almost kahler an application to donaldson s tamed to compatible question is provided

marginal proportional hazards models for multiple event time data the wei et al 1989 semiparametric approach to the analysis of multiple event time data assumes that each event time is related to covariates through a proportional hazards model with a completely unspecified baseline hazard function but does not impose any constraint on the joint distribution of different event times as a result of the order restriction it is not clear whether or not event times can simultaneously satisfy their respective marginal proportional hazards assumption while having continuous joint distribution this leads to inability to conduct simulation studies we resolve this issue by constructing parametric models for multiple event times with proper joint density functions and marginal proportional hazards simulation studies are reported that compare efficiencies of the method of wei et al 1989 and of the maximum likelihood approach

compatible complex structures on symplectic rational ruled surfaces in this article we study the topology of the spacei of complex structures compatible with a fixed symplectic form using the framework of donaldson by comparing our analysis of the spacei with results of mcduff on the spacej of compatible almost complex structures on rational ruled surfaces we find that i is contractible in this case we then apply this result to study the topology of the symplectomorphism group of a rational ruled surface extending results of abreu and mcduff

knots links and 4 manifolds in this paper we investigate the relationship between isotopy classes of knots and links in s and the di eomorphism types of homeomorphic smooth 4 manifolds as a corollary of this initial investigation we begin to uncover the surprisingly rich structure of di eomorphism types of manifolds homeomorphic to the k3 surface in order to state our theorems we need to view the seiberg witten invariant of a smooth 4 manifold as a multivariable laurent polynomial to do this recall that the seiberg witten invariant of a smooth closed oriented 4 manifold x with b2 x 1 is an integer valued function which is de ned on the set of spinc structures over x cf w km ko1 t1 in case h1 x z has no 2 torsion which will be the situation in this paper there is a natural identi cation of the spinc structures of x with the characteristic elements of h2 x z in this case we view the seiberg witten invariant as

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

existence of positive solutions for singular boundary value problem on time scales this paper deals with a class of boundary value problem of singular differential equations on time scales the conditions we used here differ from those in the majority of papers as we know an existence theorem of positive solutions is established by using the krasnosel skii fixed point theorem and an example is given to illustrate it

recent progress on symplectic embedding problems in four dimensions we survey some recent progress on understanding when one four dimensional symplectic manifold can be symplectically embedded into another in 2010 mcduff established a number theoretic criterion for the existence of a symplectic embedding of one four dimensional ellipsoid into another this result is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases

birational cobordism invariance of uniruled symplectic manifolds 1 department of mathematics zhongshan university guangzhou 510275 p r china e mail stsjxhu mail sysu edu cn 2 school of mathematics university of minnesota minneapolis mn 55455 usa e mail tjli math umn edu 3 department of mathematics university of michigan ann arbor mi 48109 1109 usa e mail ruan umich edu 4 yangtze center of mathematics sichuan university chengdu 610064 p r china

on the diffeomorphism types of certain algebraic surfaces i l invariant de donaldson la geometrie de certaines surfaces rationnelles surfaces dolgachev generalites sur des formes de type 1 n la classe canonique d une chambre et un coin le cone de kahler d une bonne surface generique une etude de p cellules les super p cellules

regression analysis of multivariate incomplete failure time data by modeling marginal distributions abstract many survival studies record the times to two or more distinct failures on each subject the failures may be events of different natures or may be repetitions of the same kind of event in this article we consider the regression analysis of such multivariate failure time observations each marginal distribution of the failure times is formulated by a cox proportional hazards model no specific structure of dependence among the distinct failure times on each subject is imposed the regression parameters in the cox models are estimated by maximizing the failure specific partial likelihoods the resulting estimators are shown to be asymptotically jointly normal with a covariance matrix that can be consistently estimated simultaneous inferential procedures are then proposed extensive monte carlo studies indicate that the normal approximation is adequate for practical use the new methods allow time dependent covariates missing observations and arbitrary patterns of censorship they are illustrat

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

the curve cone of almost complex 4 manifolds in this paper we study the curve cone of an almost complex 4 manifold which is tamed by a symplectic form in particular we prove the cone theorem as in mori theory for all such manifolds using the seiberg witten theory for small rational surfaces and minimal ruled surfaces we study the configuration of negative curves we define abstract configuration of negative curves which records the homological and intersection information of curves combinatorial blowdown is the main tool to study these configurations as an application of our investigation of the curve cone we prove the nakai moishezon type duality for all almost kahler structures on cp2 kcp2 with k 9 and minimal ruled surfaces with a negative curve this is proved using a version of gram schmidt orthogonalization process for the j tamed symplectic inflation

cauchy functions for dynamic equations on a measure chain abstract we consider the nth order linear dynamic equation px t i 0npi t x i t 0 where pi t 0 i n are real valued functions defined on t we define the cauchy function k t s for this dynamic equation and then we prove a variation of constants formula one of our main concerns is to see how the cauchy function for an equation is related to the cauchy functions for the factored parts of the operator p finally we consider the equation px t i 0npix i t 0 where each of the pi s is a constant and obtain a formula for the cauchy function for our main results we only consider the time scale t such that every point in t is isolated

symplectic conifold transitions we introduce a symplectic surgery in six dimensions which collapses lagrangian three spheres and replaces them by symplectic two spheres under mirror symmetry it corresponds to an operation on complex 3 folds studied by clemens friedman and tian we describe several examples which show that there are either many more calabi yau manifolds e g rigid ones than previously thought or there exist symplectic calabi yaus non kahler symplectic 6 folds with c1 0 the analogous surgery in four dimensions with a generalisation to ade trees of lagrangians implies that the canonical class of a minimal complex surface contains symplectic forms if and only if it has positive square

on the moduli space of diffeomorphic algebraic surfaces in this paper we show that the number of deformation types of complex structures on a fixed smooth oriented four manifold can be arbitrarily large the examples that we consider in this paper are locally simple abelian covers of rational surfaces the proof involves the algebraic description of rational blowdowns classical brill noether theory and deformation theory of normal flat abelian covers

many closed symplectic manifolds have infinite hofer zehnder capacity we exhibit many examples of closed symplectic manifolds on which there is an autonomous hamiltonian whose associated flow has no nonconstant periodic orbits the only previous explicit example in the literature was the torus t2n n 2 with an irrational symplectic structure the underlying smooth manifolds of our examples include for instance the k3 surface and also infinitely many smooth manifolds homeomorphic but not diffeomorphic to it infinitely many minimal four manifolds having any given finitely presented group as their fundamental group and simply connected minimal four manifolds realizing all but finitely many points in the first quadrant of the geography plane below the line corresponding to signature 3 the examples are constructed by performing symplectic sums along suitable tori and then perturbing the symplectic form in such a way that hypersurfaces near the neck in the symplectic sum have no closed characteristics we conjecture that any closed symplectic four manifold with b 1 admits symplectic forms with a similar property

on the win ratio statistic in clinical trials with multiple types of event pocock et al 2012 following finkelstein schoenfeld 1999 has popularized the win ratio for analysis of controlled clinical trials with multiple types of outcome event the approach uses pairwise comparisons between patients in the treatment and control groups using a primary outcome say the time to death with ties broken using a secondary outcome say the time to hospitalization in general the observed pairwise preferences and the weight they attach to the component rankings will depend on the distribution of potential follow up time we present expressions for the win and loss probabilities for general bivariate survival models when follow up of all patients is limited to a specified time horizon in the special case of a bivariate lehmann model we show that the win ratio does not depend on this horizon we show how the win ratio may be estimated nonparametrically or from a parametric model extensions to events of three or more types are described application of the method of marginal estimation due to wei et al 1989 to this problem is described

almost kahler forms on rational 4 manifolds we study nakai moishezon type question and donaldson s tamed to compatible question for almost complex structures on rational four manifolds by extending taubes subvarieties current form technique to j nef genus 0 classes we give affirmative answers of these two questions for all tamed almost complex structures on s 2 bundles over s 2 as well as for many geometrically interesting tamed almost complex structures on other rational four manifolds including the del pezzo ones

numerical characterization of the kahler cone of a compact kahler manifold the goal of this work is to give a precise numerical description of the kahler cone of a compact kahler manifold our main result states that the kahler cone depends only on the intersection form of the cohomology ring the hodge structure and the homology classes of analytic cycles if x is a compact kahler manifold the kahler cone k of x is one of the connected components of the set p of real 1 1 cohomology classes which are numerically positive on analytic cycles i e y p 0 for every irreducible analytic set y in x p dim y this result is new even in the case of projective manifolds where it can be seen as a generalization of the well known nakai moishezon criterion and it also extends previous results by campana peternell and eyssidieux the principal technical step is to show that every nef class which has positive highest self intersection numberx n 0 contains a kahler current this is done by using the calabi yau theorem and a mass concentration technique for monge ampere equations the main result admits a number of variants and corollaries including a description of the cone of numerically effective 1 1 classes and their dual cone another important consequence is the fact that for an arbitrary deformation x s of compact kahler manifolds the kahler cone of a very general fibre xt is independent of t i e invariant by parallel transport under the 1 1 component of the gauss manin connection

an alternative approach to confidence interval estimation for the win ratio statistic summary pocock et al 2012 european heart journal 33 176 182 proposed a win ratio approach to analyzing composite endpoints comprised of outcomes with different clinical priorities in this article we establish a statistical framework for this approach we derive the null hypothesis and propose a closed form variance estimator for the win ratio statistic in all pairwise matching situation our simulation study shows that the proposed variance estimator performs well regardless of the magnitude of treatment effect size and the type of the joint distribution of the outcomes

a class of proportional win fractions regression models for composite outcomes the win ratio is gaining traction as a simple and intuitive approach to analysis of prioritized composite endpoints in clinical trials to extend it from two sample comparison to regression we propose a novel class of semiparametric models that includes as special cases both the two sample win ratio and the traditional cox proportional hazards model on time to the first event under the assumption that the covariate specific win and loss fractions are proportional over time the regression coefficient is unrelated to the censoring distribution and can be interpreted as the log win ratio resulting from one unit increase in the covariate u statistic estimating functions in the form of an arbitrary covariate specific weight process integrated by a pairwise residual process are constructed to obtain consistent estimators for the regression parameter the asymptotic properties of the estimators are derived using uniform weak convergence theory for u processes visual inspection of a score process provides useful clues as to the plausibility of the proportionality assumption extensive numerical studies using both simulated and real data from a major cardiovascular trial show that the regression methods provide valid inference on covariate effects and outperform the two sample win ratio in both efficiency and robustness the proposed methodology is implemented in the r package wr publicly available from the comprehensive r archive network cran

on the orders of periodic diffeomorphisms of 4 manifolds this paper initiated an investigation on the following question sup pose a smooth 4 manifold does not admit any smooth circle actions does there exist a constant c 0 such that the manifold support no smooth zp actions of prime order for p c we gave affirmative results to this question for the case of holomorphic and symplectic actions with an interesting finding that the constant c in the holomorphic case is topological in nature while in the symplectic case it involves also the smooth structure of the manifold

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

on the reducibility of moduli spaces of stable 2 bundles over an elliptic surface the aim of this note is to give an affirmative answer to a question raised by r friedman in l f more precisely let s be a generic regular elliptic surface which is moreover relatively minimal see l f for the precise meaning of s being generic let k be a positive integer and denote by ms k co or simply mk co the moduli space of 2 bundles g s with det 0 s and c2 g k which are stable relative to a k ihler form co on s here we talk of k ihler form in place of ample line bundle in the definition of stability for convenience for certain suitably chosen ks hler form co k depending on k friedman has obtained in f a number of results on the moduli spaces ms k co k for instance it is shown in the case when s is free of multiple fibre the moduli space ms k 2 k is irreducible this is no longer the case however if s sp has a single multiple fibre of odd multiplicity p in fact in such situations it p l is known msp k e k has exactly 2 components for all k 2 l pg sp it

on the alternative hypotheses for the win ratio we extend the results of luo et al 2015 biometrics 71 139 145 regarding the alternative hypotheses for the win ratio from hazard orders to the upper quadrant stochastic order on the plane this extension substantially widens the range of alternatives against which the win ratio is known to be consistent it incorporates alternatives induced by simple and popular copula models that are left out by the characterization of luo et al 2015 we also discuss how our results may be generalized to win ratios in multivariate and stratified settings

on the diffeomorphism groups of elliptic surfaces in this paper we determine for relatively minimal elliptic surfaces with positive euler number the image of the natural representation of the group of orientation preserving self diffeomorphisms on h the second homology group reduced modulo torsion to this end we construct as many embedded spheres of square 2 such that an isometry not induced from any combination of reflections at such spheres or from complex conjugation can be shown not to be induced from some diffeomorphism at all this is done with the help of seiberg witten invariants

symplectic 4 manifolds with kodaira dimension zero we discuss the notion of the kodaira dimension for symplectic manifolds in dimension 4 in particular we propose and partially verify betti number bounds for symplectic 4 manifolds with kodaira dimension zero

on green s functions and positive solutions for boundary value problems on time scales in this paper we offer a form of self adjoint differential equations on time scales so that the associated green s function is found symmetric in the usual sense for this purpose together with the delta derivative we employ the nabla derivative as well we introduce the concepts of lebesgue delta and nabla integrals on time scales next sign properties of the green s function are investigated and existence results for positive solutions of nonlinear boundary value problems are established upper and lower bounds for these positive solutions also are given

the homotopy lie algebra of symplectomorphism groups of 3 fold blow ups of the projective plane by a result of kedra and pinsonnault we know that the topology of groups of symplectomorphisms of symplectic 4 manifolds is complicated in general however in all known very specific examples the rational cohomology rings of symplectomorphism groups are finitely generated in this paper we compute the rational homotopy lie algebra of symplectomorphism groups of the 3 point blow up of the projective plane with an arbitrary symplectic form and show that in some cases depending on the sizes of the blow ups it is infinite dimensional moreover we explain how the topology is generated by the toric structures one can put on the manifold our method involve the study of the space of almost complex structures compatible with the symplectic structure and it depends on the inflation technique of lalonde mcduff

exact lagrangians in a_n surface singularities in this paper we classify lagrangian spheres in a n surface singularities up to hamiltonian isotopy combining with a result of ritter geom funct anal 20 3 779 816 2010 this yields a complete classification of exact lagrangians in a n surface singularities our main new tool is the application of a technique which we call ball swappings and its relative version

obstructing pseudoconvex embeddings and contractible stein fillings for brieskorn spheres abstract a question in low dimensional symplectic topology asks whether every compact contractible 4 manifold admits the structure of a stein domain a related conjecture due to gompf asserts that no nontrivial brieskorn homology sphere admits a pseudoconvex embedding in c 2 with either orientation we give the first known example of a contractible boundary irreducible 4 manifold that admits no stein structure with either orientation though its boundary has stein fillings with both orientations we also verify gompf s conjecture with one orientation for a family of brieskorn spheres of which some are known to admit a smooth embedding in c 2 a byproduct of our example is the construction of a cork that does not admit a stein structure with either orientation

enumerative geometry of calabi yau 4 folds gromov witten theory is used to define an enumerative geometry of curves in calabi yau 4 folds the main technique is to find exact solutions to moving multiple cover integrals the resulting invariants are analogous to the bps counts of gopakumar and vafa for calabi yau 3 folds we conjecture the 4 fold invariants to be integers and expect a sheaf theoretic explanation

the embedding capacity of 4 dimensional symplectic ellipsoids this paper calculates the function c a whose value at a is the inmum of the size of a ball that contains a symplectic image of the ellipsoide 1 a here a 1 is the ratio of the area of the large axis to that of the smaller axis the structure of the graph of c a is surprisingly rich the volume constraint implies that c a is always greater than or equal to the square root of a and it is not hard to see that this is equality for large a however for a less than the fourth power 4 of the golden ratio c a is piecewise linear with graph that alternately lies on a line through the origin and is horizontal we prove this by showing that there are exceptional curves in blow ups of the complex projective plane whose homology classes are given by the continued fraction expansions of ratios of fibonacci numbers on the interval 4 7 we nd c a a 1 3 for a 7 the function c a coincides with the square root except on a nite number of intervals where it is again piecewise linear the embedding constraints coming from embedded contact homology give rise to another capacity function cech which may be computed by counting lattice points in appropriate right angled triangles according to hutchings and taubes the functorial properties of embedded contact homology imply that cech a c a for all a we show here that cech a c a for all a

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

surgery in cusp neighborhoods and the geography of irreducible 4 manifolds since its inception the theory of smooth 4 manifolds has relied upon complex surface theory to provide its basic examples this is especially true for simply connected 4 manifolds a longstanding conjecture held that every smooth simply connected closed 4 manifold is the connected sum of manifolds each admitting a complex structure with one of its orientations for this conjecture the 4 sphere was considered as the empty connected sum quite recently this was disproved by gompf and mrowka gm1 who produced infinite families of examples of 4 manifolds homeomorphic to the k3 surface and which admit no complex structure with either orientation the discovery of these dramatic counterexamples to the h cobordism theorem in dimension 4 was the most recent success in a long line of applications of donaldson invariants to the study of smooth structures on 4 manifolds beginning with donaldson s d4 and followed by fm1 ko ov1 ov2 which depended on donaldson s f invariant or a suitable generalization and fmm dk e2 eo1 mn2 sa using donaldson s polynomial invariant a common thread running through many of these counterexamples to the h cobordism conjecture is the process of logarithmic transformation which introduces multiple fibres in an elliptic surface in controlled situations this process will change the diffeomorphism type of a given elliptic surface while keeping its homotopy type fixed taking advantage of the complex structure on an elliptic surface this change can often be detected by using the relationship between anti self dual connections over a complex surface and stable holomorphic bundles d2 an alternative and more differential geometric

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

higher order dynamic equations on measure chains wronskians disconjugacy and interpolating families of functions this paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations which cover simultaneously as special cases among others both differential equations and difference equations we also define markov fekete and descartes interpolating systems of functions the main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator the results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations

sturm liouville eigenvalue problems on time scales for sturm liouville eigenvalue problems on time scales with separated boundary conditions we give an oscillation theorem and establish rayleigh s principle our results not only unifly the corresponding theories for differential and difference equations but are also new in the discrete case

isotopy of symplectic balls gromov s radius and the structure of ruled symplectic 4 manifolds there are various criteria enriques castelnuovo mori in algebraic geometry of complex surfaces that characterize rational or ruled surfaces up to birationality mori s criterion in particular states that a minimal compact algebraic surface is biholomorphic to cp 2 or to a ruled rational or irrational surface exactly when it contains a curve of strictly positive chern index this criterion has been partly generalized to symplectic 4 manifold by mcduff who showed the following any symplectic 4 manifold which contains an embedded symplectic sphere or immersed with positive normal double points of chern index larger than i is symplectomorphic to a manifold obtained by blowing up a finite number of symplectic balls either on p2 with its standard kahler structure or on a symplectic s2 fibration over a closed oriented real surface we need the answer to the following two problems in order to complete the classification 1 the classification of irrational symplectic s2 fibrations is not complete the statement of theorem 1 3 of 1 9 is not correct in the irrational case in particular it does not fully take into account the kahler structures coming from the projectivization of non split holomorphic rank 2 bundles the sharpest results on this problem are those of the recent article 1 11 when the area of the base of a symplectic s2 fibration v co s o over a surface of genus g is sufficiently large with respect to the area of the fiber the cohomology class of a symplectic form determines its isotopy class and therefore determines the symplectic type of the manifold see theorem 1 2 below actually under this cohomological hypothesis the symplectic ruled manifold v o may be obtained by cutting and pasting from a rational ruled

properties of composite time to first event versus joint marginal analyses of multiple outcomes many clinical studies eg cardiovascular outcome trials investigate the effect of an intervention on multiple event time outcomes the most common method of analysis is a so called composite analysis of a composite outcome defined as the time to the first component event other approaches have been proposed including the win ratio or win difference for ordered outcomes and the application of the wei lachin test herein we assess the influence of the marginal and joint distributions of the component events and their correlation structures on the operating characteristics of these methods for the analysis of multiple events the operating characteristics are investigated using a bivariate exponential model with a shared frailty under which these properties are obtained in closed form while the composite time to first event analysis provides an unbiased test of the hypothesis of equality of the distribution of the time to first event we show that it can provide a biased test of the joint null hypothesis of equal marginal hazards when the correlation of event times differs between groups the same applies to the win ratio however the operating characteristics of the wei lachin or other tests of the joint equality of the marginal hazards are unaffected furthermore when the correlations are equal the wei lachin test is more powerful to detect a difference in marginal hazards than the composite analysis test careful consideration of the properties of the various methods for analysis of composite outcome measures are in order before adopting one as primary analysis in a clinical study