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Level Sets (level + set)
Terms modified by Level Sets Selected AbstractsPLUG-IN ESTIMATION OF GENERAL LEVEL SETSAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 1 2006Antonio Cuevas Summary Given an unknown function (e.g. a probability density, a regression function, ,) f and a constant c, the problem of estimating the level set L(c) ={f,c} is considered. This problem is tackled in a very general framework, which allows f to be defined on a metric space different from . Such a degree of generality is motivated by practical considerations and, in fact, an example with astronomical data is analyzed where the domain of f is the unit sphere. A plug-in approach is followed; that is, L(c) is estimated by Ln(c) ={fn,c}, where fn is an estimator of f. Two results are obtained concerning consistency and convergence rates, with respect to the Hausdorff metric, of the boundaries ,Ln(c) towards ,L(c). Also, the consistency of Ln(c) to L(c) is shown, under mild conditions, with respect to the L1 distance. Special attention is paid to the particular case of spherical data. [source] A CFL-like constraint for the fast marching method in inhomogeneous chemical kineticsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2008Ramón Escobedo Abstract Level sets and fast marching methods are a widely used technique for problems with moving interfaces. Chemical kinetics has been recently added to this family, for the description of reaction paths and chemical waves in homogeneous media, in which the velocity of the interface is described by a given field. A more general framework must consider variable velocities due to inhomogeneities induced by chemical changes. In this case, a constraint must be satisfied for the correct use of fast marching method. We deduce an analytical expression of this constraint when the Godunov scheme is used to solve the Eikonal equation, and we present numerical simulations of a case which must be enforced to obey the constraint. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Sub-Voxel Topology Control for Level-Set SurfacesCOMPUTER GRAPHICS FORUM, Issue 3 2003Stephan Bischoff Active contour models are an efficient, accurate, and robust tool for the segmentation of 2D and 3D image data. In particular, geometric deformable models (GDM) that represent an active contour as the level set of an implicitfunction have proven to be very effective. GDMs, however, do not provide any topology control, i.e. contours maymerge or split arbitrarily and hence change the genus of the reconstructed surface. This behavior is inadequate insettings like the segmentation of organic tissue or other objects whose genus is known beforehand. In this paperwe describe a novel method to overcome this limitation while still preserving the favorable properties of the GDMsetup. We achieve this by adding (sparse) topological information to the volume representation at locations whereit is necessary to locally resolve topological ambiguities. Since the sparse topology information is attached to theedges of the voxel grid, we can reconstruct the interfaces where the deformable surface touches itself at sub-voxelaccuracy. We also demonstrate the efficiency and robustness of our method. [source] Piecewise constant level set method for structural topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Peng Wei Abstract In this paper, a piecewise constant level set (PCLS) method is implemented to solve a structural shape and topology optimization problem. In the classical level set method, the geometrical boundary of the structure under optimization is represented by the zero level set of a continuous level set function, e.g. the signed distance function. Instead, in the PCLS approach the boundary is described by discontinuities of PCLS functions. The PCLS method is related to the phase-field methods, and the topology optimization problem is defined as a minimization problem with piecewise constant constraints, without the need of solving the Hamilton,Jacobi equation. The result is not moving the boundaries during the iterative procedure. Thus, it offers some advantages in treating geometries, eliminating the reinitialization and naturally nucleating holes when needed. In the paper, the PCLS method is implemented with the additive operator splitting numerical scheme, and several numerical and procedural issues of the implementation are discussed. Examples of 2D structural topology optimization problem of minimum compliance design are presented, illustrating the effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd. [source] ODDLS: A new unstructured mesh finite element method for the analysis of free surface flow problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2008Julio Garcia-Espinosa Abstract This paper introduces a new stabilized finite element method based on the finite calculus (Comput. Methods Appl. Mech. Eng. 1998; 151:233,267) and arbitrary Lagrangian,Eulerian techniques (Comput. Methods Appl. Mech. Eng. 1998; 155:235,249) for the solution to free surface problems. The main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem. The aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids. Free surface capturing is based on the solution to a level set equation. The Navier,Stokes equations are solved using an iterative monolithic predictor,corrector algorithm (Encyclopedia of Computational Mechanics. Wiley: New York, 2004), where the correction step is based on imposing the divergence-free condition in the velocity field by means of the solution to a scalar equation for the pressure. Examples of application of the ODDLS formulation (for overlapping domain decomposition level set) to the analysis of different free surface flow problems are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] Numerical simulation of free-surface flow using the level-set method with global mass correctionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Yali Zhang Abstract A new numerical method that couples the incompressible Navier,Stokes equations with the global mass correction level-set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier,Stokes equations with the two-step projection method on a staggered Cartesian grid. The free-surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third-order essentially non-oscillatory schemes and a five stage Runge,Kutta method, to accomplish advection and re-distancing of the level-set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS-VOF method. The simulations reveal some interesting free-surface phenomena such as the free-surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. Copyright © 2009 John Wiley & Sons, Ltd. [source] A level set-based immersed interface method for solving incompressible viscous flows with the prescribed velocity at the boundaryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010Zhijun Tan Abstract A second-order accurate immersed interface method (IIM) is presented for solving the incompressible Navier,Stokes equations with the prescribed velocity at the boundary, which is an extension of the IIM of Le et al. (J. Comput. Phys. 2006; 220:109,138) to a level set representation of the boundary in place of the Lagrangian representation of the boundary using control points on a uniform Cartesian grid. In order to enforce the prescribed velocity boundary condition, the singular forces at the immersed boundary are applied on the fluid. These forces are related to the jump in pressure and the jumps in the derivatives of both the pressure and velocity, and are approximated via using the local Hermite cubic spline interpolation. The strength of singular forces is determined by solving a small system of equations at each time step. The Navier,Stokes equations are discretized via using finite difference method with the incorporation of jump conditions on a staggered Cartesian grid and solved by a second-order accurate projection method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate the viscous flows in irregular domains. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Lagrangian level-set approach for the simulation of incompressible two-fluid flows,INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10-11 2005F. S. Sousa Abstract A Lagrangian level-set method to solve incompressible two-dimensional two-fluid flows is presented. The Navier,Stokes equations are discretized by a Galerkin finite element method. A projection method is employed to decouple the system of non-linear equations. The interface between fluids is represented by the zero level set of a function , plus additional marker points of the computational mesh. In the standard Eulerian level-set method, this function is advected through the domain by solving a pure advection equation. To reduce mass conservation errors that can arise from this step, our method employs a Lagrangian technique which moves the nodes of the finite element mesh, and consequently, the information stored in each node. The quality of the mesh is controlled by a remeshing procedure, avoiding bad triangles by flipping edges, inserting or removing vertices from the triangulation. Results of numerical simulations are presented, illustrating the improvements in mass conservation and accuracy of this new methodology. Copyright © 2005 John Wiley & Sons, Ltd. [source] Influence of psychosocial factors on the development of sleep bruxism among childrenINTERNATIONAL JOURNAL OF PAEDIATRIC DENTISTRY, Issue 5 2009JUNIA M. SERRA-NEGRA Background., Bruxism is described as an orofacial parafunction that affects both children and adults. The maintenance of the childhood habit into adulthood may compromise health. As there are few studies on this issue, there is a need for further research on sleep bruxism among children. Aim., The aim of this study was to assess the prevalence of sleep bruxism in children and the influence of psychosocial factors. Methods., A cross-sectional study was carried out on 652 randomly selected children aged 7,10 years at public and private schools in Belo Horizonte, Brazil. The instruments used were: questionnaire for parents, Child Stress Scale, and the scales on neuroticism and responsibility from the prevalidated Big Five Questionnaire for Children. Psychological tests were administered and evaluated by psychologists. Sleep bruxism among children was reported by parents. The Social Vulnerability Index from the city hall database was used to determine the social classification of the families. The chi-squared test, binary and multivariate logistic regressions were used, with the significance level set at 5%. Results., A 35.3% prevalence of bruxism was found. No association was found between bruxism and stress, gender, age, or social vulnerability. The adjusted logistic model determined that children with high levels of neuroticism (OR = 1.9, CI 1.3,2.6) and responsibility (OR = 2.2, CI 1.0,5.0) are twice as likely to have the habit of sleep bruxism when compared to those who have low levels of these personality traits. Conclusions., A high degree of responsibility and neuroticism, which are individual personality traits, are determinant factors for the development of sleep bruxism among children. [source] Microbiological survey of prepackaged pâté and ham in New ZealandLETTERS IN APPLIED MICROBIOLOGY, Issue 2 2005T.L. Wong Abstract Aims:, To gauge the effectiveness of pâté and ham manufacturers' management of the microbial safety and quality of their products. Methods and Results:, A survey of 60 batches of prepackaged pâté showed that 41·7% of the batches had aerobic plate counts (APC) exceeding 105 CFU g,1, one of pâté sample contained a Bacillus cereus count of >5000 CFU g,1 and another contained 1700 CFU g,1 of Listeria monocytogenes. No other pathogens were isolated from any of the samples. The survey of prepackaged ham showed that only 1% (1/104) of the ham samples were positive for L. monocytogenes (50 CFU g,1). Conclusions:, The presence of microbial hazards in these foods has generally declined since the early 1990s in New Zealand. Noncomplying APC levels may be due to an over-estimation of product shelf life or poor food handling practices during manufacture. Significance and Impact of the Study:, Few of the samples tested contained pathogens at significant levels. The prevalences of L. monocytogenes in pâté and ham were low. The presence of 1700 CFU g,1 of L. monocytogenes in a pâté sample indicates that occasionally, the population can be exposed to levels of L. monocytogenes above the zero tolerance level set in New Zealand. [source] Determination of a controllable set for a class of non-linear stochastic control systemsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 3 2003Yazeng Liu Abstract A controllable set of a class of non-linear stochastic control systems to a given set is defined. A value function associated with an optimal control problem is introduced. Under some reasonable conditions, the controllable set is characterized by a level set of the viscosity solution of a Hamilton,Jacobi,Bellman equation. Copyright © 2003 John Wiley & Sons, Ltd. [source] Inverse problem in seismic imagingPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007Maria Cameron We address the problem of estimating sound speeds (seismic velocities) inside the earth which is necessary for obtaining seismic images in regular Cartesian coordinates. The main goals are to develop algorithms to convert time migration velocities to true seismic velocities, and to convert time-migrated images to depth images in regular Cartesian coordinates. Our main results are three-fold. First, we establish a theoretical relation between the seismic velocities and the time migration velocities using the paraxial ray tracing theory. Second, we formulate an appropriate inverse problem describing the relation between time migration velocities and depth velocities and show that this problem is mathematically ill-posed, i.e., unstable to small perturbations. Third, we develop numerical algorithms to solve regularized versions of these equations which can be used to recover smoothed velocity variations. Our algorithms consist of efficient time-to-depth conversion algorithms based on Dijkstra-like Fast Marching Methods, as well as level set and ray tracing algorithms for transforming Dix velocities into seismic velocities. Our algorithms are applied to both two-dimensional and three-dimensional problems and we test them on a collection of both synthetic examples and field data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Behavior of the Electrocardiographic T Peak to End Interval in ChildhoodANNALS OF NONINVASIVE ELECTROCARDIOLOGY, Issue 1 2010Abraham Benatar M.B., Ch.B., F.A.C.C., F.C.P.(S.A.), Ph.D. Background: The T-wave peak to T-wave end (TpTe) interval reflects spatial and transmural dispersion in repolarization and serves as an arrhythmogenic index. Normal TpTe interval data in children are lacking. We evaluated the effects of age, gender, heart rate, leads (II and V5) on TpTe and T-wave voltage. Methods: Four hundred healthy children (age 4 days to 16.7 years) were enrolled. From a resting 12-lead digital ECG, TpTe, RR, QT, JT intervals, and T amplitude were measured (leads II and V5). Bazett and Fridericia formulas were applied to TpTe for heart rate correction and TpTe/QT and TpTe/JT were calculated. Descriptive and analytical statistics were applied, significance level set at P , 0.05. Results: TpTe in leads II and V5 correlate well. Contrary to adults, no gender differences in TpTe were observed in childhood. TpTe lengthens with increasing age, and is inversely related to heart rate. TpTe 98th percentile is 85 msec in first 5 years, increasing to 92 msec in adolescence. TpTe Fridericia is a good correction formula in childhood; TpTe Bazett overcorrects in the younger age. TpTe/QT and TpTe/JT are longer in younger subjects due to greater QT shortening than the TpTe interval at higher heart rates. Conclusions: In children, TpTe in lead II and V5 correlate well. The TpTe interval lengthens with advancing age as heart rate diminishes. TpTe Fridericia is a good correction formula in children. Younger subjects have higher TpTe/QT and TpTe/JT indices compared to older children. T-wave voltage increases with age, tallest in the 5,10-year-age group particularly in V5. Ann Noninvasive Electrocardiol 2010;15(1):11,16 [source] Particle Level Set Advection for the Interactive Visualization of Unsteady 3D FlowCOMPUTER GRAPHICS FORUM, Issue 3 2008Nicolas Cuntz Abstract Typically, flow volumes are visualized by defining their boundary as iso-surface of a level set function. Grid-based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particle-based methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advantages of both approaches by interchanging the information between the grid and the particles. Our work demonstrates that the PLS technique can be adapted to volumetric dye advection via streak volumes, and to the visualization by time surfaces and path volumes. We achieve this with a modified and extended PLS, including a model for dye injection. A new algorithmic interpretation of PLS is introduced to exploit the efficiency of the GPU, leading to interactive visualization. Finally, we demonstrate the high quality and usefulness of PLS flow visualization by providing quantitative results on volume preservation and by discussing typical applications of 3D flow visualization. [source] Extraction of media and plaque boundaries in intravascular ultrasound images by level sets and min/max flowEXPERT SYSTEMS, Issue 2 2010Ali Iskurt Abstract: Estimation of the plaque area in intravascular ultrasound images after extraction of the media and plaque,lumen interfaces is an important application of computer-aided diagnosis in medical imaging. This paper presents a novel system for fully automatic and fast calculation of plaque quantity by capturing the surrounding ring called media. The system utilizes an algorithm that consists of an enhanced technique for noise removal and a method of detecting different iso levels by sinking the image gradually under zero level. Moreover, an important novelty with this technique is the simultaneous extraction of media and lumen,plaque interfaces at satisfactory levels. There are no higher dimensional surfaces and evolution of contours, stopping at high image gradients. Thus, the system runs really fast with curvature velocity only and has no complexity. Experiments also show that this shape-recovering curvature term not only removes the noisy behaviour of ultrasound images but also strengthens very weak boundaries and even completes the missing walls of the media. In addition, the lumen,plaque interface can be detected simultaneously. For validation, a new and very useful algorithm is developed for labelling of intravascular ultrasound images, taken from video sequences of 15 patients, and a comparison-based verification is done between manual contours by experts and the contours extracted by our system. [source] A partition-of-unity-based finite element method for level setsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2008Stéphane Valance Abstract Level set methods have recently gained much popularity to capture discontinuities, including their possible propagation. Typically, the partial differential equations that arise in level set methods, in particular the Hamilton,Jacobi equation, are solved by finite difference methods. However, finite difference methods are less suited for irregular domains. Moreover, it seems slightly awkward to use finite differences for the capturing of a discontinuity, while in a subsequent stress analysis finite elements are normally used. For this reason, we here present a finite element approach to solving the governing equations of level set methods. After a review of the governing equations, the initialization of the level sets, the discretization on a finite domain, and the stabilization of the resulting finite element method will be discussed. Special attention will be given to the proper treatment of the internal boundary condition, which is achieved by exploiting the partition-of-unity property of finite element shape functions. Finally, a quantitative analysis including accuracy analysis is given for a one-dimensional example and a qualitative example is given for a two-dimensional case with a curved discontinuity. Copyright © 2008 John Wiley & Sons, Ltd. [source] Arbitrary discontinuities in space,time finite elements by level sets and X-FEMINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Jack Chessa Abstract An enriched finite element method with arbitrary discontinuities in space,time is presented. The discontinuities are treated by the extended finite element method (X-FEM), which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper-surface which is described by level sets. A space,time weak form for conservation laws is developed where the Rankine,Hugoniot jump conditions are natural conditions of the weak form. The method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non-linear Burgers' equations. By capturing the discontinuity in time as well as space, results are improved over capturing the discontinuity in space alone and the method is remarkably accurate. Implications to standard semi-discretization X-FEM formulations are also discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] Convexity in x of the level sets of the first Dirichlet eigenfunctionMATHEMATISCHE NACHRICHTEN, Issue 13-14 2007Chie-Ping ChuArticle first published online: 7 SEP 200 Abstract On a planar domain which is convex in x, the level sets of the first Dirichlet eigenfunction for Laplacian are also convex in x. This gives an affirmative answer to a conjecture proposed by B. Kawohl. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Projected Gradient Flows for BV/Level Set RelaxationPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2005Martin Burger This paper introduces a new level set method based on projected gradient flows for problems that can be solved by a recently introduced relaxation approach. For the class of problems the relaxation is exact, it can be shown that the solution of the flow converges to a solution of the relaxed problem for large time, and the level sets of the limit are solutions of the original problem. We introduce a simple computational scheme based on explicit time discretization and apply the method to imaging examples. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Gaussian curvature estimates for the convex level sets of p -harmonic functionsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 7 2010Xi-Nan Ma We give a positive lower bound for the Gaussian curvature of the convex level sets of p -harmonic functions with the Gaussian curvature of the boundary and the norm of the gradient on the boundary. Combining the deformation process, this estimate gives a new approach to studying the convexity of the level sets of the p -harmonic function. © 2010 Wiley Periodicals, Inc. [source] Anisotropic smoothness spaces via level setsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 9 2008Ronald A. DeVore It has been understood for sometime that the classical smoothness spaces, such as the Sobolev and Besov classes, are not satisfactory for certain problems in image processing and nonlinear PDEs. Their deficiency lies in their isotropy. Functions in these smoothness spaces must be simultaneously smooth in all directions. The anisotropic generalizations of these spaces also have the deficiency that they are biased in coordinate directions. While they allow different smoothness in certain directions, these directions must be aligned to the coordinate axes. In the application areas mentioned above, it would be desirable to measure smoothness in new ways that would allow one to have more local control over the smoothness directions. We introduce one possible approach to this problem based on defining smoothness via level sets. We present this approach in the case of functions defined on ,d. Our smoothness spaces depend on two smoothness indices (s1, s2). The first reflects the smoothness of the level sets of the function, while the second index reflects how smoothly the level sets themselves are changing. As a motivation, we start with d = 2 and investigate Besov smooth domains. © 2007 Wiley Periodicals, Inc. [source] Postoperative serum carcinoembryonic antigen levels in patients with pathologic stage IA nonsmall cell lung carcinomaCANCER, Issue 4 2004Subnormal levels as an indicator of favorable prognosis Abstract BACKGROUND Elevated serum carcinoembryonic antigen (CEA) levels are sometimes attributable to the production of CEA by malignant cells, and in turn, the antigen itself can enhance the metastatic potential of malignant cells. The authors speculated that low serum CEA levels might be indicative of relatively low levels of malignant cells and a low probability of disease recurrence. This hypothesis led them to investigate whether low CEA levels in serum represented a useful prognostic factor for patients with pathologic Stage IA nonsmall cell lung carcinoma. METHODS Between 1993 and 2001, 724 patients underwent surgery for NSCLC at Toneyama National Hospital (Toyonaka, Japan). Of these patients, the 242 who were diagnosed with pathologic Stage IA disease were included in the current study. Smoking behavior, gender, age, tumor diameter, disease histology, and preoperative and postoperative serum CEA levels were chosen as study variables, with the cutoff level between subnormal and normal serum CEA levels set at 2.5 ng/mL and the cutoff level between normal and high serum CEA levels set at 5.0 ng/mL. Prognostic indicators were evaluated using a Cox hazard model. In addition, survival probabilities were calculated using the Kaplan,Meier method, and differences in survival were assessed by log-lank analysis. RESULTS Subnormal postoperative serum CEA levels were found to be an independent prognostic indicator (hazard ratio, 2.3; 95% confidence interval, 1.1,4.7; P = 0.03 for comparison with patients who had normal CEA levels) on multivariate analysis. Furthermore, the 5-year survival rate was 87% for patients with subnormal postoperative CEA levels (n = 146), compared with 75% for patients with normal postoperative CEA levels (n = 80) and 53% for patients with high postoperative CEA levels (n = 16) (P < 0.0001). CONCLUSIONS Among patients with pathologic Stage IA NSCLC, those who had an extremely favorable prognosis were distinguished by their subnormal postoperative serum CEA levels. Cancer 2004. © 2004 American Cancer Society. [source] | |||||||||||||||||||