a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

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

a proportional hazards model for arbitrarily censored and truncated data turnbull 1976 journal of royal statistical society series b 38 290 295 proposed a method for nonparametric estimation of the distribution function when the data are incomplete because of censoring and truncation however as noted by frydman 1994 journal of royal statistical society series b 56 71 74 turnbull s method has to be modified to accommodate both truncation and censoring this paper presents a detailed correction of turnbull s method and an extension to the regression analysis a method of fitting the proportional hazards model for arbitrarily censored and truncated data is developed the method allows partial testing for zero regression coefficients the test can be performed using the likelihood ratio test or the wald test the methodology is applied to estimate the distribution of the induction time of patients diagnosed with transfusion associated aids and to estimate the distribution of time from diabetes onset to development of diabetic nephropathy for insulin dependent diabetics

weighted logrank tests for interval censored data when assessment times depend on treatment we consider weighted logrank tests for interval censored data when assessment times may depend on treatment and for each individual we only use the two assessment times that bracket the event of interest it is known that treating finite right endpoints as observed events can substantially inflate the type i error rate under assessment treatment dependence atd but the validity of several other implementations of weighted logrank tests score tests permutation tests multiple imputation tests has not been studied in this situation with a bounded number of unique assessment times the score test under the grouped continuous model retains the type i error rate asymptotically under atd however although the approximate permutation test based on the permutation central limit theorem is not asymptotically valid under every atd scenario we show through simulation that in many atd scenarios it retains the type i error rate better than the score test we show a case where the approximate permutation test retains the type i error rate when the exact permutation test does not we study and modify the multiple imputation logrank tests of huang lee and yu 2008 statistics in medicine 27 3217 3226 showing that the distribution of the rank like scores asymptotically does not depend on the assessment times we show through simulations that our modifications of the multiple imputation logrank tests retain the type i error rate in all cases studied even with atd and a small number of individuals in each treatment group simulations were performed using the interval r package us government work in the public domain

an iterated radau method for time dependent pdes this paper is concerned with the time integration of semi discretized multi dimensional pdes of advection diffusion reaction type to cope with the stiffness of these odes an implicit method has been selected viz the two stage third order radau iia method the main topic of this paper is the efficient solution of the resulting implicit relations first a modified newton process has been transformed into an iteration process in which the 2 stages are decoupled and moreover can exploit the same lu factorization of the iteration matrix next we apply a so called approximate matrix factorization amf technique to solve the linear systems in each newton iteration this amf approach is very efficient since it reduces the multi dimensional system to a series of one dimensional systems the total amount of linear algebra work involved is reduced enormously by this approach the idea of applying amf to two dimensional problems is quite old and goes back to peaceman and rachford in the early fifties the situation in three space dimensions is less favourable and will be analyzed here in more detail both theoretically and experimentally furthermore we analyze a variant in which the amf technique has been used to really solve until convergence the underlying radau iia method so that we can rely on its excellent stability and accuracy characteristics finally the method has been tested on several examples also a comparison has been made with the existing codes vodpk and imexrkc and the efficiency cpu time versus accuracy is shown to be at least competitive with the efficiency of these solvers

irkc an imex solver for stiff diffusion reaction pdes the fortran 90 code irkc is intended for the time integration of systems of partial differential equations pdes of diffusion reaction type for which the reaction jacobian has real negative eigenvalues it is based on a family of implicit explicit runge kutta chebyshev methods which are unconditionally stable for reaction terms and which impose a stability constraint associated with the diffusion terms that is quadratic in the number of stages special properties of the family make it possible for the code to select at each step the most efficient stable method as well as the most efficient step size moreover they make it possible to apply the methods using just a few vectors of storage a further step towards minimal storage requirements and optimal efficiency is achieved by exploiting the fact that the implicit terms originating from the stiff reactions are not coupled over the spatial grid points hence the systems to be solved have a small dimension viz equal to the number of pdes these characteristics of the code make it especially attractive for problems in several spatial variables irkc is a successor to the rkc code b p sommeijer l f shampine j g verwer rkc an explicit solver for parabolic pdes j comput appl math 88 1997 315 326 that solves similar problems without stiff reaction terms

error estimators for stiff differential equations abstract when solving ordinary differential equations numerically the local error is estimated at each step in the classical situation of small step sizes it is clear what is required of the error estimators stiff problems are solved with large step sizes the quality of error estimators is studied in this situatuion and it is shown how to modify unsatisfactory estimators so as to improve them greatly several formulas from the literature are treated as examples

nonparametric estimation of a markov illness death process from interval censored observations with application to diabetes survival data summary the nonparametric estimation of the cumulative transition intensity functions in a threestate time nonhomogeneous markov process with irreversible transitions an illness death model is considered when times of the intermediate transition e g onset of a disease are interval censored the times of death are assumed to be known exactly or to be rightcensored in addition the observed process may be left truncated data of this type arise when the process is sampled periodically for example when the patients are monitored through periodic examinations the observations on times of change in their disease status will be interval censored under the sampling scheme considered here the nelson aalen estimator aalen 1978 for a cumulative transition intensity is not applicable in the proposed method the maximum likelihood estimators of some of the transition intensities are derived from the estimators of the corresponding subdistribution functions the maximum likelihood estimators are shown to have a self consistency property the self consistency algorithm is developed for the computation of the estimators this approach generalises the results from turnbull 1976 and frydman 1992 the methods are illustrated with diabetes survival data

a semiparametric proportional odds regression model for the analysis of current status data abstract an approach to covariate analysis of current status data is described the method is applicable when the logit of the conditional probability of survival given the covariates is some increasing function of time plus a linear combination of the covariates the approach is based on approximating the infinite dimensional nuisance parameter the baseline log odds of failure with a step function and carrying out a maximum likelihood procedure the resulting finite dimensional parameter estimates for the regression parameters are shown to be asymptotically normal and semiparametric efficient numerical studies with small and moderate samples are discussed

regression analysis of interval censored survival data with covariates using log linear models we considered the regression analysis of the event time data with left right or interval censored observations we extended life table techniques for censored survival data using log linear models to incorporate interval censored failures the em algorithm was used to calculate maximum likelihood estimates for the parameters we assumed that the hazard function was a stepwise function over disjoint intervals of time thus the nonparametric model the parametric exponential model and the semiparametric cox proportional hazard model were easily implemented as special cases we adapted the restricted em algorithm to test hypotheses and to construct confidence intervals for the parameters these methods were applied in an analysis of the recurrence time for treated melanoma patients

a class of high order runge kutta chebyshev stability polynomials the analytic form of a new class of factorized runge kutta chebyshev frkc stability polynomials of arbitrary order n is presented roots of frkc stability polynomials of degree l m n are used to construct explicit schemes comprising l forward euler stages with internal stability ensured through a sequencing algorithm which limits the internal amplification factors to l 2 the associated stability domain scales as m 2 along the real axis marginally stable real valued points on the interior of the stability domain are removed via a prescribed damping procedure by construction frkc schemes meet all linear order conditions for nonlinear problems at orders above 2 complex splitting or butcher series composition methods are required linear order conditions of the frkc stability polynomials are verified at orders 2 4 and 6 in numerical experiments comparative studies with existing methods show the second order unsplit frkc2 scheme and higher order 4 and 6 split frkcs schemes are efficient for large moderately stiff problems

regression analysis of failure time data with informative interval censoring interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed most existing approaches for analysing interval censored failure time data assume that the censoring mechanism is independent of the true failure time however there are situations where this assumption may not hold in this paper we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed the method makes use of the proportional hazards frailty model and an em algorithm is presented for estimation finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an aids study

two classes of implicit explicit multistep methods for nonlinear stiff initial value problems the initial value problems of nonlinear ordinary differential equations which contain stiff and nonstiff terms often arise from many applications in order to reduce the computation cost implicit explicit imex methods are often applied to these problems i e the stiff and non stiff terms are discretized by using implicit and explicit methods respectively in this paper we mainly consider the nonlinear stiff initial value problems satisfying the one sided lipschitz condition and a class of singularly perturbed initial value problems and present two classes of the imex multistep methods by combining implicit one leg methods with explicit linear multistep methods and explicit one leg methods respectively the order conditions and the convergence results of these methods are obtained some efficient methods are constructed some numerical examples are given to verify the validity of the obtained theoretical results

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

an implicit explicit runge kutta chebyshev scheme for diffusion reaction equations an implicit explicit imex extension of the explicit runge kutta chebyshev rkc scheme designed for parabolic pdes is proposed for diffusion reaction problems with severely stiff reaction terms the imex scheme treats these reaction terms implicitly and diffusion terms explicitly within the setting of linear stability theory the new imex scheme is unconditionally stable for reaction terms having a jacobian matrix with a real spectrum for diffusion terms the stability characteristics remain unchanged a numerical comparison for a stiff nonlinear radiation diffusion problem between an rkc solver an imex rkc solver and the popular implicit bdf solver vodpk using the krylov solver gmres illustrates the excellent performance of the new scheme

a flexible computationally efficient method for fitting the proportional hazards model to interval censored data the proportional hazards model ph is currently the most popular regression model for analyzing time to event data despite its popularity the analysis of interval censored data under the ph model can be challenging using many available techniques this article presents a new method for analyzing interval censored data under the ph model the proposed approach uses a monotone spline representation to approximate the unknown nondecreasing cumulative baseline hazard function formulating the ph model in this fashion results in a finite number of parameters to estimate while maintaining substantial modeling flexibility a novel expectation maximization em algorithm is developed for finding the maximum likelihood estimates of the parameters the derivation of the em algorithm relies on a two stage data augmentation involving latent poisson random variables the resulting algorithm is easy to implement robust to initialization enjoys quick convergence and provides closed form variance estimates the performance of the proposed regression methodology is evaluated through a simulation study and is further illustrated using data from a large population based randomized trial designed and sponsored by the united states national cancer institute

high order upwind compact finite difference lattice boltzmann method for viscous incompressible flows abstract in this work a high order upwind compact finite difference lattice boltzmann method ucdlbm is developed to efficiently solve viscous incompressible flow problems a fifth order upwind compact difference scheme is adopted to discretize the spatial derivatives of the lattice boltzmann equation and the third order total variation diminishing runge kutta scheme is utilized for the discretization of the temporal term compared to the existing central compact finite difference lattice boltzmann method cfdlbm the present ucdlbm can prevent non physical oscillations without filtering due to the natural dissipative property of upwind schemes three benchmark problems involving the taylor green vortex problem the doubly periodic shear layer flow problem and the lid driven square cavity flow problem are numerically solved to demonstrate the accuracy and efficiency of the present method numerical results computed are in good agreement with the analytical solution or other available numerical results and the present ucdlbm is less time consuming than the cfdlbm without degenerating the order of accuracy of the numerical solutions

a local likelihood proportional hazards model for interval censored data we discuss the use of local likelihood methods to fit proportional hazards regression models to right and interval censored data the assumed model allows for an arbitrary smoothed baseline hazard on which a vector of covariates operates in a proportional manner and thus produces an interpretable baseline hazard function along with estimates of global covariate effects for estimation we extend the modified em algorithm suggested by betensky lindsey ryan and wand we illustrate the method with data on times to deterioration of breast cosmeses and hiv 1 infection rates among haemophiliacs

rank based inference in the proportional hazards model for interval censored data summary a marginal likelihood approach to fitting the proportional hazards model to interval censored or grouped data is proposed this approach maximises a likelihood that is the sum over all rankings of the data that are consistent with the observed censoring intervals as in the usual proportional hazards model the method does not require specification of the baseline hazard function the score equations determining the maximum marginal likelihood estimator can be written as the expected value of the score of the usual proportional hazards model with respect to a certain distribution of rankings a gibbs sampling scheme is given to generate rankings from this distribution and stochastic approximation is used to solve the score equations simulation results under various censoring schemes give point estimates that are close to estimates obtained using actual failure times

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

numerical approximation of turing patterns in electrodeposition by adi methods in this paper we study the numerical approximation of turing patterns corresponding to steady state solutions of a pde system of reaction diffusion equations modeling an electrodeposition process we apply the method of lines mol and describe the semi discretization by high order finite differences in space given by the extended central difference formulas ecdfs that approximate neumann boundary conditions bcs with the same accuracy we introduce a test equation to describe the interplay between the diffusion and the reaction time scales we present a stability analysis of a selection of time integrators imex 2 sbdf method crank nicolson cn alternating direction implicit adi method for the test equation as well as for the schnakenberg model prototype of nonlinear reaction diffusion systems with turing patterns eventually we apply the adi ecdf schemes to solve the electrodeposition model until the stationary patterns spots worms and only spots are reached we validate the model by comparison with experiments on cu film growth by electrodeposition

ignorability and coarse data we present a general statistical model for data coarsening which includes as special cases rounded heaped censored partially categorized and missing data formally with coarse data observations are made not in the sample space of the random variable of interest but rather in its power set grouping is a special case in which the degree of coarsening is known and nonstochastic we establish simple conditions under which the possible stochastic nature of the coarsening mechanism can be ignored when drawing bayesian and likelihood inferences and thus the data can be validly treated as grouped data the conditions are that the data be coarsened at random a generalization of the condition missing at random and that the parameters of the data and the coarsening process be distinct applications of the general model and the ignorability condition are illustrated in a numerical example and described briefly in a variety of special cases

a weighted logistic regression model for estimation of recurrence of adenomas in a colorectal polyp prevention trial some participants might have their follow up colonoscopy conducted before the scheduled time i e at the end of the trial this results in variable follow up lengths for participants and the data of recurrence status at the end of the trial can be considered as current status data in this paper we use a weighted logistic regression model to estimate recurrence rate of adenoma data at the end of the trial the weights are used to adjust for variable follow up we show that logistic regression tends to underestimate recurrence rate in a simulation study we show that kaplan meier estimator derived from the right endpoint of the current status data tends to overestimate recurrence rate in contrast to logistic regression and the weighted logistic regression method can produce reasonable estimates of recurrence rate even under a high non compliance rate compared to conventional logistic regression and kaplan meier estimator the method described here is illustrated with an example from a colon cancer study

finite difference lattice boltzmann methods for binary fluids we investigate two fluid bhatnagar gross krook bgk kinetic methods for binary fluids the developed theory works for asymmetric as well as symmetric systems for symmetric systems it recovers sirovich s theory and is summarized in models a and b for asymmetric systems it contributes models c d and e which are especially useful when the total masses and or local temperatures of the two components are greatly different the kinetic models are discretized based on an octagonal discrete velocity model the discrete velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations the combination of a discrete velocity kinetic model and an appropriate finite difference scheme composes a finite difference lattice boltzmann method the validity of the formulated methods is verified by investigating i uniform relaxation processes ii isothermal couette flow and iii diffusion behavior

implementation of a high order compact finite difference lattice boltzmann method in generalized curvilinear coordinates abstract in this work the implementation of a high order compact finite difference lattice boltzmann method cfdlbm is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non uniform grids the incompressible form of the discrete boltzmann equation with the bhatnagar gross krook bgk approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates herein the spatial derivatives in the resulting lattice boltzmann lb equation in the computational plane are discretized by using the fourth order compact finite difference scheme and the temporal term is discretized with the fourth order runge kutta scheme to provide an accurate and efficient incompressible flow solver a high order spectral type low pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions flow non linearities and grid non uniformity all boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates the accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems a sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are unsteady couette flow and steady flow in a 2 d cavity with non uniform grid and steady and unsteady flows over a circular cylinder and the naca0012 hydrofoil at different flow conditions results obtained for the above test cases are in good agreement with the existing numerical and experimental results the study shows the present solution methodology based on the implementation of the high order compact finite difference lattice boltzmann method cfdlbm in the generalized curvilinear coordinates is robust efficient and accurate for solving steady and unsteady incompressible flows over practical geometries

amf runge kutta formulas and error estimates for the time integration of advection diffusion reaction pdes the convergence of a family of amf runge kutta methods in short amf rk for the time integration of evolutionary partial differential equations pdes of advection diffusion reaction type semi discretized in space is considered the methods are based on very few inexact newton iterations applied to implicit runge kutta formulas by combining the use of a natural splitting for the underlying jacobians and the approximate matrix factorization amf technique this approach allows a very cheap implementation of the runge kutta formula under consideration particular amf rk methods based on radau iia formulas are considered these methods have given very competitive results when compared with important formulas in the literature for multidimensional systems of non linear parabolic pde problems uniform bounds for the global time space errors on semi linear pdes when simultaneously the time step size and the spatial grid resolution tend to zero are derived numerical illustrations supporting the theory are presented

a class of estimators of the survival function from interval censored data a model of interval censorship of a failure time t is considered when there is only one inspection time y the observable data are n independent copies of the pair y where t y we construct a class of self consistent estimators of the survival function of t defined implicitly through two equations and show their strong consistency under certain conditions the properties of the nonparametric maximum likelihood estimator are also investigated

chebyshev collocation spectral lattice boltzmann method for simulation of low speed flows in this study the chebyshev collocation spectral lattice boltzmann method ccslbm is developed and assessed for the computation of low speed flows both steady and unsteady flows are considered here the discrete boltzmann equation with the bhatnagar gross krook approximation based on the pressure distribution function is considered and the space discretization is performed by the chebyshev collocation spectral method to achieve a highly accurate flow solver to provide accurate unsteady solutions the time integration of the temporal term in the lattice boltzmann equation is made by the fourth order runge kutta scheme to achieve numerical stability and accuracy physical boundary conditions based on the spectral solution of the governing equations implemented on the boundaries are used an iterative procedure is applied to provide consistent initial conditions for the distribution function and the pressure field for the simulation of unsteady flows the main advantage of using the ccslbm over other high order accurate lattice boltzmann method lbm based flow solvers is the decay of the error at exponential rather than at polynomial rates note also that the ccslbm applied does not need any numerical dissipation or filtering for the solution to be stable leading to highly accurate solutions three two dimensional 2d test cases are simulated herein that are a regularized cavity the taylor vortex problem and doubly periodic shear layers the results obtained for these test cases are thoroughly compared with the analytical and available numerical results and show excellent agreement the computational efficiency of the proposed solution methodology based on the ccslbm is also examined by comparison with those of the standard streaming collision classical lbm and two finite difference lbm solvers the study indicates that the ccslbm provides more accurate and efficient solutions than these lbm solvers in terms of cpu and memory usage and an exponential convergence is achieved rather than polynomial rates the solution methodology proposed the ccslbm is also extended to three dimensions and a 3d regularized cavity is simulated the corresponding results are presented and validated indications are that the ccslbm developed and applied herein is robust efficient and accurate for computing 2d and 3d low speed flows note also that high accuracy solutions obtained by applying the ccslbm can be used as benchmark solutions for the assessment of other lbm based flow solvers

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

chapman enskog analysis for finite volume formulation of lattice boltzmann equation the classical chapman enskog expansion is performed for the recently proposed finite volume formulation of lattice boltzmann equation lbe method d v patil k n lakshmisha finite volume tvd formulation of lattice boltzmann simulation on unstructured mesh j comput phys 228 2009 5262 5279 first a modified partial differential equation is derived from a numerical approximation of the discrete boltzmann equation then the multi scale small parameter expansion is followed to recover the continuity and the navier stokes ns equations with additional error terms the expression for apparent value of the kinematic viscosity is derived for finite volume formulation under certain assumptions the attenuation of a shear wave taylor green vortex flow and driven channel flow are studied to analyze the apparent viscosity relation

a spectral element discontinuous galerkin lattice boltzmann method for nearly incompressible flows we present a spectral element discontinuous galerkin lattice boltzmann method for solving nearly incompressible flows decoupling the collision step from the streaming step offers numerical stability at high reynolds numbers in the streaming step we employ high order spectral element discontinuous galerkin discretizations using a tensor product basis of one dimensional lagrange interpolation polynomials based on gauss lobatto legendre grids our scheme is cost effective with a fully diagonal mass matrix advancing time integration with the fourth order runge kutta method we present a consistent treatment for imposing boundary conditions with a numerical flux in the discontinuous galerkin approach we show convergence studies for couette flows and demonstrate two benchmark cases with lid driven cavity flows for re 400 5000 and flows around an impulsively started cylinder for re 550 9500 computational results are compared with those of other theoretical and computational work that used a multigrid method a vortex method and a spectral element model

an expectation maximization algorithm for fitting the generalized odds rate model to interval censored data the generalized odds rate model is a class of semiparametric regression models which includes the proportional hazards and proportional odds models as special cases there are few works on estimation of the generalized odds rate model with interval censored data because of the challenges in maximizing the complex likelihood function in this paper we propose a gamma poisson data augmentation approach to develop an expectation maximization algorithm which can be used to fit the generalized odds rate model to interval censored data the proposed expectation maximization algorithm is easy to implement and is computationally efficient the performance of the proposed method is evaluated by comprehensive simulation studies and illustrated through applications to datasets from breast cancer and hemophilia studies in order to make the proposed method easy to use in practice an r package icgor was developed copyright 2016 john wiley sons ltd

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

ignorability and coarse data some biomedical examples heitjan and rubin 1991 annals of statistics 19 2244 2253 define data to be coarse when one observes not the exact value of the data but only some set a subset of the sample space that contains the exact value this definition covers a number of incomplete data problems arising in biomedicine including rounded heaped censored and missing data in analyzing coarse data it is common to proceed as though the degree of coarseness is fixed in advance in a word to ignore the randomness in the coarsening mechanism when coarsening is actually stochastic however inferences that ignore this randomness may be seriously misleading heitjan and rubin 1991 have proposed a general model of data coarsening and established conditions under which it is appropriate to ignore the stochastic nature of the coarsening the conditions are that the data be coarsened at random a generalization of missing at random rubin 1976 biometrika 63 581 592 and that the parameters of the data and the coarsening process be distinct this article presents detailed applications of the general model and the ignorability conditions to a variety of coarse data problems arising in biomedical statistics a reanalysis of the stanford heart transplant data crowley and hu 1977 journal of the american statistical association 72 27 36 reveals significant evidence that censoring of pretransplant survival times by transplantation was nonignorable suggesting a greater benefit from cardiac transplantation than previous analyses had found

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

on stabilized integration for time dependent pdes an integration method is discussed which has been designed to treat parabolic and hyperbolic terms explicitly and stiff reaction terms implicitly the method is a special two step form of the one step imex implicit explicit rkc runge kutta chebyshev method the special two step form is introduced with the aim of getting a non zero imaginary stability boundary which is zero for the one step method having a non zero imaginary stability boundary allows for example the integration of pure advection equations space discretized with centered schemes the integration of damped or viscous wave equations the integration of coupled sound and heat flow equations etc for our class of methods it also simplifies the choice of temporal step sizes satisfying the von neumann stability criterion by embedding a thin long rectangle inside the stability region embedding rectangles or other tractable domains with this purpose is an idea of wesseling

power series cure rate model for spatially correlated interval censored data based on generalized extreme value distribution abstract in this work we propose a flexible cure rate model to allow for spatial correlations by including spatial frailty in the interval censored data setting the proposed model is quite flexible and generalizes the bernoulli geometric poisson and logarithmic models it can be tested for the best fit in a straightforward way our approach enables different underlying activation mechanisms that lead to the event of interest and the number of competing causes that can be responsible for the occurrence of the event of interest follows a flexible exponential discrete power series distribution mcmc methods are used in bayesian inference for the proposed models and bayesian comparison criteria are used for model comparison moreover we conduct influence diagnostics through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions in the analysis results finally the proposed models are used to analyze a real dataset

remission duration an example of interval censored observations remission duration data from two observational studies the german all aul study on acute lymphoblastic and acute undifferentiated leukaemia and the kiel lymphoma study are used to demonstrate the adequacy of an interval censoring approach the turnbull estimator is contrasted with the conventionally used kaplan meier estimator in addition a parametric model is used for estimation or simulation of the delay times of complete remission diagnosis and relapse diagnosis two possible consequences of the conventional approach are discussed biased estimation for example overestimation of remission duration and underestimation of the true error variance which may lead to false positive results on the other hand the applicability of the interval censoring approach is doubtful when the censoring mechanism examination pattern patient s behaviour is confounded with the endpoints

three time integration methods for incompressible flows with discontinuous galerkin boltzmann method abstract this paper presents three time integration methods for incompressible flows with finite element method in solving the lattice bgk boltzmann equation the space discretization is performed using nodal discontinuous galerkin method which employs unstructured meshes with triangular elements and high order approximation degrees the time discretization is performed using three different kinds of time integration methods namely direct decoupling and splitting from the storage cost temporal accuracy numerical stability and time consumption we systematically compare three time integration methods then benchmark fluid flow simulations are performed to highlight efficient time integration methods numerical results are in good agreement with others or exact solutions

performance evaluation of the general characteristics based off lattice boltzmann scheme and dugks for low speed continuum flows the general characteristics based off lattice boltzmann scheme proposed by bardow et al 1 hereafter bardow s scheme and the discrete unified gas kinetic scheme dugks 2 are two methods that successfully overcome the time step restriction by the collision time which is commonly seen in many other kinetic schemes in this work we first perform a theoretical analysis of the two schemes in the finite volume framework by comparing their numerical flux evaluations it is found that the effect of collision term is considered in the evaluation of the cell interface distribution function in both schemes which explains why they can overcome the time step restriction and can give accurate results even as the time step is much larger than the collision time the difference between the two schemes lies in the treatment of the integral of the collision term when evaluating the cell interface distribution function in which bardow s scheme uses the rectangular rule while dugks uses the trapezoidal rule the performance of the two schemes i e accuracy stability and efficiency are then compared by simulating several two dimensional flows including the unsteady taylorgreen vortex flow the steady lid driven cavity flow and the laminar boundary layer problem it is observed that dugks can give more accurate results than bardow s scheme with a same mesh size furthermore the numerical stability of bardow s scheme decreases as the courantfriedrichslewy cfl number approaches to 1 while the stability of dugks is not affected by the cfl number apparently as long as cfl 1 it is also observed that dugks is twice as expensive as the bardow s scheme with the same mesh size

macroscopic model and truncation error of discrete boltzmann method a derivation procedure to secure the macroscopically equivalent equation and its truncation error for discrete boltzmann method is proffered in this paper essential presumptions of two time scales and a small parameter in the chapman enskog expansion are disposed of in the present formulation equilibrium particle distribution function instead of its original non equilibrium form is chosen as key variable in the derivation route taylor series expansion encompassing fundamental algebraic manipulations is adequate to realize the macroscopically differential counterpart a self contained and comprehensive practice for the linear one dimensional convection diffusion equation is illustrated in details numerical validations on the incurred truncation error in one and two dimensional cases with various distribution functions are conducted to verify present formulation as shown in the computational results excellent agreement between numerical result and theoretical prediction are found in the test problems straightforward extensions to more complicated systems including convection diffusion reaction multi relaxation times in collision operator as well as multi dimensional navier stokes equations are also exposed in the appendix to point out its expediency in solving complicated flow problems

viscosity of finite difference lattice boltzmann models two dimensional finite difference lattice boltzmann models for single component fluids are discussed and the corresponding macroscopic equations for mass and momentum conservation are derived by performing a chapman enskog expansion in order to recover the correct mass equation characteristic based finite difference schemes should be associated with the forward euler scheme for the time derivative while the space centered and second order upwind schemes should be associated to second order schemes for the time derivative in the incompressible limit the characteristic based schemes lead to spurious numerical contributions to the apparent value of the kinematic viscosity in addition to the physical value that enters the navier stokes equation formulae for these spurious numerical viscosities are in agreement with results of simulations for the decay of shear waves

finite difference lattice boltzmann method with arbitrary specific heat ratio applicable to supersonic flow simulations abstract the current finite difference lattice boltzmann method fdlbm gives a fixed specific heat ratio because internal energy is limited to the translational freedom of the space yan et al and kataoka et al clarified the conditions for deriving models with arbitrary specific heat ratio and proposed euler models however these model applications to numerical simulations showed the weakness in the numerical stability in this paper a two dimensional fdlbm navier stokes model and a three dimensional fdlbm euler model which allow arbitrary values to be set for the specific heat ratio were proposed these models stably performed numerical simulations from subsonic to supersonic ranges

a second order exponential time differencing scheme for non linear reaction diffusion systems with dimensional splitting abstract a second order l stable exponential time differencing etd method is developed by combining an etd scheme with approximating the matrix exponentials by rational functions having real distinct poles rdp together with a dimensional splitting integrating factor technique a variety of non linear reaction diffusion equations in two and three dimensions with either dirichlet neumann or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second order implicit explicit schemes an additional performance boost is gained through further use of basic parallelization techniques

designing follow up intervals when an examination is needed to determine if an event has occurred there will be a loss of efficiency in using the resulting interval censored data instead of the exact event times in designing follow up intervals this loss for longer intervals needs to be weighed against extra visits required by shorter intervals we obtain results to quantify this for the estimation of the median and mean survival and for covariates in parametric regression models with equally spaced examination times asymptotic information loss for the log normal and weibull distributions are similar when comparisons are made between corresponding members of the two families for distributions with coefficients of variation of 50 per cent or more a choice of interval from 0 25 to 0 7 times the median is recommended copyright 2004 john wiley sons ltd

tests of proportional hazards and proportional odds models for grouped survival data summary in this paper we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data these models are embedded within a power family transformation in order to obtain the score tests in simple cases some small sample results are obtained for the score statistics using monte carlo simulations score statistics have distributions well approximated by the chi squared distribution real examples illustrate the proposed tests

rkc an explicit solver for parabolic pdes the fortran program rkc is intended for the time integration of parabolic partial differential equations discretized by the method of lines it is based on a family of runge kutta chebyshev formulas with a stability bound that is quadratic in the number of stages remarkable properties of the family make it possible for the program to select at each step the most efficient stable formula as well as the most efficient step size moreover they make it possible to evaluate the explicit formulas in just a few vectors of storage these characteristics of the program make it especially attractive for problems in several spatial variables rkc is compared to the bdf solver vodpk on two test problems in three spatial variables

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial