absolute risk regression for competing risks interpretation link functions and prediction in survival analysis with competing risks the transformation model allows different functions between the outcome and explanatory variables however the model s prediction accuracy and the interpretation of parameters may be sensitive to the choice of link function we review the practical implications of different link functions for regression of the absolute risk or cumulative incidence of an event specifically we consider models in which the regression coefficients have the following interpretation the probability of dying from cause d during the next t years changes with a factor exp for a one unit change of the corresponding predictor variable given fixed values for the other predictor variables the models have a direct interpretation for the predictive ability of the risk factors we propose some tools to justify the models in comparison with traditional approaches that combine a series of cause specific cox regression models or use the fine gray model we illustrate the methods with the use of bone marrow transplant data

modeling flow and transport in highly heterogeneous three dimensional aquifers ergodicity gaussianity and anomalous behavior 2 approximate semianalytical solution 1 flow and transport take place in a heterogeneous medium of lognormal distribution of the conductivity k flow is uniform in the mean and the system is defined by u mean velocity y2 log conductivity variance and integral scale i transport is analyzed in terms of the breakthrough curve of the solute identical to the traveltime distribution at control planes at distance x from the source the self consistent approximation is used where the traveltime is approximated by the sum of pertinent to the different separate inclusions and the neglected interaction between inclusions is accounted for by using the effective conductivity the pdf f x where x is the control plane distance is derived by a simple convolution it is found that f x has an early arrival time portion that captures most of the mass and a long tail which is related to the slow solute particles that are trapped in blocks of low k the macrodispersivity is very large and is independent of x the tail f x is highly skewed and only for extremely large x i depending on y2 the plume becomes gaussian comparison with numerical simulations shows very good agreement in spite of the absence of parameter fitting it is found that finite plumes are not ergodic and a cutoff of f x is needed in order to fit the mass flux of a finite plume depending on y2 and x i the bulk of f x can be approximated by a gaussian shape with fitted equivalent parameters the issue of anomalous behavior is examined with the aid of the model

on the self averaging of dispersion for transport in quasi periodic random media in this study we present a numerical analysis for the self averaging of the longitudinal dispersion coefficient for transport in heterogeneous media this is done by investigating the mean square sample to sample fluctuations of the dispersion for finite times and finite numbers of modes for a random field using analytical arguments as well as numerical simulations we consider transport of point like injections in a quasi periodic random field with a gaussian correlation function in particular we focus on the asymptotic and pre asymptotic behaviour of the fluctuations with the aid of a probability density function for the dispersion and we verify the logarithmic growth of the sample to sample fluctuations as earlier reported in eberhard 2004 j phys a math gen 37 2549 71 we also comment on the choice of the relevant parameters to generate quasi periodic realizations with respect to the self averaging of transport in statistically homogeneous gaussian velocity fields

solute transport in highly heterogeneous aquifers the paper deals with the transport of nonreactive solute in heterogeneous formations with prescribed statistical properties of the hydraulic log conductivity y ln k available solutions obtained from perturbation methods are limited to first and second order solutions valid only for small values of the log conductivity variance 2y published numerical investigations give comparative results with finite values of 2y but some discrepancies among the results generate doubts about the capability of numerical methods to capture high order effects for media with large variance values when these large 2y values are encountered in natural formations the related nonlinear effects could be significant in the velocity statistics and in the overall dispersion process the nonlinearity consequences are here investigated in two dimensional isotropic porous media by the monte carlo technique coupled with a finite element analysis the analysis includes 2y values from 0 05 to 4 enhancing the relevance of the nonlinear effects in the dispersion tensor solution to dissipate the doubts related to the numerical approach the accuracy of the solutions was defined by checking the influence of the factors which can affect the solution and by giving an estimation of the related errors the numerical results confirm the validity of the first order and second order analyses when 2y 0 the second order solution captures the nonlinear effects in a small range of log conductivity variance close to zero the nonlinear terms neglected in the first order formulation for higher 2y values give 1 late travel time longitudinal dispersion values greater than the linear solution 2 notably non gaussian distribution of the lagrangian velocity and particle displacements and 3 travel times to approach the asymptotic fickian regime longer than those obtained using the linear solution

is transverse macrodispersivity in three dimensional groundwater transport equal to zero a counterexample 1 in advective transport through weakly heterogeneous aquifers of random stationary and isotropic three dimensional permeability distribution transverse macrodispersivity t is found to be zero this was determined in the past by solving the transport equation at first order in the log conductivity variance 2 y however field findings indicate the presence of small but finite t the aim of the paper is to determine t for highly heterogeneous formations using a model that contains inclusions of conductivity k submerged in a matrix of conductivity k 0 for large k k 0 in the dilute medium approximation valid for small volume fraction n but arbitrary and for spherical inclusions it is found that t 0 because of the axisymmetry of flow past a sphere a medium made up of rotational ellipsoids of arbitrary random orientation macroscopically isotropic and of the same and n is devised as a counterexample it is found that because of the intertwining of streamlines t 0 being of order 1 4 for 1 these findings are confirmed by accurate numerical simulations of flow through a large number of interacting inclusions for 10 and n 0 2 jamming limit the large value t l 0 15 is attained the numerical simulations display the strong permanent deformation of stream tubes responsible for this phenomenon coined as advective mixing the two point covariance used in practice in order to characterize the aquifer structure is not able to detect the structures that produce advective mixing nevertheless the presence of high conductivity lenses inclined with respect to the mean flow may explain the occurrence of finite t in field applications

maximum likelihood estimation of semiparametric mixture component models for competing risks data summary in the analysis of competing risks data the cumulative incidence function is a useful quantity to characterize the crude risk of failure from a specific event type in this article we consider an efficient semiparametric analysis of mixture component models on cumulative incidence functions under the proposed mixture model latency survival regressions given the event type are performed through a class of semiparametric models that encompasses the proportional hazards model and the proportional odds model allowing for time dependent covariates the marginal proportions of the occurrences of cause specific events are assessed by a multinomial logistic model our mixture modeling approach is advantageous in that it makes a joint estimation of model parameters associated with all competing risks under consideration satisfying the constraint that the cumulative probability of failing from any cause adds up to one given any covariates we develop a novel maximum likelihood scheme based on semiparametric regression analysis that facilitates efficient and reliable estimation statistical inferences can be conveniently made from the inverse of the observed information matrix we establish the consistency and asymptotic normality of the proposed estimators we validate small sample properties with simulations and demonstrate the methodology with a data set from a study of follicular lymphoma

new lower bounds on eigenvalue of the hadamard product of an m matrix and its inverse abstract some new lower bounds for the minimum eigenvalue of the hadamard product of an m matrix and its inverse are given these bounds improve the results of h b li t z huang s q shen h li lower bounds for the minimum eigenvalue of hadamard product of an m matrix and its inverse linear algebra appl 420 2007 235 247

generalised linear models for correlated pseudo observations with applications to multi state models will be in a given state at some time is a complex nonlinear function of the intensity regression coefficients we present a technique which models the state probabilities directly this method is based on the pseudo values from a jackknife statistic constructed from simple summary statistic estimates of the state probabilities these pseudo values are then used in a generalised estimating equation to obtain estimates of the model parameters we illustrate how this technique works by studying examples of common regression problems we apply the technique to model acute graft versus host disease in bone marrow transplants

asymptotic theory of generalized estimating equations based on jack knife pseudo observations a general asymptotic theory of estimates from estimating functions based on jack knife pseudo observations is established by requiring that the underlying estimator can be expressed as a smooth functional of the empirical distribution using results in p variation norms the theory is applied to important estimators from time to event analysis namely the kaplan meier estimator and the aalen johansen estimator in a competing risks model and the corresponding estimators of restricted mean survival and cause specific lifetime lost under an assumption of completely independent censorings this allows for estimating parameters in regression models of survival cumulative incidences restricted mean survival and cause specific lifetime lost considering estimators as functionals and applying results in p variation norms is apparently an excellent way of studying the asymptotics of such estimators

numerical assessment of 3 d macrodispersion in heterogeneous porous media 1 hydrodynamic dispersion is a key controlling factor of solute transport in heterogeneous porous media that critically depends on dimensionality the transverse macrodispersion asymptotic dispersion transverse to the mean velocity direction is known to vanish only in 2 d and not in 3 d using classical gaussian correlated permeability fields with a lognormal distribution of variance y2 we determine numerically the longitudinal and transverse dispersivities as functions of heterogeneity and dimensionality we show that the transverse macrodispersion steeply increases with y2 underlying the essential role of flow lines braiding a mechanism specific to 3 d systems that we qualitatively characterize by the increasing expansion of the flow lines transversally to the flow direction the transverse macrodispersion remains however at least two orders of magnitude smaller than the longitudinal macrodispersion which increases even more steeply with y2 at moderate to high levels of heterogeneity the transverse dispersion also converges much faster to its asymptotic regime than do the longitudinal dispersion braiding cannot be thus taken as the sole mechanism responsible for the high longitudinal macrodispersions it could be either supplemented or superseded by stronger velocity correlations in 3 d than in 2 d this assumption is supported by the much larger longitudinal macrodispersions obtained in 3 d than in 2 d up to a factor of 5 for y2 6 25

stochastic analysis of unsaturated steady flows above the water table steady flowtakes place into a three dimensional partially saturated porous medium where due to their spatial variability the saturated conductivity ks and the relative conductivity kr are modeled as random space functions rsf s as a consequence the flow variables fvs i e pressure head and specific flux are also rsfs the focus of the present paper consists into quantifying the uncertainty of the fvs above the water table the simple expressions most of which in closed form of the second order moments pertaining to the fvs allow one to follow the transitional behavior from the zone close to the water table where the fvs are non stationary till to their far field limit where the fvs become stationary rsfs in particular it is shown how the stationary limits and the distance from the water table at which stationarity is attained depend upon the statistical structure of the rsfs ks kr and the infiltrating rate the mean pressure head k l has been also computed and it is expressed as k l 0 1 being a characteristic heterogeneity function which modifies the zero order approximation 0 of the pressure head valid for a vadose zone of uniform soil properties to account for the spatial variability of ks and kr two asymptotic limits i e close near field and away far field from the water table are derived into a very general manner whereas the transitional behavior of between the near far field can be determined after specifying the shape of the various input soil properties besides the theoretical interest results of the present paper are useful for practical purposes as well indeed the model is tested against to real data and in particular it is shown how it is possible for the specific case study to grasp the behavior of the fvs within an environment i e the vadose zone close to the water table which is generally very difficult to access by direct inspection

estimating subject specific dependent competing risk profile with censored event time observations in a longitudinal study suppose that the primary endpoint is the time to a specific event this response variable however may be censored by an independent censoring variable or by the occurrence of one of several dependent competing events for each study subject a set of baseline covariates is collected the question is how to construct a reliable prediction rule for the future subject s profile of all competing risks of interest at a specific time point for risk benefit decision makings in this paper we propose a two stage procedure to make inferences about such subject specific profiles for the first step we use a parametric model to obtain a univariate risk index score system we then estimate consistently the average competing risks for subjects which have the same parametric index score via a nonparametric function estimation procedure we illustrate this new proposal with the data from a randomized clinical trial for evaluating the efficacy of a treatment for prostate cancer the primary endpoint for this study was the time to prostate cancer death but had two types of dependent competing events one from cardiovascular death and the other from death of other causes

numerical investigations on ergodicity of solute transport in heterogeneous aquifers 1 darcy velocities for lognormal hydraulic conductivity with small variance and finite correlation length were approximated by periodic random fields accurate simulations of two dimensional advection dispersion processes were achieved with the global random walk algorithm using 1010 particles in every transport realization reliable statistical estimations were obtained by averaging over 256 realizations the main result is a numerical evidence for the mean square convergence of the actual concentrations to the macrodispersion process predicted by a known limit theorem for small initial plumes the ergodic behavior can be expected after thousands of advection timescales when the deviation from the theoretical prediction of the cross section space averaged concentration monotonously decays and falls under 20 the increase of the transverse dimension of the initial plume slows down the approach to the quasi ergodic state and has a nonlinear effect on the variability of the actual concentrations and dispersivities

modeling three dimensional flow about ellipsoidal inhomogeneities with application to flow to a gravel packed well and flow through lens shaped inhomogeneities analytic functions are superimposed to model three dimensional steady groundwater flow in regions containing one or more inhomogeneities shaped like prolate or oblate ellipsoids of revolution each function and the sum of such functions are solutions of laplace s equation the governing differential equation for steady groundwater flow the functions are implemented in a manner that provides exact continuity of flow across the entire boundary of each inhomogeneity in general continuity of head is provided at specified control points on the boundary and is approximated between control points for the case of one inhomogeneity in a uniform flow field it turns out that there is exact continuity of head across the entire surface of the inhomogeneity the method is implemented in a computer program written by the author two applications are demonstrated 1 flow to a gravel packed well and 2 flow through a series of lens shaped inhomogeneities the examples demonstrate that the approximation of continuity of head can be made acceptable for many problems a possible application of the technique would be testing various theories regarding contaminant migration and dispersion by simulating flow and chemical diffusion through large numbers of lens shaped inhomogeneities

a random forest approach for competing risks based on pseudo values random forest is a supervised learning method that combines many classification or regression trees for prediction here we describe an extension of the random forest method for building event risk prediction models in survival analysis with competing risks in case of right censored data the event status at the prediction horizon is unknown for some subjects we propose to replace the censored event status by a jackknife pseudo value and then to apply an implementation of random forests for uncensored data because the pseudo responses take on values on a continuous scale the node variance is chosen as split criterion for growing regression trees in a simulation study the pseudo split criterion is compared with the gini split criterion when the latter is applied to the uncensored event status to investigate the resulting pseudo random forest method for building risk prediction models we analyze it in a simulation study of predictive performance where we compare it to cox regression and random survival forest the method is further illustrated in two real data sets copyright 2013 john wiley sons ltd

characteristics and controlling factors of dispersion in bounded heterogeneous porous media 1 in this study we present first order in terms of the log conductivity variance analytical solutions to displacement covariances xij and macrodispersion coefficients dij for transport of conservative solutes in two dimensional bounded heterogeneous porous media these solutions are presented as infinity series and are explicit functions of the statistics of the log hydraulic conductivity using numerical examples the convergence of these solutions in terms of the number of terms in truncated finite summations is first investigated and the accuracy of these solutions is examined by comparing them with results from monte carlo simulations and the semianalytical solutions of osnes 1998 through several examples the general features of time dependent xij and dij are discussed unlike in unbounded domains the longitudinal macrodispersivity d11 for bounded domains does not approach an asymptotic value at large dimensionless time but instead increases quickly near the downstream constant head boundary in addition d11 for bounded domains is always larger than that in unbounded domains and accordingly the transverse macrodispersivity d22 in bounded domains is smaller than that in unbounded domains these differences stem from the lateral no flow boundaries in our bounded domain models we also investigated the effect of domain sizes on xij and dij our study shows that both xij and dij depend not only on the dimensionless size of the domain but also on its aspect ratio the dependence of xij and dij on the particles initial location has also been investigated at detail our results indicate that while this dependence is very small for x11 and d11 the release location has a significant impact on both x22 and d22 our solutions to both displacement covariances and macrodispersivity are compared against those derived from tracer test data at the borden site the comparison shows that our solutions are quite close to observed data indicating that they may be applicable to predict solute transport at the field scale

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

weighted npmle for the subdistribution of a competing risk direct regression modeling of the subdistribution has become popular for analyzing data with multiple competing event types all general approaches so far are based on nonlikelihood based procedur

finite analytic numerical method for two dimensional fluid flow in heterogeneous porous media starting from the investigation on the detailed flow pattern finite analytic numerical method is developed to solve the two dimensional fluid flows in heterogeneous porous media it is shown that only for some specific permeability distributions the pressure has the piecewise linear distribution where harmonic average scheme works very well in general case the pressure will have the power law behavior and its gradient will diverge as approaching the node joining the different permeability areas the nodal flow effects cause the flow fingering into the high permeability region it is a challenge problem to numerically describe the nodal fingering effects with the help of the specific properties of pressure and its gradient around the node a local analytical nodal solution is derived and then applied to construct a finite analytic numerical scheme numerical examples show that the detailed flow pattern can be reconstructed with the proposed numerical scheme under few grid refinements only with 2x2 or 3x3 subdivisions the proposed numerical scheme can provide rather accurate solutions the convergent speed of the numerical scheme is independent of the permeability heterogeneity in contrast the refinement ratio for the grid cell needs to be increased dramatically to get an accurate result when the traditional numerical method is used for strong heterogeneous cases

asymptotic dispersion in 2d heterogeneous porous media determined by parallel numerical simulations we determine the asymptotic dispersion coefficients in 2d exponentially correlated lognormally distributed permeability fields by using parallel computing fluid flow is computed by solving the flow equation discretized on a regular grid and transport triggered by advection and diffusion is simulated by a particle tracker to obtain a well defined asymptotic regime under ergodic conditions initial plume size much larger than the correlation length of the permeability field the characteristic dimension of the simulated computational domains was of the order of 103 correlation lengths with a resolution of ten cells by correlation length we determine numerically the asymptotic effective longitudinal and transverse dispersion coefficients over 100 simulations for a broad range of heterogeneities s 2 0 9 where s 2 is the lognormal permeability variance for purely advective transport the asymptotic longitudinal dispersion coefficient depends linearly on s 2 for s 2 1 and the asymptotic transverse dispersion coefficient is zero addition of homogeneous isotropic diffusion induces an increase of transverse dispersion and a decrease of longitudinal dispersion

regression modeling of competing risks data based on pseudovalues of the cumulative incidence function typically regression models for competing risks outcomes are based on proportional hazards models for the crude hazard rates these estimates often do not agree with impressions drawn from plots of cumulative incidence functions for each level of a risk factor we present a technique which models the cumulative incidence functions directly the method is based on the pseudovalues from a jackknife statistic constructed from the cumulative incidence curve these pseudovalues are used in a generalized estimating equation to obtain estimates of model parameters we study the properties of this estimator and apply the technique to a study of the effect of alternative donors on relapse for patients given a bone marrow transplant for leukemia

on the inverses of general tridiagonal matrices in this work the sign distribution for all inverse elements of general tridiagonal h matrices is presented in addition some computable upper and lower bounds for the entries of the inverses of diagonally dominant tridiagonal matrices are obtained based on the sign distribution these bounds greatly improve some well known results due to ostrowski 1952 23 shivakumar and ji 1996 26 nabben 1999 21 22 and recently given by peluso and politi 2001 24 peluso and popolizio 2008 25 and so forth it is also stated that the inverse of a general tridiagonal matrix may be described by 2n 2 parameters k k 2n and k k 1n 1 instead of 2n 2 ones as given by el mikkawy 2004 3 el mikkawy and karawia 2006 4 and huang and mccoll 1997 10 according to these results a new symbolic algorithm for finding the inverse of a tridiagonal matrix without imposing any restrictive conditions is presented which improves some recent results finally several applications to the preconditioning technology the numerical solution of differential equations and the birth death processes together with numerical tests are given

predicting cumulative incidence probability by direct binomial regression we suggest a new simple approach for estimation and assessment of covariate effects for the cumulative incidence curve in the competing risks model we consider a semiparametric regression model where some effects may be time varying and some may be constant over time our estimator can be implemented by standard software our simulation study shows that the estimator works well and has finite sample properties comparable with the subdistribution approach we apply the method to bone marrow transplant data and estimate the cumulative incidence of death in complete remission following a bone marrow transplantation here death in complete remission and relapse are two competing events

estimation of a 1 for weakly chained diagonally dominant m matrices abstract let a be a weakly chained diagonally dominant wcdd m matrix an upper bound for a 1 is presented and further applied to establish an lower bound for the smallest eigenvalue of a effectiveness of the new upper bound is shown numerically

kaplan meier marginal or conditional probability curves in summarizing competing risks failure time data in the context of competing risks the kaplan meier estimator is often unsuitable for summarizing failure time data we discuss some alternative descriptive methods including marginal probability and conditional probability estimators two sample test statistics are also presented

flow and transport in highly heterogeneous formations 1 conceptual framework and validity of first order approximations 1 flow of uniform mean velocity u takes place in a formation of spatially variable random conductivity k x advective transport of a plume of an inert solute is investigated by the lagrangean approach the aim of the study is to determine the spatial moments of the plume i e of fluid particle trajectories for highly heterogeneous aquifers for which y 1 where y ln k a multi indicator model of the permeability structure which is different from the common multi gaussian one is proposed the formation is modeled as a collection of n blocks of different k j the structure is defined by the distribution of k j the blocks shape and the coordinates of their centroids the following simplifications are adopted the blocks are inclusions of a regular shape circles spheres for isotropic media investigated here defined by the radius a and the inclusions are not overlapping and their centroids are distributed uniformly and independently in space at the continuous limit the model is characterized by the joint pdf f y a the model is shown to be quite general and to comprise binary bimodal indicator variograms and unimodal distributions of y as particular cases the study is focused on the latter case with y normal n y y2 and stationary covariance of given integral scale iy these are the parameters commonly estimated for sedimentary formations this leaves still freedom in selecting the pdf f a the simple model selected for semianalytical and numerical analysis is that of inclusions of radius r and volume fraction n submerged in a matrix of effective conductivity kef the latter represents the effect of inclusions of much smaller radius which appear as a nugget in the log conductivity two point covariance an approximate analytical solution of the flow is obtained by using a self consistent approximation while a fully numerical one is derived in part 3 jankovic et al 2003a transport is solved by particle tracking and the time dependent spatial moments trajectories variance skewness kurtosis are presented in part 2 fiori et al 2003 in the self consistent approximation the asymptotic longitudinal macrodispersivity l which is a function of y shows strong nonlinear effects inclusions of large positive y lead to a finite l whereas l grows unbounded for those of negative y this effect is not captured by the common first order approximation in y which is symmetrical and overestimates l for y 0 and underestimates it for y 0 as a result the second spatial moment is predicted accurately by the first order approximation by cancellation of errors provided that f y is symmetrical however the transient regime and higher order moments are not captured by the first order approximation

flow and travel time statistics in highly heterogeneous porous media 1 in this paper we present flow and travel time ensemble statistics based on a new simulation methodology the adaptive fup monte carlo method afmcm as a benchmark case we considered two dimensional steady flow in a rectangular domain characterized by multi gaussian heterogeneity structure with an isotropic exponential correlation and lnk variance y2 up to 8 advective transport is investigated using the travel time framework where lagrangian variables e g velocity transverse displacement or travel time depend on space rather than on time we find that eulerian and lagrangian velocity distributions diverge for increasing lnk variance due to enhanced channeling transverse displacement is a nonnormal for all y2 and control planes close to the injection area but after xiy 20 was found to be nearly normal even for high y2 travel time distribution deviates from the fickian model for large lnk variance and exhibits increasing skewness and a power law tail for large lnk variance the slope of which decreases for increasing distance from the source no anomalous features are found second moment of advective transport is analyzed with respect to the covariance of two lagrangian velocity variables slowness and slope which are directly related to the travel time and transverse displacement variance which are subsequently related to the longitudinal and transverse dispersion we provide simple estimators for the eulerian velocity variance travel time variance slowness and longitudinal dispersivity as a practical contribution of this analysis both two parameter models considered the advection dispersion equation and the lognormal model provide relatively poor representations of the initial part of the travel time probability density function in highly heterogeneous porous media we identify the need for further theoretical and experimental scrutiny of early arrival times and the need for computing higher order moments for a more accurate characterization of the travel time probability density function a brief discussion is presented on the challenges and extensions for which afmcm is suggested as a suitable approach

flow and transport in highly heterogeneous formations 3 numerical simulations and comparison with theoretical results 1 in parts 1 dagan et al 2003 and 2 fiori et al 2003 a multi indicator model of heterogeneous formations is devised in order to solve flow and transport in highly heterogeneous formations the isotropic medium is made up from circular 2 d or spherical 3 d inclusions of different conductivities k submerged in a matrix of effective conductivity this structure is different from the multi gaussian one even for equal log conductivity distribution and integral scale a snapshot of a two dimensional plume in a highly heterogeneous medium of lognormal conductivity distribution shows that the model leads to a complex transport picture the present study was limited however to investigating the statistical moments of ergodic plumes two approximate semianalytical solutions based on a self consistent model sc and on a first order perturbation in the log conductivity variance fo are used in parts 1 and 2 in order to compute the statistical moments of flow and transport variables for a lognormal conductivity pdf in this paper an efficient and accurate numerical procedure based on the analytic element method strack 1989 is used in order to validate the approximate results the solution satisfies exactly the continuity equation and at high accuracy the continuity of heads at inclusion boundaries the dimensionless dependent variables depend on two parameters the volume fraction n of inclusions in the medium and the log conductivity variance y2 for inclusions of uniform radius the largest n was 0 9 2 d and 0 7 3 d whereas the largest y2 was equal to 10 the sc approximation underestimates the longitudinal eulerian velocity variance for increasing n and increasing y2 in 2 d and to a lesser extent in 3 d as compared to numerical results the fo approximation overestimates these variances and these effects are larger in the transverse direction the longitudinal velocity pdf is highly skewed and negative velocities are present at high y2 especially in 2 d the main results are in the comparison of the macrodispersivities computed with the aid of the lagrangian velocity covariances as functions of travel time for the longitudinal macrodispersivity the sc approximation yields results close to the numerical ones in 2 d for n 0 4 but underestimates them for n 0 9 the asymptotic large travel time values of macrodispersivities in the sc and fo approximations are close for low to moderate y2 as shown and explained in part 1 however while the slow tendency to fickian behavior is well reproduced by sc it is much quicker in the fo approximation in 3 d the sc approximation is closer to numerical one for the highest n 0 7 and the different y2 2 4 8 and the comparison improves if molecular diffusion is taken into account transverse macrodispersivity for small travel times is underestimated by sc in 2 d and is closer to numerical results in 3 d whereas fo overestimates them transverse macrodispersivity asymptotically tends to zero in 2 d for large travel times in 3 d the numerical simulations lead to a small but persistent transverse macrodispersivity for large travel times whereas it tends to zero in the approximate solutions the results suggest that the self consistent semianalytical approximation provides a valuable tool to model transport in highly heterogeneous isotropic formations of a 3 d structure in terms of trajectories statistical moments it captures effects like slow transition to fickian behavior and to gaussian trajectory distribution which are neglected by the first order approximation

decomposition of number of life years lost according to causes of death we study the competing risks model and show that the cause j cumulative incidence function integrated from 0 to has a natural interpretation as the expected number of life years lost due to cause j before time this is analogous to the restricted mean lifetime which is the survival function integrated from 0 to it is discussed how the number of years lost may be related to subject specific explanatory variables in a regression model based on pseudo observations and the method is exemplified using data from a bone marrow transplantation study finally inclusion of standard mortality rates is discussed copyright 2013 john wiley sons ltd

proof of a conjecture of fiedler and markham let a be an n n nonsingular m matrix for the hadamard product a a 1 m fiedler and t l markham conjectured in linear algebra appl 10l 1988 1 that q a a 1 2 n where q a a 1 is the smallest eigenvalue in modulus of a a 1 we considered this conjecture in linear algebra appl 288 1999 259 having observed an incorrect proof in linear algebra appl 144 1991 171 and obtained that q a a 1 2 n n 1 n the present paper gives a proof for this conjecture

on some new bounds for eigenvalues of the hadamard product and the fan product of matrices abstract let a and b be nonnegative matrices a new upper bound on the spectral radius a b is obtained meanwhile a new lower bound on the smallest eigenvalue q a b for the fan product and a new lower bound on the minimum eigenvalue q b a 1 for the hadamard product of b and a 1 of two nonsingular m matrices a and b are given these bounds improve some results of li et al 9 and generalize some corresponding results the new estimating formulae are only depending on the entries of matrices a and b therefore they are easy to calculate

flow and transport in highly heterogeneous formations 2 semianalytical results for isotropic media 1 flow and transport of nonreactive solutes in heterogeneous porous media is studied by adopting a multi indicator model of permeability structure the porous formation is modeled as a collection of blocks of uniform permeability k implanted at random in a matrix of constant conductivity k0 the multi indicator model leads to simple semianalytical solutions based on the self consistent argument which are valid for a high degree of heterogeneity the methodology is applied to isotropic formations to derive a few statistical moments of the velocity field and of the solute particles trajectory as functions of time and of the log conductivity variance y2 along the common models of aquifer permeability distribution the distribution of y ln k is assumed to be normal all the semianalytical results degenerate in the well known first order results when y2 1 in particular it is shown that the first order longitudinal dispersivity l seems to hold for values of the log conductivity variance much larger than expected up to y2 4 this results from a compensation of errors associated with the first order approximation in contrast for y2 1 the asymptotic l grows exponentially with y2 the effect of molecular diffusion is considered in a simple manner by introducing a cutoff c for the conductivity contrast the time to reach the asymptotic l grows with the log conductivity variance it is thus observed that transport in highly heterogeneous formations can be characterized by a very prolonged non fickian stage with dispersivity l growing continuously with time further analysis of third order moment of trajectory indicates that for growing values of y2 the time needed for the plume to become gaussian can be quite large

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

an indirect assessment on the impact of connectivity of conductivity classes upon longitudinal asymptotic macrodispersivity solute transport takes place in heterogeneous porous formations with the log conductivity y ln k modeled as a stationary random space function of given univariate normal probability density fu

competing risks regression for stratified data for competing risks data the fine gray proportional hazards model for subdistribution has gained popularity for its convenience in directly assessing the effect of covariates on the cumulative incidence function however in many important applications proportional hazards may not be satisfied including multicenter clinical trials where the baseline subdistribution hazards may not be common due to varying patient populations in this article we consider a stratified competing risks regression to allow the baseline hazard to vary across levels of the stratification covariate according to the relative size of the number of strata and strata sizes two stratification regimes are considered using partial likelihood and weighting techniques we obtain consistent estimators of regression parameters the corresponding asymptotic properties and resulting inferences are provided for the two regimes separately data from a breast cancer clinical trial and from a bone marrow transplantation registry illustrate the potential utility of the stratified fine gray model

an inequality for the hadamard product of an m matrix and an inverse m matrix abstract an estimate from below the smallest eigenvalue q a c of the hadamard product a c of an m matrix a and an inverse m matrix c is proved in particular if a is an m matrix of order n we obtain the inequality q a a 1 1 n

simulation of dispersion in heterogeneous porous formations statistics first order theories convergence of computations this paper discusses the results of numerical analysis of dispersion of passive solutes in two dimensional heterogeneous porous formations statistics of flow and transport variables the accuracy and the role of approximations implicit in existing first order theories and the convergence of computational results are investigated the results suggest that quite different rates of convergence with monte carlo runs hold for different spatial moments and that over 1000 realizations are required to stabilize second moments even for relatively mild heterogeneity sigma y 2 1 6 this has implications for the extent of the spatial domain for single realization numerical studies of the same type a comparison of the variance of plumes with the results of linear theories 0 05 sigma y 2 1 6 shows an unexpectedly broad validity field for the theoretical solution obtained from a suitable linearization of flow and transport reformulation of the same problem linearizing in tum the flow or the transport equations shows opposite deviations from the linear theory the interesting consequence is that the errors induced by linearizations in the flow or the transport equations have different signs and their effects on the moments of dispersing plumes are compensating thereby yielding consistent formulations unexpected features of the statistics of probability distributions of longitudinal and transverse velocities and travel times are also computed and discussed

significance of higher moments for complete characterization of the travel time probability density function in heterogeneous porous media using the maximum entropy principle 1 the travel time formulation of advective transport in heterogeneous porous media is of interest both conceptually e g for incorporating retention processes and in applications where typically the travel time peak early and late arrivals of contaminants are of major concern in a regulatory or remediation context furthermore the travel time moments are of interest for quantifying uncertainty in advective transport of tracers released from point sources in heterogeneous aquifers in view of this interest the travel time distribution has been studied in the literature however the link to the hydraulic conductivity statistics has been typically restricted to the first two moments here we investigate the influence of higher travel time moments on the travel time probability density function pdf in heterogeneous porous media combining monte carlo simulations with the maximum entropy principle the monte carlo experimental pdf is obtained by the adaptive fup monte carlo method afmcm for advective transport characterized by a multi gaussian structure with exponential covariance considering two injection modes in flux and resident and lnk variance up to 8 a maximum entropy maxent algorithm based on fup basis functions is used for the complete characterization of the travel time pdf all travel time moments become linear with distance initial nonlinearity is found mainly for the resident injection mode which exhibits a strong nonlinearity within first 5iy for high heterogeneity for the resident injection mode the form of variance and all higher moments changes from the familiar concave form predicted by the first order theory to a convex form for the in flux mode linearity is preserved even for high heterogeneity the number of moments sufficient for a complete characterization of the travel time pdf mainly depends on the heterogeneity level mean and variance completely describe travel time pdf for low and mild heterogeneity skewness is dominant for lnk variance around 4 while kurtosis and fifth moment are required for lnk variance higher than 4 including skewness seems sufficient for describing the peak and late arrivals linearity of travel time moments enables the prediction of asymptotic behavior of the travel time pdf which in the limit converges to a symmetric distribution and fickian transport however higher order travel time moments may be important for most practical purposes and in particular for advective transport in highly heterogeneous porous media for a long distance from the source

solute transport in low heterogeneity sandboxes the role of correlation length and permeability variance this work examines how heterogeneity structure in particular correlation length controls flow and solute transport we used two dimensional 2d sandboxes 21 9 cm 20 6 cm and four modeling approaches including 2d advection dispersion equation ade with explicit heterogeneity structure 1d ade with average properties and nonlocal continuous time random walk ctrw and fractional ade fade the goal is to answer two questions 1 how and to what extent does correlation length control effective permeability and breakthrough curves btc 2 which model can best reproduce data under what conditions sandboxes were packed with the same 20 v v fine and 80 v v coarse sands in three patterns that differ in correlation length the mixed cases contain uniformly distributed fine and coarse grains the four zone and one zone cases have four and one square fine zones respectively a total of seven experiments were carried out with permeability variance of 0 10 lc 0 22 mc and 0 43 hc experimental data show that the btc curves depend strongly on correlation length especially in the hc cases the hc one zone hco case shows distinct breakthrough steps arising from fast advection in the coarse zone slow advection in the fine zone and slow diffusion while the lco and mco btcs do not exhibit such behavior with explicit representation of heterogeneity structure 2d ade reproduces btcs well in all cases ctrw reproduces temporal moments with smaller deviation from data than fade in all cases except hco where fade has the lowest deviation

impact of aquifer heterogeneity structure and local scale dispersion on solute concentration uncertainty in this paper we study the influence of high log conductivity variance sigma 2 y and local scale dispersion on the first two concentration moments as well as on higher order moments skewness

a trace inequality for m matrices and the symmetrizability of a real matrix by a positive diagonal matrix abstract the question of whether a real matrix is symmetrizable via multiplication by a diagonal matrix with positive diagonal entries is reduced to the corresponding question for m matrices and related to hadamard products in the process for a nonsingular m matrix a it is shown that tr a 1 a t n with equality if and only if a is symmetric and that the minimum eigenvalue of a 1 a is 1 with equality in the irreducible case if and only if a is positive diagonally symmetrizable

direct modeling of regression effects for transition probabilities in the progressive illness death model in this work we present direct regression analysis for the transition probabilities in the possibly non markov progressive illness death model the method is based on binomial regression where the response is the indicator of the occupancy for the given state along time randomly weighted score equations that are able to remove the bias due to censoring are introduced by solving these equations one can estimate the possibly time varying regression coefficients which have an immediate interpretation as covariate effects on the transition probabilities the performance of the proposed estimator is investigated through simulations we apply the method to data from the registry of systematic lupus erythematosus relesser a multicenter registry created by the spanish society of rheumatology specifically we investigate the effect of age at lupus diagnosis sex and ethnicity on the probability of damage and death along time copyright 2017 john wiley sons ltd

estimates of clinically useful measures in competing risks survival analysis competing risks occur frequently in follow up clinical studies to assess treatment or covariate effects measures of clinical impact based on crude cumulative incidence should be considered such as relative risks or the absolute risk reduction in this work transformation models through suitable link functions provide a straightforward approach to obtain point and interval estimates of such measures an extension of the klein and andersen proposal based on pseudo values is considered non additive effects were tested by interactions between baseline spline function on time and covariates the methods are applied to the evaluation of the impact of axillary lymph node nanometastases on metastatic relapse of breast cancer patients further a literature data set on prostate cancer was used for illustration

prediction of velocity statistics in three dimensional multi gaussian hydraulic conductivity fields 1 to study statistics of velocity fields in three dimensional heterogeneous multi gaussian saturated hydraulic conductivity fields and the accuracy of their prediction we performed high resolution monte carlo mc analyses the mc analyses included variances of the log hydraulic conductivity in the range of 0 5 y2 3 0 and anisotropy ratios in the range of 0 017 e 1 the statistics of the velocity fields from the mc analyses are compared with analytical solutions of the first and second order approximations of the stochastic flow equation this paper shows that the second order approximations fit significantly better to the univariate statistics of the darcy velocity from the mc analyses for isotropic cases the second order approximations correspond fairly well to the univariate statistics of the velocity for anisotropic cases the accordance is given only for the mean velocity and the variance of the transverse vertical component of the velocity the mc analyses show that the spatial correlation of the velocity decreases more rapidly with increasing y2 this was more pronounced for the anisotropic than for the isotropic case the negative correlations in absolute terms of the transverse velocity components simultaneously decrease with increasing y2 this is in contrast to the first order approximation of the spatial correlations of the velocity it is assumed that the discrepancies between approximate solutions of the stochastic flow equation and the results of the mc analyses are strongly dependent on the nonnormality of the probability density distributions of the velocity

regression analysis of mean quality adjusted survival time based on pseudo observations regression models for the mean quality adjusted survival time are specified from hazard functions of transitions between two states and the mean quality adjusted survival time may be a complex function of covariates we discuss a regression model for the mean quality adjusted survival qas time based on pseudo observations which has the advantage of directly modeling the effect of covariates in the qas time both monte carlo simulations and a real data set are studied

a lower bound for the minimum eigenvalue of the hadamard product of matrices abstract suppose both a and b are n n nonsingular m matrices an estimate from below for the smallest eigenvalue a b 1 in modulus of the hadamard product a b 1 of a and b 1 is derived as a special case we obtain the inequality a a 1 2 n n 2

quantile regression for left truncated semicompeting risks data summary semicompeting risks is often encountered in biomedical studies where a terminating event censors a nonterminating event but not vice versa in practice left truncation on the terminating event may arise and can greatly complicate the regression analysis on the nonterminating event in this work we propose a quantile regression method for left truncated semicompeting risks data which provides meaningful interpretations as well as the flexibility to accommodate varying covariate effects we develop estimation and inference procedures that can be easily implemented by existing statistical software asymptotic properties of the resulting estimators are established including uniform consistency and weak convergence the finite sample performance of the proposed method is evaluated via simulation studies an application to a registry dataset provides an illustration of our proposals

on a conjecture of fiedler and markham abstract for the hadamard product a a 1 of an m matrix a and its inverse a 1 fiedler and markham conjectured that q a a 1 2 n see m fiedler and t l markham linear algebra appl 101 1988 1 8 where q a a 1 is the smallest eigenvalue in modulus of a a 1 the present paper studies this conjecture an incorrect proof is given in li ching and chen ji cheng linear algebra appl 144 1991 171 178 and establishes q a a 1 2 n n 1 n for some special matrices the conjecture is proved

lower bounds for the minimum eigenvalue of hadamard product of an m matrix and its inverse for the hadamard product a a 1 of an m matrix a and its inverse a 1 we give new lower bounds for the minimum eigenvalue of a a 1 these bounds are strong enough to prove the conjecture of fiedler and markham an inequality for the hadamard product of an m matrix and inverse m matrix linear algebra appl 101 1988 1 8

joint inference for competing risks survival data abstractthis article develops joint inferential methods for the cause specific hazard function and the cumulative incidence function of a specific type of failure to assess the effects of a variable on the time to the type of failure of interest in the presence of competing risks joint inference for the two functions are needed in practice because i they describe different characteristics of a given type of failure ii they do not uniquely determine each other and iii the effects of a variable on the two functions can be different and one often does not know which effects are to be expected we study both the group comparison problem and the regression problem we also discuss joint inference for other related functions our simulation shows that our joint tests can be considerably more powerful than the bonferroni method which has important practical implications to the analysis and design of clinical studies with competing risks data we illustrate our method using a hodgkin disease data and a

an upper bound for a 1 of strictly diagonally dominant m matrices abstract let a be a real strictly diagonally dominant m matrix we give a sharp upper bound for a 1 furthermore the lower bound of the smallest eigenvalue q a is established

on the sign patterns of the smallest signless laplacian eigenvector abstract let h be a connected bipartite graph whose signless laplacian matrix is q h suppose that the bipartition of h is s t and that x is the eigenvector of the smallest eigenvalue of q h it is well known that x is positive and constant on s and negative and constant on t the resilience of the sign pattern of x under addition of edges into the subgraph induced by either s or t is investigated and a number of cases in which the sign pattern of x persists are described