some upwinding techniques for finite element approximations of convection diffusion equations a uniform framework for the study of upwinding schemes is developed the standard finite element galerkin discretization is chosen as the reference discretization and differences between other discretization schemes and the reference are written as artificial diffusion terms these artificial diffusion terms are spanned by a four dimensional space of element diffusion matrices three basis matrices are symmetric rank one diffusion operators associated with the edges of the triangle the fourth basis matrix is skew symmetric and is associated with a rotation by 2 while finite volume discretizations may be written as upwinded galerkin methods the converse does not appear to be true our approach is used to examine several upwinding schemes including the streamline diffusion method the box method the scharfetter gummel discretization and a divergence free scheme

a characterization of hybridized mixed methods for second order elliptic problems in this paper we give a new characterization of the approximate solution given by hybridized mixed methods for second order self adjoint elliptic problems we apply this characterization to obtain an explicit formula for the entries of the matrix equation for the lagrange multiplier unknowns resulting from hybridization we also obtain necessary and sufficient conditions under which the multipliers of the raviart thomas and the brezzi douglas marini methods of similar order are identical

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

nonparametric analysis of covariance for censored data the fully nonparametric model for nonlinear analysis of covariance proposed in akritas et al 2000 is considered in the context of censored observations under this model the distributions for each factor level combination and covariate value are not restricted to comply to any parametric or semiparametric model the data can be continuous or ordinal categorical the possibility of different shapes of covariate effect in different factor level combinations is also allowed this generality is useful whenever modelling assumptions such as additive risks proportional hazards or proportional odds appear suspect test statistics are obtained for the nonparametric hypotheses of no main effect and of no interaction effect which adjusts for the presence of a covariate they are quadratic forms based on averages over the covariate values of beran estimators of the conditional distribution of the survival time given each covariate value the derivation of the asymptotic chi 2 distribution of the test statistics uses a recently obtained asymptotic representation of the bekan estimator as average of independent random variables a real data set is analysed and results of simulation studies are reported

alternative variance and efficiency calculations for the case cohort design summary we define a bootstrap sampling plan for the case cohort design and present bootstrap variance estimates and confidence intervals for the log relative hazard the coverages of these confidence intervals are found to be near nominal levels in simulations a simple null variance calculation based on a superpopulation model is shown to provide good estimates of the power and efficiency of the case cohort design

bootstrap for the case cohort design the case cohort design facilitates economical investigation of risk factors in a large survival study with covariate data collected only from the cases and a simple random subset of the full cohort methods that accommodate the design have been developed for various semiparametric models but most inference procedures are based on asymptotic distribution theory such inference can be cumbersome to derive and implement and does not permit confidence band construction while bootstrap is an obvious alternative how to resample is unclear because of complications from the two stage sampling design we establish an equivalent sampling scheme and propose a novel and versatile nonparametric bootstrap for robust inference with an appealingly simple single stage resampling theoretical justification and numerical assessment are provided for a number of procedures under the proportional hazards model

regression with censored data summary there are four regression techniques currently available for use with censored data which do not assume particular parametric families of survival distributions they are due to i cox 1972 ii miller 1976 iii buckley james 1979 and iv koul susarla van ryzin 1981 these four methods are described and their performances compared on the updated stanford heart transplant data conclusions on the usefulness of the four procedures are drawn

local symplectic operators and structures related to them matrices with entries being differential operators that endow the phase space of an evolution system with a pre symplectic structure are considered special types of such structures are explicitly described links with integrability geometry of loop spaces and backlund transformations are traces

a unified approach to semiparametric transformation models under general biased sampling schemes we propose a unified estimation method for semiparametric linear transformation models under general biased sampling schemes the new estimator is obtained from a set of counting process based unbiased estimating equations developed through introducing a general weighting scheme that offsets the sampling bias the usual asymptotic properties including consistency and asymptotic normality are established under suitable regularity conditions a closed form formula is derived for the limiting variance and the plug in estimator is shown to be consistent we demonstrate the unified approach through the special cases of left truncation length bias the case cohort design and variants thereof simulation studies and applications to real datasets are presented

numerical discretization of energy transport models for semiconductors with nonparabolic band structure the energy transport models describe the flow of electrons through a semiconductor crystal influenced by diffusive electrical and thermal effects they consist of the continuity equations for the mass and the energy coupled with poisson s equation for the electric potential these models can be derived from the semiconductor boltzmann equation this paper consists of two parts the first part concerns the modeling of the energy transport system the diffusion coefficients and the energy relaxation term are computed in terms of the electron density and temperature under the assumptions of nondegenerate statistics and nonparabolic band diagrams the equations can be rewritten in a drift diffusion formulation which is used for the numerical discretization in the second part the stationary energy transport equations are discretized using the exponential fitting mixed finite element method in one space dimension numerical simulations of a ballistic diode are performed

a monotone finite element scheme for convection diffusion equations a simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection diffusion problems in any spatial dimension by properly averaging the pde coefficients on element edges the resulting finite element stiffness matrix is an m matrix under some mild assumption for the underlying generally unstructured finite element grids as a consequence the proposed edge averaged finite element scheme is particularly interesting for the discretization of convection dominated problems this scheme admits a simple variational formulation it is easy to analyze and it is also suitable for problems with a relatively smooth flux variable some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems

survival model predictive accuracy and roc curves summary the predictive accuracy of a survival model can be summarized using extensions of the proportion of variation explained by the model or r2 commonly used for continuous response models or using extensions of sensitivity and specificity which are commonly used for binary response models in this article we propose new time dependent accuracy summaries based on time specific versions of sensitivity and specificity calculated over risk sets we connect the accuracy summaries to a previously proposed global concordance measure which is a variant of kendall s tau in addition we show how standard cox regression output can be used to obtain estimates of time dependent sensitivity and specificity and time dependent receiver operating characteristic roc curves semiparametric estimation methods appropriate for both proportional and nonproportional hazards data are introduced evaluated in simulations and illustrated using two familiar survival data sets

combined estimating equation approaches for semiparametric transformation models with length biased survival data summary survival data are subject to length biased sampling when the survival times are left truncated and the underlying truncation time random variable is uniformly distributed substantial efficiency gains can be achieved by incorporating the information about the truncation time distribution in the estimation procedure wang 1989 journal of the american statistical association 84 742 748 wang 1996 biometrika 83 343 354 under the semiparametric transformation models the maximum likelihood method is expected to be fully efficient yet it is difficult to implement because the full likelihood depends on the nonparametric component in a complicated way moreover its asymptotic properties have not been established in this article we extend the martingale estimating equation approach chen et al 2002 biometrika 89 659 668 kim et al 2013 journal of the american statistical association 108 217 227 and the pseudo partial likelihood approach severini and wong 1992 the annals of statistics 4 1768 1802 zucker 2005 journal of the american statistical association 100 1264 1277 for semiparametric transformation models with right censored data to handle left truncated and right censored data in the same spirit of the composite likelihood method huang and qin 2012 journal of the american statistical association 107 946 957 we further construct another set of unbiased estimating equations by exploiting the special probability structure of length biased sampling thus the number of estimating equations exceeds the number of parameters and efficiency gains can be achieved by solving a simple combination of these estimating equations the proposed methods are easy to implement as they do not require additional programming efforts moreover they are shown to be consistent and asymptotically normally distributed a data analysis of a dementia study illustrates the methods

on some mixed finite element methods with numerical integration in this paper a new family of mixed finite volume methods is analyzed for the approximation of a reaction diffusion problem all the methods are obtained starting from the dual mixed formulation of the problem and then employing the lowest order raviart thomas finite element spaces plus a suitable quadrature formula for the mass matrix this allows for the use of different averages of the inverse diffusion coefficient to enforce the constitutive law for the fluxes at the interelement boundary in a finite volume fashion the soundness of the methods is supported by an error analysis which shows optimal cal o h convergence rate with respect to the standard mixed finite element norm in the case of both smooth and piecewise smooth coefficients numerical results on test problems with both smooth and nonsmooth coefficients support the theoretical estimates

on estimation of partially linear transformation models we study a general class of partially linear transformation models which extend linear transformation models by incorporating nonlinear covariate effects in survival data analysis a new martingale based estimating equation approach consisting of both global and kernel weighted local estimation equations is developed for estimating the parametric and nonparametric covariate effects in a unified manner we show that with a proper choice of the kernel bandwidth parameter one can obtain the consistent and asymptotically normal parameter estimates for the linear effects asymptotic properties of the estimated nonlinear effects are established as well we further suggest a simple resampling method to estimate the asymptotic variance of the linear estimates and show its effectiveness to facilitate the implementation of the new procedure an iterative algorithm is developed numerical examples are given to illustrate the finite sample performance of the procedure supplementary materials are available online

maximum likelihood estimation in the proportional odds model abstract we consider maximum likelihood estimation of the parameters in the proportional odds model with right censored data the estimator of the regression coefficient is shown to be asymptotically normal with efficient variance the maximum likelihood estimator of the unknown monotonic transformation of the survival time converges uniformly at a parametric rate to the true transformation estimates for the standard errors of the estimated regression coefficients are obtained by differentiation of the profile likelihood and are shown to be consistent a likelihood ratio test for the regression coefficient is also considered

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

hamiltonian formulation of the kdv equation we consider the canonical formulation of whitham s variational principle for the kdv equation this lagrangian is degenerate and we have found it necessary to use dirac s theory of constrained systems in constructing the hamiltonian earlier discussions of the hamiltonian structure of the kdv equation were based on various different decompositions of the field which is avoided by this new approach

partial rank estimation of duration models with general forms of censoring abstract in this paper we propose estimators for the regression coefficients in censored duration models which are distribution free impose no parametric specification on the baseline hazard function and can accommodate general forms of censoring the estimators are shown to have desirable asymptotic properties and monte carlo simulations demonstrate good finite sample performance among the data features the new estimators can accommodate are covariate dependent censoring double censoring and fixed individual or group specific effects we also examine the behavior of the estimator in an empirical illustration

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

estimation and testing in a two sample generalized odds rate model abstract the generalized odds ratio for a survival variable t is defined as t t c c 1 1 sc t sc t for c 0 and log s t for c 0 where s t pr t t this ratio coincides with the integrated hazard for c 0 and the odds ratio for c 1 when the distribution of t depends on a covariate vector we assume that conditionally on the covariates log t t c is linear in the covariates this model is a generalization of the proportional hazard model phm which has an interpretation both as a phm with random nuisance effects clayton and cuzick 1986 and as a proportional odds rate model with the odds rate defined from the response times of series systems harrington and fleming 1982 and bickel 1986a considered rank tests for this semiparametric model clayton and cuzick 1986 considered estimation we use the odds rate representation to define a class of estimates of the proportionality parameter in the two sample case we show that the estimates are consistent and asymptotica

dirac s theory of constraints in field theory and the canonical form of hamiltonian differential operators a simple algorithm for constructing the canonical form of hamiltonian systems of evolution equations with constant coefficient hamiltonian differential operators is given the result of the construction is equivalent to the canonical system derived using dirac s theory of constraints from the corresponding degenerate lagrangian

error analysis of variable degree mixed methods for elliptic problems via hybridization a new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree raviart thomas method for second order elliptic problems the approach gives error estimates for the lagrange multipliers without using error estimates for the other variables error estimates for the primal and flux variables then follow from those for the lagrange multipliers in contrast traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the lagrange multipliers the new approach not only gives new error estimates for the new variable degree raviart thomas method but also new error estimates for the classical uniform degree method with less stringent regularity requirements than previously known estimates the error analysis is achieved by using a variational characterization of the lagrange multipliers wherein the other unknowns do not appear this approach can be applied to other hybridized mixed methods as well

third order maximum principle satisfying direct discontinuous galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes we develop 3rd order maximum principle satisfying direct discontinuous galerkin methods 8 9 19 21 for convection diffusion equations on unstructured triangular mesh we carefully calculate the normal derivative numerical flux across element edges and prove that with proper choice of parameter pair 0 1 in the numerical flux formula the quadratic polynomial solution satisfies strict maximum principle the polynomial solution is bounded within the given range and third order accuracy is maintained there is no geometric restriction on the meshes and obtuse triangles are allowed in the partition a sequence of numerical examples are carried out to demonstrate the accuracy and capability of the maximum principle satisfying limiter

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

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

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

an adaptive mixed scheme for energy transport simulations of field effect transistors energy transport models are used in semiconductor simulations to account for thermal effects the model consists of the continuity equations for the number and energy of the electrons coupled to the poisson equation for the electrostatic potential the movement of the holes is modeled by drift diffusion equations and shockley read hall recombination generation processes are taken into account the stationary equations are discretized using a mixed hybrid finite element method introduced by marini and pietra the two dimensional mesh is adaptively refined using an error estimator motivated by results of hoppe and wohlmuth the numerical scheme is applied to the simulation of a two dimensional double gate mesfet and a deep submicron mosfet device

efficient estimation of semiparametric transformation models for the cumulative incidence of competing risks summary the cumulative incidence is the probability of failure from the cause of interest over a certain time period in the presence of other risks a semiparametric regression model proposed by fine and gray has become the method of choice for formulating the effects of covariates on the cumulative incidence its estimation however requires modelling of the censoring distribution and is not statistically efficient we present a broad class of semiparametric transformation models which extends the fine and gray model and we allow for unknown causes of failure we derive the non parametric maximum likelihood estimators and develop simple and fast numerical algorithms using the profile likelihood we establish the consistency asymptotic normality and semiparametric efficiency of the non parametric maximum likelihood estimators in addition we construct graphical and numerical procedures to evaluate and select models finally we demonstrate the advantages of the proposed methods over the existing methods through extensive simulation studies and an application to a major study on bone marrow transplantation

semiparametric transformation models for the case cohort study a general class of semiparametric transformation models is studied for analysing survival data from the case cohort design which was introduced by prentice 1986 weighted estimating equations are proposed for simultaneous estimation of the regression parameters and the transformation function it is shown that the resulting regression estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to a case cohort dataset from the atherosclerosis risk in communities study is also given to illustrate the methodology

differential geometric poisson bivectors in one space variable the connection of a nondegenerate k weight differential geometric poisson bivector is proved to be symmetric and integrable for any k 1 in the cases k 1 2 3 it is shown that the bivector has constant form if and only if its 2 0 tensor is parallel this is always the case if k 1 but is not generally true if k 2 the normal forms for k 2 are described a class of nondegenerate three weight poisson bivectors without constant form is described finally it is proved that if the sum of two homogeneous bivectors is poisson then the bivectors are separately poisson

compatibility conditions for hamiltonian pairs conditions necessary for pairs of hamiltonian operators of first through fifth order to form hamiltonian pairs are computed in the case of bi hamiltonian systems involving a hamiltonian pair one operator of which is a first third or a certain type of fifth order operator a technical condition in magri s theorem can be dropped

on estimation of optimal treatment regimes for maximizing t year survival probability a treatment regime is a deterministic function that dictates personalized treatment based on patients individual prognostic information there is increasing interest in finding optimal treatment regimes which determine treatment at one or more treatment decision points so as to maximize expected long term clinical outcome where larger outcomes are preferred for chronic diseases such as cancer or hiv infection survival time is often the outcome of interest and the goal is to select treatment to maximize survival probability we propose two nonparametric estimators for the survival function of patients following a given treatment regime involving one or more decisions i e the so called value based on data from a clinical or observational study we estimate an optimal regime by maximizing these estimators for the value over a prespecified class of regimes because the value function is very jagged we introduce kernel smoothing within the estimator to improve performance asymptotic properties of the proposed estimators of value functions are established under suitable regularity conditions and simulations studies evaluate the finite sample performance of the proposed regime estimators the methods are illustrated by application to data from an aids clinical trial

robust risk prediction with biomarkers under two phase stratified cohort design identification of novel biomarkers for risk prediction is important for disease prevention and optimal treatment selection however studies aiming to discover which biomarkers are useful for risk prediction often require the use of stored biological samples from large assembled cohorts and thus the depletion of a finite and precious resource to make efficient use of such stored samples two phase sampling designs are often adopted as resource efficient sampling strategies especially when the outcome of interest is rare existing methods for analyzing data from two phase studies focus primarily on single marker analysis or fitting the cox regression model to combine information from multiple markers however the cox model may not fit the data well under model misspecification the composite score derived from the cox model may not perform well in predicting the outcome under a general two phase stratified cohort sampling design we present a novel approach to combining multiple markers to optimize prediction by fitting a flexible nonparametric transformation model using inverse probability weighting to account for the outcome dependent sampling we propose to estimate the model parameters by maximizing an objective function which can be interpreted as a weighted c statistic for survival outcomes regardless of model adequacy the proposed procedure yields a sensible composite risk score for prediction a major obstacle for making inference under two phase studies is due to the correlation induced by the finite population sampling which prevents standard inference procedures such as the bootstrap from being used for variance estimation we propose a resampling procedure to derive valid confidence intervals for the model parameters and the c statistic accuracy measure we illustrate the new methods with simulation studies and an analysis of a two phase study of high density lipoprotein cholesterol hdl c subtypes for predicting the risk of coronary heart disease

predicting survival probabilities with semiparametric transformation models abstract prediction of survival probabilities for future patients is one of the main goals of fitting survival data with regression models in this article we consider a large class of semiparametric transformation models which includes the well known proportional hazards and proportional odds models for the analysis of failure time data specifically we propose pointwise and simultaneous confidence interval procedures for the survival probability of future patients with specific covariates these procedures can be easily implemented through simulation and are illustrated with the data from two well known clinical studies

nonnegativity of exact and numerical solutions of some chemotactic models we investigate nonnegativity of exact and numerical solutions to a generalized keller segel model this model includes the so called minimal keller segel model but can cover more general chemistry we use maximum principles and invariant sets to prove that all components of the solution of the generalized model are nonnegative we then derive numerical methods using finite element techniques for the generalized keller segel model adapting the ideas in our proof of nonnegativity of exact solutions to the discrete setting we are able to show nonnegativity of discrete solutions from the numerical methods under certain standard assumptions one of the numerical methods is then applied to the minimal keller segel model recalling known results on the qualitative behavior of this model we are able to choose parameters that yield convergence to a nonhomogeneous stationary solution while proceeding to exhibit these stationary patterns we also demonstrate how naive choices of numerical methods can give physically unrealistic solutions thereby justifying the need to study positivity preserving methods

semiparametric transformation models for causal inference in time to event studies with all or nothing compliance we consider causal inference in randomized survival studies with right censored outcomes and all or nothing compliance using semiparametric transformation models to estimate the distribution of survival times in treatment and control groups conditional on covariates and latent compliance type estimands depending on these distributions for example the complier average causal effect cace the complier effect on survival beyond time t and the complier quantile effect are then considered maximum likelihood is used to estimate the parameters of the transformation models using a specially designed expectation maximization em algorithm to overcome the computational difficulties created by the mixture structure of the problem and the infinite dimensional parameter in the transformation models the estimators are shown to be consistent asymptotically normal and semiparametrically efficient inferential procedures for the causal parameters are developed a simulation study is conducted to evaluate the finite sample performance of the estimated causal parameters we also apply our methodology to a randomized study conducted by the health insurance plan of greater new york to assess the reduction in breast cancer mortality due to screening

low order hamiltonian operators having momentum abstract we describe all fifth order hamiltonian operators in one dependent and one independent variable that possess momentum i e for which there exists a hamiltonian associated with translation in the independent variable similar results for first and third order hamiltonian operators were obtained earlier by mokhov

evaluating prediction rules for t year survivors with censored regression models suppose that we are interested in establishing simple but reliable rules for predicting future t year survivors through censored regression models in this article we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate sensitivity and specificity and positive and negative predictive values specifically under various working models we derive consistent estimators for the above measures through substitution and cross validation estimation procedures furthermore we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified confidence intervals for example for the difference of the precision measures between two competing rules can then be constructed all of the proposals are illustrated with real examples and their finite sample properties are evaluated through a simulation study

semiparametric regression analysis for clustered failure time data inference procedures based on the partial likelihood function for the cox proportional hazards model have been generalised to the case in which the data consist of a large number of independent small groups of correlated failure time observations lee wei amato 1992 liang self chang 1993 cai prentice 1997 however the cox model may not fit the data well a class of linear transformation models which includes the proportional hazards and odds models as special cases has been studied extensively for univariate event times in this paper statistical methods to analyse such correlated observations are proposed for these models we use the data from a recent study of the genetic aetiology of alcoholism to illustrate the new procedures for estimation prediction and model selection

a mixed finite element discretization of the energy transport model for semiconductors energy transport models describe the flow of electrons through a semiconductor device influenced by diffusive electrical and thermal effects they consist of the continuity equations for the mass and energy coupled with poisson s equation for the electrostatic potential the energy transport model can be written in a drift diffusion formulation which is used for the numerical approximation the stationary equations are discretized with an exponential fitting mixed finite element method in two space dimensions numerical simulations of a ballistic diode are performed and numerical convergence rates are computed furthermore a two dimensional metal semiconductor field effect transistor device with parabolic band structure is simulated

inference for a family of survival models encompassing the proportional hazards and proportional odds models for survival data regression the cox proportional hazards model is the most popular model but in certain situations the cox model is inappropriate various authors have proposed the proportional odds model as an alternative yang and prentice recently presented a number of easily implemented estimators for the proportional odds model here we show how to extend the methods of yang and prentice to a family of survival models that includes the proportional hazards model and proportional odds model as special cases the model is defined in terms of a box cox transformation of the survival function indexed by a transformation parameter this model has been discussed by other authors and is related to the harrington fleming g family of tests and to frailty models we discuss inference for the case where is known and the case where must be estimated we present a simulation study of a pseudo likelihood estimator and a martingale residual estimator we find that the methods perform reasonably we apply our model to a real data set copyright 2005 john wiley sons ltd

quantile regression for doubly censored data double censoring often occurs in registry studies when left censoring is present in addition to right censoring in this work we propose a new analysis strategy for such doubly censored data by adopting a quantile regression model we develop computationally simple estimation and inference procedures by appropriately using the embedded martingale structure asymptotic properties including the uniform consistency and weak convergence are established for the resulting estimators moreover we propose conditional inference to address the special identifiability issues attached to the double censoring setting we further show that the proposed method can be readily adapted to handle left truncation simulation studies demonstrate good finite sample performance of the new inferential procedures the practical utility of our method is illustrated by an analysis of the onset of the most commonly investigated respiratory infection pseudomonas aeruginosa in children with cystic fibrosis through the use of the u s cystic fibrosis registry

maximum likelihood estimation for the proportional odds model with random effects in this article we study the semiparametric proportional odds model with random effects for correlated right censored failure time data we establish that the maximum likelihood estimators for the parameters of this model are consistent and asymptotically gaussian furthermore the limiting variances achieve the semiparametric efficiency bounds and can be consistently estimated simulation studies show that the asymptotic approximations are accurate for practical sample sizes and that the efficiency gains of the proposed estimators over those of cai cheng and wei can be substantial a real example is provided to illustrate the proposed methods

semiparametric profile likelihood estimation for continuous outcomes with excess zeros in a random threshold damage resistance model continuous outcome data with a proportion of observations equal to zero often referred to as semicontinuous data arise frequently in biomedical studies typical approaches involve two part models with one part a logistic model for the probability of observing a zero and some parametric continuous distribution for modeling the positive part of the data we propose a semiparametric model based on a biological system with competing damage manifestation and resistance processes this allows us to derive a closed form profile likelihood based on the retro hazard function leading to a flexible procedure for modeling continuous data with a point mass at zero a simulation study is presented to examine the properties of the method in finite samples we apply the method to a data set consisting of pulmonary capillary hemorrhage area in lab rats subjected to diagnostic ultrasound copyright 2017 john wiley sons ltd

hamiltonian perturbation theory in noncanonical coordinates the traditional methods of hamiltonian perturbation theory in classical mechanics are first presented in a way which clearly displays their differential geometric foundations these are then generalized to the case of noncanonical in phase space in the new method the hamiltonian h is treated not as a scalar in phase space but as one component of the fundamental form p dq hdt the perturbation analysis is applied to this entire form in all of its components

semiparametric transformation models for point processes in this article we propose a family of semiparametric transformation models for point processes with positive jumps of arbitrary sizes these models offer great flexibilities in formulating the effects of covariates on the mean function of the point process while leaving the stochastic structure completely unspecified we develop a class of estimating equations for the baseline mean function and the vector valued regression parameter based on censored point processes and covariate data these equations can be solved easily by the standard newton raphson algorithm the resultant estimator of the regression parameter is consistent and asymptotically normal with a covariance matrix that can be estimated consistently furthermore the estimator of the baseline mean function is uniformly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function we demonstrate through extensive simulation studies that the proposed inference procedu

analysis of clustered interval censored data using a class of semiparametric partly linear frailty transformation models a flexible class of semiparametric partly linear frailty transformation models is considered for analyzing clustered interval censored data which arise naturally in complex diseases and dental research this class of models features two nonparametric components resulting in a nonparametric baseline survival function and a potential nonlinear effect of a continuous covariate the dependence among failure times within a cluster is induced by a shared unobserved frailty term a sieve maximum likelihood estimation method based on piecewise linear functions is proposed the proposed estimators of the regression dependence and transformation parameters are shown to be strongly consistent and asymptotically normal whereas the estimators of the two nonparametric functions are strongly consistent with optimal rates of convergence an extensive simulation study is conducted to study the finite sample performance of the proposed estimators we provide an application to a dental study for illustration

the maximum principle violations of the mixed hybrid finite element method applied to diffusion equations the affluent literature of finite element methods applied to linear parabolic problems generally produces numerical procedures with satisfactory properties from a numerical approximation point of view however some initial boundary conditions or abrupt sink source terms may cause large gradients at some points and consequently jumps in the solution that usually needs a certain period of time to become more and more smooth this intuitive fact of the diffusion process necessitates when applying numerical methods varying the mesh size in time and space according to the smoothness of the solution in this work the numerical behavior of the time dependent solutions for such problems during small time duration obtained by using the mixed hybrid finite element method mhfem is investigated numerical comparisons with the standard galerkin finite element fe as well as the finite difference fd methods are checked up on due to the fact that the mixed methods violate the discrete maximum principle some numerical experiments showed that the mhfem leads sometimes to non physical peaks in the solution a diffusivity criterion relating the mesh steps for an artificial initial boundary value problem will be presented one of the propositions given to avoid any non physical oscillations is to use the mass lumping techniques

likelihood approaches for proportional likelihood ratio model with right censored data regression methods for survival data with right censoring have been extensively studied under semiparametric transformation models such as the cox regression model and the proportional odds model however their practical application could be limited because of possible violation of model assumption or lack of ready interpretation for the regression coefficients in some cases as an alternative in this paper the proportional likelihood ratio model introduced by luo and tsai is extended to flexibly model the relationship between survival outcome and covariates this model has a natural connection with many important semiparametric models such as generalized linear model and density ratio model and is closely related to biased sampling problems compared with the semiparametric transformation model the proportional likelihood ratio model is appealing and practical in many ways because of its model flexibility and quite direct clinical interpretation we present two likelihood approaches for the estimation and inference on the target regression parameters under independent and dependent censoring assumptions based on a conditional likelihood approach using uncensored failure times a numerically simple estimation procedure is developed by maximizing a pairwise pseudo likelihood we also develop a full likelihood approach and the most efficient maximum likelihood estimator is obtained by a profile likelihood simulation studies are conducted to assess the finite sample properties of the proposed estimators and compare the efficiency of the two likelihood approaches an application to survival data for bone marrow transplantation patients of acute leukemia is provided to illustrate the proposed method and other approaches for handling non proportionality the relative merits of these methods are discussed in concluding remarks

conditional transformation models the ultimate goal of regression analysis is to obtain information about the conditional distribution of a response given a set of explanatory variables this goal is however seldom achieved because most established regression models only estimate the conditional mean as a function of the explanatory variables and assume that higher moments are not aected by the regressors the underlying reason for such a restriction is the assumption of additivity of signal and noise we propose to relax this common assumption in the framework of transformation models the novel class of semiparametric regression models proposed herein allows transformation functions to depend on explanatory variables these transformation functions are estimated by regularised optimisation of scoring rules for probabilistic forecasts e g the continuous ranked probability score the corresponding estimated conditional distribution functions are consistent based on applications from dierent domains we show that these conditional transformation models are useful for describing possible heteroscedasticity comparing spatially varying distributions identifying extreme events deriving prediction intervals and selecting variables beyond mean regression eects an empirical investigation based on a heteroscedastic varying coecient simulation model demonstrates that semiparametric estimation of conditional distribution functions can be more benecial than kernel based non parametric approaches or parametric generalised additive models for location scale and shape

an a priori error estimate for a monotone mixed finite element discretization of a convection diffusion problem we present a local exponential fitting hybridized mixed finite element method for convection diffusion problem on a bounded domain with mixed dirichlet neuman boundary conditions with a new technique that interpretes the algebraic system after static condensation as a bilinear form acting on certain lifting operators we prove an a priori error estimate on the lagrange multipliers that requires minimal regularity while an extension of more classical arguments provide an estimate for the other solution components

classification results and the darboux theorem for low order hamiltonian operators hamiltonian operators and their behavior under differential substitutions are studied scalar hamiltonian operators are classified up to fifth order and it is shown that all such operators may be obtained from the first order gardner operator dx by differential substitutions thus proving an infinite dimensional darboux theorem for hamiltonian systems of evolution equations corresponding to such operators

marginal hazards model for case cohort studies with multiple disease outcomes case cohort study designs are widely used to reduce the cost of large cohort studies while achieving the same goals especially when the disease rate is low a key advantage of the case cohort study design is its capacity to use the same subcohort for several diseases or for several subtypes of disease in order to compare the effect of a risk factor on different types of diseases times to different events need to be modelled simultaneously valid statistical methods that take the correlations among the outcomes from the same subject into account need to be developed to this end we consider marginal proportional hazards regression models for case cohort studies with multiple disease outcomes we also consider generalized case cohort designs that do not require sampling all the cases which is more realistic for multiple disease outcomes we propose an estimating equation approach for parameter estimation with two different types of weights consistency and asymptotic normality of the proposed estimators are established large sample approximation works well in small samples in simulation studies the proposed methods are applied to the busselton health study

biometrika centenary survival analysis although papers relating to survival analysis have appeared in biometrika since the very first issue the current emphasis on the topic in this journal is fairly new especially as it relates to applications in biostatistics this survey traces the development of survival analysis throughout the twentieth century as reflected in the pages of biometrika focusing primarily on work published since 1980

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

semiparametric regression analysis for doubly censored data summary we analyse doubly censored data using semiparametric transformation models we provide inference procedures for the regression parameters and derive the asymptotic distributions of the proposed estimators procedures for model checking and model selection are also discussed we illustrate our approach with a viral load dataset from a recent aids clinical trial

multi hamiltonian structure of the born infeld equation the multi hamiltonian structure conservation laws and higher order symmetries for the born infeld equation are exhibited a new transformation of the born infeld equation to the equations of a chaplygin gas is presented and explored the born infeld equation is distinguished among two dimensional hyperbolic systems by its wealth of such multi hamiltonian structures

censored regression with the multistate accelerated sojourn times model many disease processes are characterized by two or more successive health states and it is often of interest and importance to assess state specific covariate effects however with incomplete follow up data such inference has not been satisfactorily addressed in the literature we model the logarithm transformed sojourn time in each state as linearly related to the covariates however neither the distributional form of the error term nor the dependence structure of the states needs to be specified we propose a regression procedure to accommodate incomplete follow up data asymptotic theory is presented along with some tools for goodness of fit diagnostics simulation studies show that the proposal is reliable for practical use we illustrate it by application to a cancer clinical trial

analyzing length biased data with semiparametric transformation and accelerated failure time models right censored time to event data are often observed from a cohort of prevalent cases that are subject to length biased sampling informative right censoring of data from the prevalent cohort within the population often makes it difficult to model risk factors on the unbiased failure times for the general population because the observed failure times are length biased in this paper we consider two classes of flexible semiparametric models the transformation models and the accelerated failure time models to assess covariate effects on the population failure times by modeling the length biased times we develop unbiased estimating equation approaches to obtain the consistent estimators of the regression coefficients large sample properties for the estimators are derived the methods are confirmed through simulations and illustrated by application to data from a study of a prevalent cohort of dementia patients

case cohort and case control analysis with cox s model prentice 1986 proposed the case cohort design and studied a pseudolikelihood estimator of regression parameters in cox s model we derive a class of estimating equations for case cohort sampling each depending on a different estimator of the population distribution which lead naturally to simple estimators that improve on prentice s pseudolikelihood estimator we also discuss an equivalence between case control and case cohort sampling in terms of the estimation of regression parameters in cox s model

darboux theorem for hamiltonian differential operators it is proved that any one dimensional first order hamiltonian differential operator can be put into constant coefficient form by a suitable change of variables consequently there exist canonical variables for any such hamiltonian operator in the course of the proof a complete characterization of all first order hamiltonian differential operators as well as the general formula for the behavior of a hamiltonian operator under a change of variables involving both the independent and the dependent variables are found

symplectic integration of hamiltonian wave equations the numerical integration of a wide class of hamiltonian partial differential equations by standard symplectic schemes is discussed with a consistent hamiltonian approach we discretize the hamiltonian and the poisson structure separately then form the the resulting ode s the stability accuracy and dispersion of different explicit splitting methods are analyzed and we give the circumstances under which the best results can be obtained in particular when the hamiltonian can be split into linear and nonlinear terms many different treatments and examples are compared

testing goodness of fit for proportional hazards model with censored observations abstract a numerical omnibus test of fit for the two sample proportional hazards model is proposed for randomly censored observations the test is derived from cox s partial likelihood and does not need a dummy time dependent covariate or any partition of the time axis consistency of the test is established examples are provided for illustration

a comparison of a posteriori error estimators for mixed finite element discretizations by raviart thomas elements we consider mixed finite element discretizations of linear second order elliptic boundary value problems with respect to an adaptively generated hierarchy of possibly highly nonuniform simplicial triangulations in particular we present and analyze four different kinds of error estimators a residual based estimator a hierarchical one error estimators relying on the solution of local subproblems and on a superconvergence result respectively finally we examine the relationship between the presented error estimators and compare their local components

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

a sieve semiparametric maximum likelihood approach for regression analysis of bivariate interval censored failure time data abstractinterval censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis however most of the existing methods are for univariate data and there exists only limited research on bivariate data especially on regression analysis of bivariate interval censored data we present a class of semiparametric transformation models for the problem and for inference a sieve maximum likelihood approach is developed the model provides a great flexibility in particular including the commonly used proportional hazards model as a special case and in the approach bernstein polynomials are employed the strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore the estimators are shown to be asymptotically efficient extensive simulation studies are conducted and indicate that the proposed method works well for practical situations supplementary materials for this article are

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

two dimensional exponential fitting and applications to drift diffusion models a class of methods is introduced that generalizes the so called exponential fitting method to two dimensional problems and more specifically to equations of the type operatorname div underset raise0 3em hbox smash scriptscriptstyle nabla u u underset raise0 3em hbox smash scriptscriptstyle nabla psi f with psi given and underset raise0 3em hbox smash scriptscriptstyle nabla psi big in a part of the domain the basic idea is the following i write the equation as operatorname div e psi underset raise0 3em hbox smash scriptscriptstyle nabla rho f through the change of variables u rho e psi ii discretize the symmetric equation by means of a method that uses some kind of harmonic average for the coefficient e psi mixed hybrid etc iii write the discrete scheme in terms of the nodal values of u e psi rho this produces an m matrix

fitting semiparametric transformation regression models to data from a modified case cohort design summary we consider the problem of fitting semiparametric transformation regression models to data from a modified case cohort study in which the censoring times of all the censored subjects in the cohort are observed we propose to maximise a conditional profile likelihood to obtain the estimator of the regression parameter under the assumption that the censoring is independent of the covariates the estimator is shown to be consistent and asymptotically normally distributed numerical studies suggest that the relative efficiency of the estimator is very high and that the estimator is often less biased than the estimator from the complete case analysis and more accurate than the pseudolikelihood estimator

gamma frailty transformation models for multivariate survival times we propose a class of transformation models for multivariate failure times the class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time nonparametric maximum likelihood estimation is used for inference the maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal and their asymptotic variances attain the semiparametric efficiency bound simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes the method is illustrated using data from a cardiovascular study