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

the numerical solution of the exterior dirichlet problem for helmholtz s equation via modified green s functions approach abstract in the 1970s a modified green s function approach for solving the helmholtz equation was proposed by jones and ursell and in the 1980s was clarified by kleinman roach and kress but to date there are no numerical results available for this approach in this paper a global galerkin method is used to numerically solve the exterior dirichlet problem for the helmholtz equation in three dimensions based on jones modified integral equation approach theoretical and computational details of the method are presented

the generalized estimating equation approach when data are not missing completely at random abstract we propose two methods for handling missing data in generalized estimating equation gee analyses mean imputation and multiple imputation each provides valid gee estimates when data are missing at random missing outcomes are imputed sequentially starting from the outcome nearest in time to the observed outcome the estimators from the two kinds of imputation are compared with the weighting method of robins et al we show that multiple imputation with an infinite number of replications is asymptotically equivalent to mean imputation the methods are applied to a stroke study in which neurological outcomes are measured over time after stroke but some outcomes are missing due to death or loss to follow up

ignorability in general incomplete data models summary rubin 1976 defined ignorability conditions for frequentist and bayes likelihood analyses of data subject to missing observations more recently heitjan rubin 1991 and heitjan 1993 generalised the rubin model to encompass other forms of incompleteness establishing ignorability conditions for bayes likelihood inferences only this paper extends the heitjan rubin model by explicitly defining the observed degree of coarseness as a data element this permits the development of a frequentist theory including a generalisation of missing completely at random the frequentist ignorability condition for missing data the model is applied in a number of incomplete data problems of general interest

nonparametric estimation of the sojourn time distributions for a multipath model summary we use a multipath multistate model to describe data with multiple end points statistical inference based on the intermediate end point is challenging because of the problems of nonidentifiability and dependent censoring we study nonparametric estimation for the path probability and the sojourn time distributions between the states the methodology proposed can be applied to analyse cure models which account for the competing risk of death asymptotic properties of the estimators proposed are derived simulation shows that the methods proposed have good finite sample performance the methodology is applied to two data sets

a modification of the redistribution to the right algorithm using disease markers summary disease markers are time dependent covariates which describe progression towards development of disease traditional methods in survival analysis do not make use of available data on these markers to recover additional information from censored individuals using a heuristic modification of the redistribution to the right algorithm efron 1967 a new approach for recovering information for censored individuals using disease markers is proposed additionally the statistical properties of the proposed method are examined there are two possible advantages to this modification i bias reduction when censoring is informative and ii an increase in efficiency in the case of truly noninformative censoring

piecewise polynomial collocation for boundary integral equations this paper considers the numerical solution of boundary integral equations of the second kind for laplace s equation delta u 0 on connected regions d in bf r 3 with boundary s the boundary s is allowed to be smooth or piecewise smooth and we let delta k 1 leq k leq n be a triangulation of s the numerical method is collocation with approximations which are piecewise quadratic in the parametrization variables leading to a numerical solution u n superconvergence results for u n are given for s a smooth surface and for a special type of refinement strategy for the triangulation we show that u u n is o delta 4 log delta at the collocation node points with delta being the mesh size for delta k error analyses are given are given for other quantities and an important error analysis is given for the approximation of s by piecewise quadratic interpolation on each triangular element with s either smooth or piecewise smooth the convergence result we

fast collocation methods for second kind integral equations in this paper we develop fast collocation methods for integral equations of the second kind with weakly singular kernels for this purpose we construct multiscale interpolating functions and collocation functionals having vanishing moments moreover we propose a truncation strategy for the coefficient matrix of the corresponding discrete system which forms a basis for fast algorithms an optimal order of convergence of the approximate solutions obtained from the fast algorithms is proved and the computational complexity of the algorithms is estimated the stability of the numerical method and the condition number of the truncated coefficient matrix are analyzed

boundary knot method for some inverse problems associated with the helmholtz equation the boundary knot method is an inherently meshless integration free boundary type radial basis function collocation technique for the solution of partial differential equations in this paper the method is applied to the solution of some inverse problems for the helmholtz equation including the highly ill posed cauchy problem since the resulting matrix equation is badly ill conditioned a regularized solution is obtained by employing truncated singular value decomposition while the regularization parameter for the regularization method is provided by the l curve method numerical results are presented for both smooth and piecewise smooth geometry the stability of the method with respect to the noise in the data is investigated by using simulated noisy data the results show that the method is highly accurate computationally efficient and stable and can be a competitive alternative to existing methods for the numerical solution of the problems copyright 2005 john wiley sons ltd

nonparametric estimation of successive duration times under dependent censoring summary this paper considers nonparametric inference for duration times of two successive events since the second duration process becomes observable only if the first event has occurred the length of the first duration affects the probability of the second duration being censored dependent censoring arises if the two duration times are correlated which is often the case standard approaches to this problem fail because of dependent censoring mechanism a new product limit estimator for the second duration variable and a pathdependent joint survival function estimator are proposed both modified for the dependent censoring properties of the estimators are discussed an example from lawless 1982 is studied for illustrative purposes as well as a simulation study

properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints summary a nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients but results are available for a surrogate endpoint for a larger sample of patients the test is an adaptation of the wilcoxon mann whitney two sample test with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints the validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study this assumption is viable in trials in which the final endpoint is evaluated at a landmark timepoint in the patients natural history a small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated when compared with the conventional test based only on the final endpoints the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint our research indicates that in the absence of modeling assumptions auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances

inverse regression estimation for censored data an inverse regression methodology for assessing predictor performance in the censored data setup is developed along with inference procedures and a computational algorithm the technique developed here allows for conditioning on the unobserved failure time along with a weighting mechanism that accounts for the censoring the implementation is nonparametric and computationally fast this provides an efficient methodological tool that can be used especially in cases where the usual modeling assumptions are not applicable to the data under consideration it can also be a good diagnostic tool that can be used in the model selection process we have provided theoretical justification of consistency and asymptotic normality of the methodology simulation studies and two data analyses are provided to illustrate the practical utility of the procedure

inference for imputation estimators we derive an estimator of the asymptotic variance of both single and multiple imputation estimators we assume a parametric imputation model but allow for non and semiparametric analysis models our variance estimator in contrast to the estimator proposed by rubin 1987 is consistent even when the imputation and analysis models are misspecified and incompatible with one another

a kernel method for incorporating information on disease progression in the analysis of survival summary this paper considers incorporating information on disease progression in the analysis of survival a three state model is assumed with the distribution of each transition estimated separately the distribution of survival following progression can depend on the time of progression kernel methods are used to give consistent estimators under general forms of dependence the estimators for the individual transitions are then combined into an overall estimator of the survival distribution a test statistic for equality of survival between treatment groups is proposed based on the tests of pepe fleming 1989 1991 in simulations the kernel method successfully incorporated dependence on the time of progression in some reasonable settings but under extreme forms of dependence the tests had substantial bias if survival beyond progression can be predicted fairly accurately then gains in power over standard methods that ignore progression can be substantial but the gains are smaller when survival beyond progression is more variable the methodology is illustrated with an application to a breast cancer clinical trial

partial identification and inference in censored quantile regression abstract in this paper we study partial identification and inference in a linear quantile regression where the dependent variable is subject to possibly unknown dependent censoring characterized by an archimedean copula an outer set of the identified set for the regression coefficient is characterized via inequality constraints for one parameter ordered families of archimedean copulas we construct a simple confidence set by inverting an asymptotically pivotal statistic a bootstrap confidence set is also constructed sensitivity of the identified set to possible misspecification of the true copula and the finite sample performance of the boostrap confidence set are investigated numerically

a note on wave number dependence of wavelet matrix compression for integral equations with oscillatory kernel this paper analyzes the effect of large wave numbers on the wavelet method for integral equations arising in electromagnetic applications it is shown that the compression of the stiffness matrix deteriorates with increasing wave number a characteristic that has been reported before in the literature here however the exact dependence on the wave number is calculated analytically for the two dimensional helmholtz problem

weighted kaplan meier statistics a class of distance tests for censored survival data a class of statistics based on the integrated weighted difference in kaplan meier estimators is introduced for the two sample censored data problem with positive weight functions these statistics are intuitive for and sensitive against the alternative of stochastic ordering the standard weighted log rank statistics are not always sensitive against this alternative particularly if the hazard functions cross qualitative comparisons are made between the weighted log rank statistics and these weighted kaplan meier wkm statistics a statement of null asymptotic distribution theory is given and the choice of weight function is discussed in some detail results from small sample simulation studies indicate that these statistics compare favorably with the log rank procedure even under the proportional hazards alternative and may perform better than it under the crossing hazards alternative

weighted kaplan meier estimators motivating to estimate hiv 1 rna reduction censored by a limit of detection measuring the magnitude of reduction in hiv 1 rna levels accurately is difficult because many patients have a censored reduction due to the limit of detection lod of the virologic assay being employed the use of censored methods has improved the analysis of such reductions compared with crude methods but implies independent censoring for hiv 1 rna reduction data the value at which a patient s hiv 1 rna reduction becomes censored is mainly determined by the patient s baseline hiv 1 rna level we suggest two possibilities based on modification of the redistribution to the right algorithm to handle the situation of dependence either from a single continuous marker that is the baseline hiv 1 rna level or from multiple markers two series of simulation one in the hiv 1 rna setting and one in the classical censoring setting compared performance of the previous methods with our suggestions our proposed estimators show good performances when the dependent censoring is due to lod overall in the classical censoring setting our suggestions perform as well as other methods including the inverse probability of censoring weighted and the kaplan meier imputation with bootstrap we applied those estimators to estimate the hiv 1 rna reduction at week 8 of 502 patients who received a raltegravir containing regimen and to data from the mayo clinic trial in primary biliary cirrhosis

semiparametric estimation of a proportional hazard model with unobserved heterogeneity the proportional hazard model with unobserved heterogeneity gives the hazard function of a random variable conditional on covariates and a second random variable representing unobserved heterogeneity this paper shows how to estimate the baseline hazard function and the distribution of the unobserved heterogeneity nonparametrically the baseline hazard function and heterogeneity distribution are assumed to satisfy smoothness conditions but are not assumed to belong to known finite dimensional parametric families existing estimators assume that the baseline hazard function or heterogeneity distribution belongs to a known parametric family thus the estimators presented here are more general than existing ones

a modification of the dewilde van der veen method for inversion of finite structured matrices abstract we study a class of block structured matrices r r ij i j 1 n with a property that the solution of the corresponding system rx y of linear algebraic equations may be performed for o n arithmetic operations in this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms these algorithms are related to those suggested by p m dewilde and a j van der veen time varying systems and computations kluwer academic publishers new york 1998 for a class of finite and infinite matrices with a small hankel rank the algorithms presented here are more transparent and are a modification of the algorithms from the above reference the approach and the proofs are essentially different from those in the above mentioned reference the paper contains also analysis of complexity and results of numerical experiments

a framework for consistent prediction rules based on markers summary recently interest has developed regarding the statistical properties and uses of marker processes in the context of the analysis of failure time data or survival analysis a marker process is a stochastic process that acts as a time dependent covariate that is internal to the unit under study in the language of kalbfleisch prentice 1980 as such the sample path of the process up to a certain point in time may carry information about the subsequent hazard for failure uses of marker processes in the analysis of survival data are manifold here we consider the specific area of prediction of future failure times at a point in time based on various forms of information about the history of the marker process we provide a stochastic framework for the consideration of prediction functions demonstrate a simple consistency condition that such functions should satisfy and discuss construction of prediction functions in a general sense several examples are used to illustrate the ideas and we show that certain recently suggested imputation schemes fail to meet the consistency condition the consistency condition also elucidates the model assumed by cox 1983 in his work on surrogate responses we also briefly consider a closely related backward prediction problem

a non parametric maximum likelihood estimator for bivariate interval censored data we derive a non parametric maximum likelihood estimator for bivariate interval censored data using standard techniques for constrained convex optimization our approach extends those taken for univariate interval censored data we illustrate the estimator with bivariate data from an aids study

toward a curse of dimensionality appropriate coda asymptotic theory for semi parametric models we argue that due to the curse of dimensionality there are major difficulties with any pure or smoothed likelihood based method of inference in designed studies with randomly missing data when missingness depends on a high dimensional vector of variables we study in detail a semi parametric superpopulation version of continuously stratified random sampling we show that all estimators of the population mean that are uniformly consistent or that achieve an algebraic rate of convergence no matter how slow require the use of the selection randomization probabilities we argue that in contrast to likelihood methods which ignore these probabilities inverse selection probability weighted estimators continue to perform well achieving uniform n 1 2 rates of convergence we propose a curse of dimensionality appropriate coda asymptotic theory for inference in non and semi parametric models in an attempt to formalize our arguments we discuss whether our results constitute a fatal blow to the likelihood principle and study the attitude toward these that a committed subjective bayesian would adopt finally we apply our coda theory to analyse the effect of the curse of dimensionality in several interesting semi parametric models including a model for a two armed randomized trial with randomization probabilities depending on a vector of continuous pretreatment covariates x we provide substantive settings under which a subjective bayesian would ignore the randomization probabilities in analysing the trial data we then show that any statistician who ignores the randomization probabilities is unable to construct nominal 95 per cent confidence intervals for the true treatment effect that have both i an expected length which goes to zero with increasing sample size and ii a guaranteed expected actual coverage rate of at least 95 per cent over the ensemble of trials analysed by the statistician during his or her lifetime however we derive a new interval estimator depending on the randomization probabilities that satisfies i and ii

estimating mean cost using auxiliary covariates we study the estimation of mean medical cost when censoring is dependent and a large amount of auxiliary information is present under missing at random assumption we propose semiparametric working models to obtain low dimensional summarized scores an estimator for the mean total cost can be derived nonparametrically conditional on the summarized scores we show that when either the two working models for cost survival process or the model for censoring distribution is correct the estimator is consistent and asymptotically normal small sample performance of the proposed method is evaluated via simulation studies finally our approach is applied to analyze a real data set in health economics

conditional empirical processes consider a sequence i xi yi i 1 of independent d 1 random vectors with common d f h text h left text x y right mathbb p left text x x y y right text left text x y right in mathbb r text d 1

analysis of accelerated failure time data with dependent censoring using auxiliary variables via nonparametric multiple imputation we consider the situation of estimating the marginal survival distribution from censored data subject to dependent censoring using auxiliary variables we had previously developed a nonparametric multiple imputation approach the method used two working proportional hazards ph models one for the event times and the other for the censoring times to define a nearest neighbor imputing risk set this risk set was then used to impute failure times for censored observations here we adapt the method to the situation where the event and censoring times follow accelerated failure time models and propose to use the buckley james estimator as the two working models besides studying the performances of the proposed method we also compare the proposed method with two popular methods for handling dependent censoring through the use of auxiliary variables inverse probability of censoring weighted and parametric multiple imputation methods to shed light on the use of them in a simulation study with time independent auxiliary variables we show that all approaches can reduce bias due to dependent censoring the proposed method is robust to misspecification of either one of the two working models and their link function this indicates that a working proportional hazards model is preferred because it is more cumbersome to fit an accelerated failure time model in contrast the inverse probability of censoring weighted method is not robust to misspecification of the link function of the censoring time model the parametric imputation methods rely on the specification of the event time model the approaches are applied to a prostate cancer dataset copyright 2015 john wiley sons ltd

sample size calculations for the two sample problem using the multiplicative intensity model in this paper we propose formulae for calculating the expected number of events or alternatively the required trial duration for clinical trials involving two treatment groups in which patients may potentially experience multiple events and the data will be analysed using a multiplicative intensity mi model we use a partial likelihood based approach and examine in detail two mi models one that includes a binary treatment variable as the only covariate and a three state markov process model in which a binary time varying covariate is added to the previous model for the simpler model our formula coincides with those derived by cook using full likelihood methods we present applications of the derived formulae to chronic granulomatous disease and breast cancer data sets

boundary integral equation method for source localization with a continuous wave sonar in this paper matched field processing is combined with the boundary integral equation method biem of scattering theory to study a sound source localization problem in a perturbed shallow ocean it is assumed that there is a known inclusion embedded in a shallow water waveguide continuous waves cw produced by a sound source are scattered by the inclusion and then received by a hydrophone array because the symmetry of the waveguide has been destroyed by the existence of the inclusion a proper procedure is required to avoid the mismatching a numerical scheme is presented that makes use of the separation of the source and the detection array and greatly reduces the computation a numerical simulation using this method is presented

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

multiple imputation based on restricted mean model for censored data most multiple imputation mi methods for censored survival data either ignore patient characteristics when imputing a likely event time or place quite restrictive modeling assumptions on the survival distributions used for imputation in this research we propose a robust mi approach that directly imputes restricted lifetimes over the study period based on a model of the mean restricted life as a linear function of covariates this method has the advantages of retaining patient characteristics when making imputation choices through the restricted mean parameters and does not make assumptions on the shapes of hazards or survival functions simulation results show that our method outperforms its closest competitor for modeling restricted mean lifetimes in terms of bias and efficiency in both independent censoring and dependent censoring scenarios survival estimates of restricted lifetime model parameters and marginal survival estimates regain much of the precision lost due to censoring the proposed method is also much less subject to dependent censoring bias captured by covariates in the restricted mean model this particular feature is observed in a full statistical analysis conducted in the context of the international breast cancer study group ludwig trial v using the proposed methodology

on the use of nonparametric regression techniques for fitting parametric regression models a new method for fitting parametric regression models is proposed it consists of applying the least squares ls principle on the pairs xi rh xi i 1 n where x denotes the explanatory variable and mn x is a location estimate of the conditional distribution of the response variable y given that x x consistency and asymptotic normality of the estimators are established under general conditions these conditions are shown to be satisfied when the data are incomplete due to random censoring or truncation usable expressions for the asymptotic variance covariance matrix of the parameters are provided in these incomplete data cases as an extra bonus this regression method allows the use of ordinary residual plots as a data analytic aide this is illustrated on two real data sets a simulation study examines the small sample behavior of the estimators and their estimated asymptotic variance extension of the method to more complicated models is discussed

efficient solution of linear systems of equations with recursive structure abstract inversion algorithms of order n2 for n n matrices with recursive structure are derived in a unified way several known algorithms as well as some new ones for toeplitz type hilbert type and vandermonde type matrices are given

joint models for efficient estimation in proportional hazards regression models in survival studies information lost through censoring can be partially recaptured through repeated measures data which are predictive of survival in addition such data may be useful in removing bias in survival estimates due to censoring which depends upon the repeated measures here we investigate joint models for survival t and repeated measurements given a vector of covariates mixture models indexed as f t f t are well suited for assessing covariate effects on survival time our objective is efficiency gains using non parametric models for in order to avoid introducing bias by misspecification of the distribution for we model t as a piecewise exponential distribution with proportional hazards covariate effect the component t has a multinomial model the joint likelihood for survival and longitudinal data is maximized using the em algorithm the estimate of covariate effect is compared to the estimate based on the standard proportional hazards model and an alternative joint model based estimate we demonstrate modest gains in efficiency when using the joint piecewise exponential joint model in a simulation the estimated efficiency gain over the standard proportional hazards model is 6 4 per cent in clinical trial data the estimated efficiency gain over the standard proportional hazards model is 10 2 per cent copyright 2003 john wiley sons ltd

direct approach to the band completion problem we study the problem of completion of a matrix with a specified band in such a way that the inverse be a band matrix with the same width for the general block matrix case a new approach to solve this and related problems is proposed the relations with the class of quasiseparable matrices play an important role

nonparametric survival estimation using prognostic longitudinal covariates one of the primary problems facing statisticians who work with survival data is the loss of information that occurs with right censored data this research considers trying to recover some of this endpoint information through the use of a prognostic covariate which is measured on each individual we begin by defining a survival estimate which uses time dependent covariates to more precisely get at the underlying survival curves in the presence of censoring this estimate has a smaller asymptotic variance than the usual kaplan meier in the presence of censoring and reduces to the kaplan meier 1958 journal of the american statistical association 53 457 481 in situations where the covariate is not prognostic or no censoring occurs in addition this estimate remains consistent when the incorporated covariate contains information about the censoring process as well as survival information because the kaplan meier estimate is known to be biased in this situation due to informative censoring we recommend use of our estimate

multiple lu factorizations of a singular matrix a singular matrix a may have more than one lu factorizations in this work the set of all lu factorizations of a is explicitly described when the lower triangular matrix l is nonsingular to this purpose a canonical form of a under left multiplication by unit lower triangular matrices is introduced this canonical form allows us to characterize the matrices that have an lu factorization and to parametrize all possible lu factorizations formulae in terms of quotient of minors of a are presented for the entries of this canonical form

nearest neighbor estimation of a bivariate distribution under random censoring we consider the problem of estimating the bivariate distribution of the random vector x y when y may be subject to random censoring the censoring variable c is allowed to depend on x but it is assumed that y and c are conditionally independent given x x the estimate of the bivariate distribution is obtained by averaging estimates of the conditional distribution of y given x x over a range of values of x the weak convergence of the centered estimator multiplied by n 1 2 is obtained and a closed form expression for the covariance function of the limiting process is given it is shown that the proposed estimator is optimal in the beran sense this is similar to an optimality property the product limit estimator enjoys using the proposed estimator of the bivariate distribution an extension of the least squares estimator to censored data polynomial regression is obtained and its asymptotic normality established

nonparametric comparison of two survival functions with dependent censoring via nonparametric multiple imputation when the event time of interest depends on the censoring time conventional two sample test methods such as the log rank and wilcoxon tests can produce an invalid test result we extend our previous work on estimation using auxiliary variables to adjust for dependent censoring via multiple imputation to the comparison of two survival distributions to conduct the imputation we use two working models to define a set of similar observations called the imputing risk set one model is for the event times and the other for the censoring times based on the imputing risk set a nonparametric multiple imputation method kaplan meier imputation is used to impute a future event or censoring time for each censored observation after imputation the conventional nonparametric two sample tests can be easily implemented on the augmented data sets simulation studies show that the sizes of the log rank and wilcoxon tests constructed on the imputed data sets are comparable to the nominal level and the powers are much higher compared with the tests based on the unimputed data in the presence of dependent censoring if either one of the two working models is correctly specified the method is illustrated using aids clinical trial data comparing zdv and placebo in which cd4 count is the time dependent auxiliary variable

lu factorization for matrices in quasiseparable form via orthogonal transformations abstract the paper presents a new algorithm to compute the lu factorization of a matrix represented in a quasiseparable or semiseparable form i e using generators it obtains the quasiseparable representations of the factors l and u of an n n block matrix via o n arithmetic operations on the block entries the algorithm uses recursions based exclusively on unitary transformations which provide numerical stability even in singular cases the method of the paper is based on the theory developed in 1 and provides an alternative to the approach proposed in 7 for strongly regular matrices the algorithm presented here works also for some matrices with possibly singular principle submatrices the results of numerical tests show that also for strongly regular matrices the new algorithm is comparable with the previous methods

multiple imputation after 18 years abstract multiple imputation was designed to handle the problem of missing data in public use data bases where the data base constructor and the ultimate user are distinct entities the objective is valid frequency inference for ultimate users who in general have access only to complete data software and possess limited knowledge of specific reasons and models for nonresponse for this situation and objective i believe that multiple imputation by the data base constructor is the method of choice this article first provides a description of the assumed context and objectives and second reviews the multiple imputation framework and its standard results these preliminary discussions are especially important because some recent commentaries on multiple imputation have reflected either misunderstandings of the practical objectives of multiple imputation or misunderstandings of fundamental theoretical results then criticisms of multiple imputation are considered and finally comparisons are made to alt

calibrating parametric subject specific risk estimation for modern evidence based medicine decisions on disease prevention or management strategies are often guided by a risk index system for each individual the system uses his her baseline information to estimate the risk of experiencing a future disease related clinical event such a risk scoring scheme is usually derived from an overly simplified parametric model to validate a model based procedure one may perform a standard global evaluation via for instance a receiver operating characteristic analysis in this article we propose a method to calibrate the risk index system at a subject level specifically we developed point and interval estimation procedures for t year mortality rates conditional on the estimated parametric risk score the proposals are illustrated with a dataset from a large clinical trial with post myocardial infarction patients

survival analysis using auxiliary variables via non parametric multiple imputation we develop an approach based on multiple imputation that estimates the marginal survival distribution in survival analysis using auxiliary variables to recover information for censored observations to conduct the imputation we use two working survival models to define a nearest neighbour imputing risk set one model is for the event times and the other for the censoring times based on the imputing risk set two non parametric multiple imputation methods are considered risk set imputation and kaplan meier imputation for both methods a future event or censoring time is imputed for each censored observation with a categorical auxiliary variable we show that with a large number of imputes the estimates from the kaplan meier imputation method correspond to the weighted kaplan meier estimator we also show that the kaplan meier imputation method is robust to mis specification of either one of the two working models in a simulation study with time independent and time dependent auxiliary variables we compare the multiple imputation approaches with an inverse probability of censoring weighted method we show that all approaches can reduce bias due to dependent censoring and improve the efficiency we apply the approaches to aids clinical trial data comparing zdv and placebo in which cd4 count is the time dependent auxiliary variable

trigonometric wavelets for hermite interpolation the aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials the pair of scaling functions which span the sample spaces are fundamental functions for hermite interpolation on a dyadic partition of nodes on the interval 0 2 two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions together with the corresponding dual functions these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences consequently this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

analysis of semi parametric regression models with non ignorable non response in this article we consider the problem of making inferences about the parameter 0 indexing the conditional mean of an outcome given a vector of regressors when a subset of the variables outcome or covariates are missing for some study subjects and the probability of non response depends upon both observed and unobserved data values that is non response is non ignorable we propose a new class of inverse probability of censoring weighted estimators that are consistent and asymptotically normal can for estimating 0 when the non response probabilities can be parametrically modelled and a can estimator exists the proposed estimators do not require full specification of the likelihood and their computation does not require numerical integration we show that the asymptotic variance of the optimal estimator in our class attains the semi parametric variance bound for the model in some models no can estimator of 0 exists we provide a general algorithm for determining when can estimators of 0 exist our results follow after specializing a general representation described in the article for the efficient score and the influence function of regular asymptotically linear estimators in an arbitrary semi parametric model with non ignorable non response in which the probability of observing complete data is bounded away from zero and the non response probabilities can be parametrically modelled 1997 by john wiley sons ltd

biometrika centenary nonparametrics summary contributions in biometrika to nonparametric statistics are surveyed with particular emphasis on more recent work it is argued that even in the journal s very early years it had interests in smoothing methods for density estimation and in techniques for nonparametric regression in addition to its more obvious focus on classical nonparametric statistics such as ranking methods biometrika s early involvement with permutation testing has links to its contemporary work on bootstrap methods emphases on different types of nonparametric statistics have evolved over time however a rapidly increasing proportion of the journal s pages is devoted to papers that include some use of nonparametric ideas or methods

a fast collocation method for acoustic scattering in shallow oceans abstract in this paper we investigate the numerical solution of the integral equation of the second kind reduced by acoustic scattering in shallow oceans with dirichlet condition based on analyzing the singularity of the truncating kernel with a sum of infinite series using our trigonometric interpolatory wavelets and collocation method we obtain the numerical solution which possesses a fast convergence rate like o 2 j moreover the entries of the stiffness matrix can be obtained by fft which lead the computational complexity to decrease obviously

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

transfer of tail information in censored regression models consider a heteroscedastic regression model y m x sigma x varepsilon where the functions m and sigma are smooth and varepsilon is independent of x the response variable y is subject to random censoring but it is assumed that there exists a region of the covariate x where the censoring of y is light under this condition it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light censoring to regions of heavy censoring crucial for this transfer is the estimator of the distribution of varepsilon based on nonparametric regression residuals whose weak convergence is obtained the idea of transferrring tail information is applied to the estimation of the conditional distribution of y given x x with information on the upper tail borrowed from the region of light censoring and to the estimation of the bivariate distribution p x leq x y leq y with no regions of undefined mass the weak convergence of the two estimators is obtained by products of this investigation include the uniform consistency of the conditional kaplan meier estimator and its derivative the location and scale estimators and the estimators of their derivatives

analysis of semiparametric regression models for repeated outcomes in the presence of missing data abstract we propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data the proposed estimators do not require full specification of the likelihood they can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random these estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable the likelihood based parametric g computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance but because of possible model misspecification the parametric g computation algorithm estimator in contrast with the proposed w

weak and strong uniform consistency of kernel regression estimates we study the estimation of a regression function by the kernel method under mild conditions on the window the bandwidth and the underlying distribution of the bivariate observations x i y i we obtain the weak and strong uniform convergence rates on a bounded interval these results parallel those of silverman 1978 on density estimation and extend those of schuster and yakowitz 1979 and collomb 1979 on regression estimation

a model informed rank test for right censored data with intermediate states the generalized wilcoxon and log rank tests are commonly used for testing differences between two survival distributions we modify the wilcoxon test to account for auxiliary information on intermediate disease states that subjects may pass through before failure for a disease with multiple states where patients are monitored periodically but exact transition times are unknown e g staging in cancer we first fit a multi state markov model to the full data set when censoring precludes the comparison of survival times between two subjects we use the model to estimate the probability that one subject will have survived longer than the other given their censoring times and last observed status and use these probabilities to compute an expected rank for each subject these expected ranks form the basis of our test statistic simulations demonstrate that the proposed test can improve power over the log rank and generalized wilcoxon tests in some settings while maintaining the nominal type 1 error rate the method is illustrated on an als data set

locally weighted censored quantile regression censored quantile regression offers a valuable supplement to cox proportional hazards model for survival analysis existing work in the literature often requires stringent assumptions such as unconditional independence of the survival time and the censoring variable or global linearity at all quantile levels moreover some of the work uses recursive algorithms making it challenging to derive asymptotic normality to overcome these drawbacks we propose a new locally weighted censored quantile regression approach that adopts the redistribution of mass idea and employs a local reweighting scheme its validity only requires conditional independence of the survival time and the censoring variable given the covariates and linearity at the particular quantile level of interest our method leads to a simple algorithm that can be conveniently implemented with r software applying recent theory of m estimation with infinite dimensional parameters we establish the consistency and asymptotic normality of the pr

inference using surrogate outcome data and a validation sample summary in the context of estimating 3 from the regression model p yi x relating response y to covariates x suppose that only a surrogate response s is available for most study subjects suppose that for a random subsample of the study cohort termed the validation sample the true outcome y is available in addition to s we consider maximum likelihood estimation of 3 from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome p s i y x an alternative semiparametric method is also considered which is nonparametric with respect to p s i y x large sample distribution theory for maximum estimated likelihood estimates is developed an illustrative example is presented

calibration plots for risk prediction models in the presence of competing risks a predicted risk of 17 can be called reliable if it can be expected that the event will occur to about 17 of 100 patients who all received a predicted risk of 17 statistical models can predict the absolute risk of an event such as cardiovascular death in the presence of competing risks such as death due to other causes for personalized medicine and patient counseling it is necessary to check that the model is calibrated in the sense that it provides reliable predictions for all subjects there are three often encountered practical problems when the aim is to display or test if a risk prediction model is well calibrated the first is lack of independent validation data the second is right censoring and the third is that when the risk scale is continuous the estimation problem is as difficult as density estimation to deal with these problems we propose to estimate calibration curves for competing risks models based on jackknife pseudo values that are combined with a nearest neighborhood smoother and a cross validation approach to deal with all three problems

a robust weighted kaplan meier approach for data with dependent censoring using linear combinations of prognostic covariates the weighted kaplan meier wkm estimator is often used to incorporate prognostic covariates into survival analysis to improve efficiency and correct for potential bias in this paper we generalize the wkm estimator to handle a situation with multiple prognostic covariates and potential dependent censoring through the use of prognostic covariates we propose to combine multiple prognostic covariates into two risk scores derived from two working proportional hazards models one model is for the event times the other model is for the censoring times these two risk scores are then categorized to define the risk groups needed for the wkm estimator a method of defining categories based on principal components is proposed we show that the wkm estimator is robust to misspecification of either one of the two working models in simulation studies we show that the robust wkm approach can reduce bias due to dependent censoring and improve efficiency we apply the robust wkm approach to a prostate cancer data set

on almost sure convergence of conditional empirical distribution functions on etudie la convergence presque sure d une distribution empirique conditionnelle de type noyau a la fois en norme sup et en norme sup ponderee

a fast improvement to the em algorithm on its own terms the em algorithm is a numerical technique for the evaluation of maximum likelihood estimates for parameters describing incomplete data models it is easy to apply in many problems and is stable but slow the algorithm fails to provide a consistent estimator of the standard errors of the maximum likelihood estimates unless the additional analysis required by the louis method is performed newton type or other gradient methods are faster and provide error estimates but tend to be unstable and require the analytical evaluation of likelihoods to derive expressions for the score function and at least approximations to the fisher information matrix the purpose of this paper is to expand on a result by fisher that permits a unification of em methodology and newton methods the evaluation of the individual observation by observation score functions of the incomplete data is a byproduct of the application of the e step of the em algorithm once these become available the fisher information matrix may be consistently estimated and the m step may be replaced by a fast newton type step

multiple imputation for interval censored data with auxiliary variables we propose a non parametric multiple imputation scheme npmle imputation for the analysis of interval censored survival data features of the method are that it converts interval censored data problems to complete data or right censored data problems to which many standard approaches can be used and that measures of uncertainty are easily obtained in addition to the event time of primary interest there are frequently other auxiliary variables that are associated with the event time for the goal of estimating the marginal survival distribution these auxiliary variables may provide some additional information about the event time for the interval censored observations we extend the imputation methods to incorporate information from auxiliary variables with potentially complex structures to conduct the imputation we use a working failure time proportional hazards model to define an imputing risk set for each censored observation the imputation schemes consist of using the data in the imputing risk sets to create an exact event time for each interval censored observation in simulation studies we show that the use of multiple imputation methods can improve the efficiency of estimators and reduce the effect of missing visits when compared to simpler approaches we apply the approach to cytomegalovirus shedding data from an aids clinical trial in which cd4 count is the auxiliary variable

a geometric optics method for high frequency electromagnetic fields computations near fold caustics part ii the energy we present the computation of the amplitudes needed to evaluate the energy deposited by the laser wave in a plasma when a fold caustic forms we first recall the eulerian method designed in benamou et al j comput appl math 156 2003 93 to compute the caustic location and the phases associated to the two ray branches on its illuminated side we then turn to the computation of the amplitudes needed to evaluate the energy we use the classical geometrical form of the amplitudes to avoid the blow up problem at the caustic as our proposed method is eulerian we have to consider transport equations for these geometrical quantities where the advection field depends on the ray flow the associated vector field structurally vanishes like the square root of the distance to the caustic when approaching the caustic this introduces an additional difficulty as traditional finite difference scheme do not retain their accuracy for such advection fields we propose a new scheme which remains of order 1 at the caustic and present a partial theoretical analysis as well as a numerical validation we also test the capability of our eulerian geometrical algorithm to produce numerical solution of the helmholtz equation and attempt to check their frequency asymptotic accuracy

semiparametric estimation of a panel data proportional hazards model with fixed effects this paper considers a panel duration model that has a proportional hazards specification with fixed effects the paper shows how to estimate the baseline and integrated baseline hazard functions without assuming that they belong to known finite dimensional families of functions existing estimators assume that the baseline hazard function belongs to a known parametric family therefore the estimators presented here are more general than existing ones this paper also presents a method for estimating the parametric part of the proportional hazards model with dependent right censoring under which the partial likelihood estimator is inconsistent the paper presents some monte carlo evidence on the small sample performance of the new estimators

smoothed cox regression nonparametric regression was shown by beran and mckeague and utikal to provide a flexible method for analysis of censored failure times and more general counting processes models in the presence of covariates we discuss application of kernel smoothing towards estimation in a generalized cox regression model with baseline intensity dependent on a covariate under regularity conditions we show that estimates of the regression parameters are asymptotically normal at rate root n and we also discuss estimation of the baseline cumulative hazard function and related parameters

nonparametric estimation of a bivariate survival function in the presence of censoring a new family of estimators of a bivariate survival function based on censored vectors is obtained from a decomposition of the bivariate survival function these estimators are uniformly consistent under bivariate censoring and are self consistent under univariate censoring

doubly robust learning for estimating individualized treatment with censored data individualized treatment rules recommend treatments based on individual patient characteristics in order to maximize clinical benefit when the clinical outcome of interest is survival time estimation is often complicated by censoring we develop nonparametric methods for estimating an optimal individualized treatment rule in the presence of censored data to adjust for censoring we propose a doubly robust estimator which requires correct specification of either the censoring model or survival model but not both the method is shown to be fisher consistent when either model is correct furthermore we establish the convergence rate of the expected survival under the estimated optimal individualized treatment rule to the expected survival under the optimal individualized treatment rule we illustrate the proposed methods using simulation study and data from a phase iii clinical trial on non small cell lung cancer

stochastic calculus as a tool in survival analysis a review this paper gives a brief survey of the uses of stochastic calculus in survival analysis the role played by martingale central limit theory in deriving asymptotic distributions of estimators and test statistics is described the nelson aalen estimator the kaplan meier estimator cox s proportional hazards model aalen s additive risk model and a goodness of fit test for cox s model are discussed sketches of the proofs of the main results are included

analysis of longitudinal binary data from multiphase sampling the efficient use of surrogate or auxiliary information has been investigated within both model based and design based approaches to data analysis particularly in the context of missing data here we consider the use of such data in epidemiological studies of disease incidence in which surrogate measures of disease status are available for all subjects at two time points but definitive diagnoses are available only in stratified subsamples we briefly review methods for the analysis of two phase studies of disease prevalence at a single time point and we discuss the extension of four of these methods to the analysis of incidence studies their performance is compared with special reference to a study of the incidence of senile dementia

estimation of regression coefficients when some regressors are not always observed abstract in applied problems it is common to specify a model for the conditional mean of a response given a set of regressors a subset of the regressors may be missing for some study subjects either by design or happenstance in this article we propose a new class of semiparametric estimators based on inverse probability weighted estimating equations that are consistent for parameter vector 0 of the conditional mean model when the data are missing at random in the sense of rubin and the missingness probabilities are either known or can be parametrically modeled we show that the asymptotic variance of the optimal estimator in our class attains the semiparametric variance bound for the model by first showing that our estimation problem is a special case of the general problem of parameter estimation in an arbitrary semiparametric model in which the data are missing at random and the probability of observing complete data is bounded away from 0 and then deriving a representation for the efficient score

estimation of exposure distribution adjusting for association between exposure level and detection limit in environmental exposure studies it is common to observe a portion of exposure measurements to fall below experimentally determined detection limits dls the reverse kaplan meier estimator which mimics the well known kaplan meier estimator for right censored survival data with the scale reversed has been recommended for estimating the exposure distribution for the data subject to dls because it does not require any distributional assumption however the reverse kaplan meier estimator requires the independence assumption between the exposure level and dl and can lead to biased results when this assumption is violated we propose a kernel smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and dl we show that the proposed estimator is consistent and asymptotically normal simulation studies demonstrate that the proposed estimator performs well in practical situations a colon cancer study is provided for illustration copyright 2017 john wiley sons ltd