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

a multiple imputation approach to cox regression with interval censored data we propose a general semiparametric method based on multiple imputation for cox regression with interval censored data the method consists of iterating the following two steps first from finite interval censored but not right censored data exact failure times are imputed using tanner and wei s poor man s or asymptotic normal data augmentation scheme based on the current estimates of the regression coefficient and the baseline survival curve second a standard statistical procedure for right censored data such as the cox partial likelihood method is applied to imputed data to update the estimates through simulation we demonstrate that the resulting estimate of the regression coefficient and its associated standard error provide a promising alternative to the nonparametric maximum likelihood estimate our proposal is easily implemented by taking advantage of existing computer programs for right censored data

rank based inference for the accelerated failure time model summary a broad class of rank based monotone estimating functions is developed for the semiparametric accelerated failure time model with censored observations the corresponding estimators can be obtained via linear programming and are shown to be consistent and asymptotically normal the limiting covariance matrices can be estimated by a resampling technique which does not involve nonparametric density estimation or numerical derivatives the new estimators represent consistent roots of the non monotone estimating equations based on the familiar weighted log rank statistics simulation studies demonstrate that the proposed methods perform well in practical settings two real examples are provided

smooth inference for survival functions with arbitrarily censored data we propose a procedure for estimating the survival function of a time to event random variable under arbitrary patterns of censoring the method is predicated on the mild assumption that the distribution of the random variable and hence the survival function has a density that lies in a class of smooth densities whose elements can be represented by an infinite hermite series truncation of the series yields a parametric expression that can well approximate any plausible survival density and hence survival function provided the degree of truncation is suitably chosen the representation admits a convenient expression for the likelihood for the parameters in the approximation under arbitrary censoring truncation that is straightforward to compute and maximize a test statistic for comparing two survival functions which is based on an integrated weighted difference of estimates of each under this representation is proposed via simulation studies and application to a number of data sets we demonstrate that the approach yields reliable inferences and can result in gains in efficiency over traditional nonparametric methods

ramanujan s theories of elliptic functions to alternative bases in his famous paper 3 10 pp 23 39 ramanujan offers several beautiful series representations for 1 pi he first states three formulas one of which is frac 4 pi sum limits mathbf n 0 infty frac left 6 mathbf n 1 right left frac 1 2 right 3 n left mathbf n right 3 4 n where a o 1 and for each positive integer n left mathbf a right n mathbf a left mathbf a 1 right left mathbf a 2 right left mathbf a mathbf n 1 right

cross validated snp density estimates abstract we consider cross validation strategies for the seminonparametric snp density estimator which is a truncation or sieve estimator based upon a hermite series expansion with coefficients determined by quasi maximum likelihood our main focus is on the use of snp density estimators as an adjunct to efficient method of moments emm structural estimation it is known that for this purpose a desirable truncation point occurs at the last point at which the integrated squared error ise curve of the snp density estimate declines abruptly we study the determination of the ise curve for iid data by means of leave one out cross validation and hold out sample cross validation through an examination of their performance over the marron wand test suite and models related to asset pricing and auction applications we find that both methods are informative as to the location of abrupt drops but that neither can reliably determine the minimum of the ise curve we validate these findings with a monte carlo study the hold out sample method is cheaper to compute because it requires fewer nonlinear optimizations we consider the asymptotic justification of hold out sample cross validation for this purpose we establish rates of convergence of the snp estimator under the hellinger norm that are of interest in their own right

empirical process approach in a two sample location scale model with censored data to compare two samples of possibly right censored failure times a location scale model without assuming the distribution form is considered for the log transformed data this new accelerated failure time model is introduced to accommodate the possible heterogeneity between within treatment variations of the two groups considered one distinct feature of this model is that with the presence of heterogeneity statistical inferences on both location and scale parameters based on log rank tests or linear rank tests will become inappropriate in this paper we propose the empirical process approach to construct a regression setup derived from the theory of strong approximation of the kaplan meier product limit empirical quantile process a generalized least squares gls estimator is obtained and shown to be semiparametric efficient also it is shown that this estimation is adaptive for a special case at the end results on the two sample setting are applied to the k sample problem

semiparametric estimation of an accelerated failure time model with time dependent covariates summary a class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates a class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored these estimates are shown to be consistent and asymptotically normal with variances that can be consistently estimated it is also shown that estimators within this class achieve the semiparametric efficiency bound we consider an accelerated failure time model for time to event data in which the survival distribution is scaled by a factor which may be a function of time dependent covariates these models directly model the effect of covariates on the length of survival this is in contrast to the more commonly used proportional hazards model which models the hazard rate itself in some applications it may be easier to visualize the concept that a treatment intervention or exposure to an environmental contaminant increases or decreases the length of survival by a certain proportion as compared to the concept that the hazard rate is changed for time independent covariates say z z1 zp the class of accelerated failure time models assumes that the survival distribution at time t given a set of covariates z z is given by f t i z f0 h z t the proportionality constant h z can be interpreted as the scale factor by which lifetime is decreased as a function of the covariates z often h z is taken to be log linear or h z exp b z in such cases if z 0 we can interpret fo t as the baseline survival distribution or the survival distribution for individuals with covariates all equal to zero a useful way of envisioning this model is to consider a hypothetical random variable u that corresponds to an individual s survival time if that individual had covariate values all equal to zero this baseline failure time u would be modified for values of the covariate different than zero for example if we denote the actual survival time by t then for an individual with covariate value z we have t e zu the parameters b in this model have a direct interpretation in terms of the increase or decrease in lifespan as a function of the covariates the assumption that u is independent of z in this hypothetical construct induces the probabilistic model

a nonparametric two sample test of the failure function with interval censoring case 2 for the setting of interval censoring case 2 a nonparametric two sample test based on a smooth functional of the nonparametric maximum pseudolikelihood estimator is developed to compare the failure functions of two populations monte carlo simulation studies on weibull distributions show that this test performs quite well in many situations in comparison with the parametric likelihood ratio test a real dataset from an study is used to illustrate the new test

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

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

cubic modular equations in two variables abstract by adding certain equianharmonic elliptic sigma functions to the coefficients of the borwein cubic theta functions an interesting set of six two variable theta functions may be derived these theta functions invert the f 1 1 3 1 3 1 3 1 x y case of appell s hypergeometric function and satisfy several identities akin to those satisfied by the borwein cubic theta functions the work of koike et al is extended and put into the context of modular equations resulting in a simpler derivation of their results as well as several new modular equations for picard modular functions an application of these results is a new two parameter family of solvable nonic equations

linear regression analysis based on buckley james estimating equation in this note we consider the problem of drawing inference about the regression parameters in a linear model with survival data a simple procedure based on the buckley james 1979 biometrika 66 429 436 estimating equation is proposed and illustrated with an example

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

numerical methods for ordinary differential equations on matrix manifolds in recent years differential systems whose solutions evolve on manifolds of matrices have acquired a certain relevance in numerical analysis a classical example of such a differential system is the well known toda flow this paper is a partial survey of numerical methods recently proposed for approximating the solutions of ordinary differential systems evolving on matrix manifolds in particular some results recently obtained by the author jointly with his co workers will be presented we will discuss numerical techniques for isospectral and isodynamical flows where the eigenvalues of the solutions are preserved during the evolution and numerical methods for odes on the orthogonal group or evolving on a more general quadratic group like the symplectic or lorentz group we mention some results for systems evolving on the stiefel manifold and also review results for the numerical solution of odes evolving on the general linear group of matrices

smooth svd on the lorentz group with application to computation of lyapunov exponents in this work we give a constructive argument to establish existence of a smooth singular value decomposition svd for a ck function x in the lorentz group we rely on the explicit structure of the polar factorization of x in order to justify the form of the svd our construction gives a simple algorithm to find the svd of x which we have used to approximate the lyapunov exponents of a differential system whose fundamental matrix solution evolves on the lorentz group algorithmic details and examples are given

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

linear mixed models with flexible distributions of random effects for longitudinal data normality of random effects is a routine assumption for the linear mixed model but it may be unrealistic obscuring important features of among individual variation we relax this assumption by approximating the random effects density by the seminonparameteric snp representation of gallant and nychka 1987 econometrics 55 363 390 which includes normality as a special case and provides flexibility in capturing a broad range of nonnormal behavior controlled by a user chosen tuning parameter an advantage is that the marginal likelihood may be expressed in closed form so inference may be carried out using standard optimization techniques we demonstrate that standard information criteria may be used to choose the tuning parameter and detect departures from normality and we illustrate the approach via simulation and using longitudinal data from the framingham study

qualitative and asymptotic performance of snp density estimators abstract the snp estimator is the most convenient nonparametric method for simultaneously estimating the parameters of a nonlinear model and the density of a latent process by maximum likelihood to determine if this convenience comes at a price we assess the qualitative behavior of snp in finite samples using the marron wand test suite and verify theoretical convergence rates by monte carlo simulation our results suggest that there is no price for convenience because the snp estimator is both qualitatively and asymptotically similar to the kernel estimator which is optimal

semiparametric inference in the proportional odds regression model abstract for fitting the proportional odds regression model with right censored survival times we introduce some weighted empirical odds functions these functions are solutions of some self consistency equations and have a nice martingale representation from these functions several classes of new regression estimators such as the pseudo maximum likelihood estimator martingale residual based estimators and minimum distance estimators are derived these estimators have desirable properties such as easy computation asymptotic normality via a martingale analysis and reliable asymptotic covariance estimation in closed form extensive numerical studies show that the minimum l 2 distance estimators have very good finite sample behaviors compared to existing methods results of some simulation studies and applications to a real dataset are given the weighted odds function based approach also provides inference on the baseline odds function and some measures for lack of fit analysis

hazard regression with interval censored data in a recent paper kooperberg stone and truong 1995a introduced hazard regression hare in which linear splines and their tensor products are used to estimate the conditional log hazard function based on possibly censored positive response data and one or more covariates model selection is carried out in an adaptive fashion using maximum likelihood estimation of the unknown coefficients rao and wald statistics to carry out stepwise addition and deletion of basis functions and the bayesian information criterion bic to select the final model in the present paper the hare methodology is extended to accommodate interval censored data time dependent covariates and cubic splines the presence of interval censored data means that the log likelihood function may no longer be concave presenting additional numerical challenges the extended methodology is applied to a data set containing both interval censoring and time dependent covariates the new software will be available in a future release of s plus

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

a penalized likelihood approach for arbitrarily censored and truncated data application to age specific incidence of dementia the cos model is the model of choice when analyzing survival data presenting only right censoring and left truncation there is a need for methods that can accommodate more complex observation schemes involving general censoring and truncation in addition it is important in many epidemiological applications to have a smooth estimate of the hazard function we show that the penalized likelihood approach gives a solution to these problems the solution of the maximum of the penalized likelihood is approximated on a basis of splines the smoothing parameter is estimated using approximate cross validation confidence bands can be given a simulation study shows that this approach gives better results than the smoothed nelson aalen estimator we apply this method to the analysis of data from a large cohort study on cerebral aging the age specific incidence of dementia is estimated and risk factors of dementia studied

estimation of regression parameters and the hazard function in transformed linear survival models summary an estimator of the regression parameters in a semiparametric transformed linear survival model is examined this estimator consists of a single newton like update of the solution to a rank based estimating equation from an initial consistent estimator an automated penalized likelihood algorithm is proposed for estimating the optimal weight function for the estimating equations and the error hazard function that is needed in the variance estimator in simulations the estimated optimal weights are found to give reasonably efficient estimators of the regression parameters and the variance estimators are found to perform well the methodology is applied to an analysis of prognostic factors in non hodgkin s lymphoma

differential equations for the analytic singular value decomposition of a matrix this paper is concerned with finding a smooth singular value decomposition for a matrix which is smoothly dependent on a parameter a previous approach to this problem was based on minimisation techniques here in contrast a system of ordinary differential equations is derived for the decomposition it is shown that the numerical solution of an initial value problem associated with these differential equations provides a feasible approach to the solution of this problem particular consideration is given to the situation which arises with equal modulus singular values which lead to indeterminacies in the evaluations needed for the numerical solution examples which illustrate the behaviour of the method are included

the singular value decomposition to approximate spectra of dynamical systems theoretical aspects abstract in this paper we consider the singular value decomposition svd of a fundamental matrix solution in order to approximate the lyapunov and exponential dichotomy spectra of a given system one of our main results is to prove that svd techniques are sound approaches for systems with stable and distinct lyapunov exponents we also show how the information which emerges with the svd techniques can be used to obtain information on the growth directions associated to given spectral intervals

the nonlinear mixed effects model with a smooth random effects density summary the fixed parameters of the nonlinear mixed effects model and the density of the random effects are estimated jointly by maximum likelihood the density of the random effects is assumed to be smooth but is otherwise unrestricted the method uses a series expansion that follows from the smoothness assumption to represent the density and quadrature to compute the likelihood standard algorithms are used for optimization empirical bayes estimates of random coefficients are obtained by computing posterior modes the method is applied to data from pharmacokinetics and properties of the method are investigated by application to simulated data

semiparametric analysis of transformation models with censored data summary a unified estimation procedure is proposed for the analysis of censored data using linear transformation models which include the proportional hazards model and the proportional odds model as special cases this procedure is easily implemented numerically and its validity does not rely on the assumption of independence between the covariates and the censoring variable the estimator is the same as the cox partial likelihood estimator in the case of the proportional hazards model moreover the asymptotic variance of the proposed estimator has a closed form and its variance estimator is easily obtained by plug in rules the method is illustrated by simulation and is applied to the veterans administration lung cancer data

smooth estimation of survival functions and hazard ratios from interval censored data using bayesian penalized b splines we discuss the use of bayesian p spline and of the composite link model to estimate survival functions and hazard ratios from interval censored data if one further assumes proportionality of the hazards the proposed strategy provides a smoothed estimate of the baseline hazard along with estimates of global covariate effects the frequentist properties of our bayesian estimators are assessed by an extensive simulation study we further illustrate the methodology by three examples showing that the proportionality of the hazards might also be found inappropriate from interval censored data

smoothing spline based score tests for proportional hazards models we propose score type tests for the proportional hazards assumption and for covariate effects in the cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate the tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero we show that the tests have a size close to the nominal level and good power against general alternatives and we apply them to data from a cancer clinical trial

some cubic modular identities of ramanujan there is a beautiful cubic analogue of jacobi s fundamental theta function identity it is sum n m infty infty q n 2 nm m 2 sum n m infty infty n m q n nm m sum n m infty infty q n 1 3 n 1 3 m 1 3 m 1 3 here exp 2 i 3 in this note we provide an elementary proof of this identity and of a related identity due to ramanujan we also indicate how to discover and prove such identities symbolically

generalized likelihood ratio statistics and wilks phenomenon likelihood ratio theory has had tremendous success in parametric inference due to the fundamental theory of wilks yet there is no general applicable approach for nonparametric inferences based on function estimation maximum likelihood ratio test statistics in general may not exist in nonparametric function estimation setting even if they exist they are hard to find and can not be optimal as shown in this paper we introduce the generalized likelihood statistics to overcome the drawbacks of nonparametric maximum likelihood ratio statistics a new s wilks phenomenon is unveiled we demonstrate that a class of the generalized likelihood statistics based on some appropriate nonparametric estimators are asymptotically distribution free and follow chi 2 distributions under null hypotheses for a number of useful hypotheses and a variety of useful models including gaussian white noise models nonparametric regression models varying coefficient models and generalized varying coefficient models we further demonstrate that generalized likelihood ratio statistics are asymptotically optimal in the sense that they achieve optimal rates of convergence given by ingster they can even be adaptively optimal in the sense of spokoiny by using a simple choice of adaptive smoothing parameter our work indicates that the generalized likelihood ratio statistics are indeed general and powerful for nonparametric testing problems based on function estimation

on the accelerated failure time model for current status and interval censored data and tianxi cai this paper introduces a novel approach to making inference about the regression parameters in the accelerated failure time model for current status and interval censored data the estimator is constructed by inverting a wald type test for testing a null proportional hazards model a numerically efficient markov chain monte carlo based resampling method is proposed for obtaining simultaneously the point estimator and a consistent estimator of its variance covariance matrix we illustrate our approach with interval censored datasets from two clinical studies extensive numerical studies are conducted to evaluate the finite sample performance of the new estimators

smooth semi nonparametric snp estimation of the cumulative incidence function this paper presents a novel approach to estimation of the cumulative incidence function in the presence of competing risks the underlying statistical model is specified via a mixture factorization of the joint distribution of the event type and the time to the event the time to event distributions conditional on the event type are modeled using smooth semi nonparametric densities one strength of this approach is that it can handle arbitrary censoring and truncation while relying on mild parametric assumptions a stepwise forward algorithm for model estimation and adaptive selection of smooth semi nonparametric polynomial degrees is presented implemented in the statistical software r evaluated in a sequence of simulation studies and applied to data from a clinical trial in cryptococcal meningitis the simulations demonstrate that the proposed method frequently outperforms both parametric and nonparametric alternatives they also support the use of ad hoc asymptotic inference to derive confidence intervals an extension to regression modeling is also presented and its potential and challenges are discussed 2017 the authors statistics in medicine published by john wiley sons ltd

smooth semiparametric regression analysis for arbitrarily censored time to event data a general framework for regression analysis of time to event data subject to arbitrary patterns of censoring is proposed the approach is relevant when the analyst is willing to assume that distributions governing model components that are ordinarily left unspecified in popular semiparametric regression models such as the baseline hazard function in the proportional hazards model have densities satisfying mild smoothness conditions densities are approximated by a truncated series expansion that for fixed degree of truncation results in a parametric representation which makes likelihood based inference coupled with adaptive choice of the degree of truncation and hence flexibility of the model computationally and conceptually straightforward with data subject to any pattern of censoring the formulation allows popular models such as the proportional hazards proportional odds and accelerated failure time models to be placed in a common framework provides a principled basis for choosing among them and renders useful extensions of the models straightforward the utility and performance of the methods are demonstrated via simulations and by application to data from time to event studies

convergence rates of snp density estimators the snp density estimator is a truncation or sieve estimator based upon a hermite series expansion other nonparametric estimators based on orthogonal series expansions have been proposed

unification of the cubic analogues of the jacobian theta function abstract a common generalization a q z of hirschhorn garvan bonvein cubic analogues a q z b q z and c q z of the classical theta functions 2 q z 3 q z and 4 q z is introduced some properties of a q z are simply established and are shown to unify several known properties of a q z b q z and c q z

estimating regression parameters using linear rank tests for censored data a class of estimates for regression parameters in a linear model with right censored data is proposed these estimates are derived by using linear rank tests for right censored data as estimating equations they are shown to be consistent and asymptotically normal with covariance matrix for which estimates are proposed efficient estimates within this class are derived together with conditions when they are fully efficient 0 introduction the problem of estimating regression coefficients using ranks has received much attention in the literature for uncensored data and the results are summarized very nicely in hettmansperger 1984 there has also been some work with censored data for the two sample problem specifically louis 1981 considered estimation of a scale change between two distributions with the use of a log rank test whereas wei and gail 1983 generalize to other linear rank tests as well we shall consider the general problem of multiple linear regression and show how linear rank tests can be used as estimating equations the resulting linear rank estimates will be shown to be asymptotically normal with variances that can be estimated consistently we shall also look at the efficiency of these estimates under various situations

on least squares regression with censored data summary the semiparametric accelerated failure time model relates the logarithm of the failure time linearly to the covariates while leaving the error distribution unspecified the present paper describes simple and reliable inference procedures based on the least squares principle for this model with right censored data the proposed estimator of the vector valued regression parameter is an iterative solution to the buckley james estimating equation with a preliminary consistent estimator as the starting value the estimator is shown to be consistent and asymptotically normal a novel resampling procedure is developed for the estimation of the limiting covariance matrix extensions to marginal models for multivariate failure time data are considered the performance of the new inference procedures is assessed through simulation studies illustrations with medical studies are provided

bayesian information criterion for censored survival models we investigate the bayesian information criterion bic for variable selection in models for censored survival data kass and wasserman 1995 journal of the american statistical association 90 928 934 showed that bic provides a close approximation to the bayes factor when a unit information prior on the parameter space is used we propose a revision of the penalty term in bic so that it is defined in terms of the number of uncensored events instead of the number of observations for a simple censored data model this revision results in a better approximation to the exact bayes factor based on a conjugate unit information prior in the cox proportional hazards regression model we propose defining bic in terms of the maximized partial likelihood using the number of deaths rather than the number of individuals in the bic penalty term corresponds to a more realistic prior on the parameter space and is shown to improve predictive performance for assessing stroke risk in the cardiovascular health study

large sample inference for log spline models let f be a continuous and positive unknown density on a known compact interval mathscr y let f denote the distribution function of f and let q f 1 denote its quantile function a finite parameter exponential family model based on b splines is constructed maximum likelihood estimation of the parameters of the model based on a random sample of size n from f yields estimates hat f f and hat q of f f and q respectively under mild conditions if the number of parameters tends to infinity in a suitable manner as n rightarrow infty these estimates achieve the optimal rate of convergence the asymptotic behavior of the corresponding confidence bounds is also investigated in particular it is shown that the standard errors of hat f and hat q are asymptotically equal to those of the usual empirical distribution function and empirical quantile function

estimation in a linear regression model with censored data we consider the semiparametric linear regression model with censored data and with unknown error distribution we describe estimation equations of the buckley james type that admit n consistent and asymptotically normal solutions the derived estimator is efficient at a particular error distribution we show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by tsiatis an extension to an estimator that is efficient everywhere is discussed

a cubic counterpart of jacobi s identity and the agm we produce exact cubic analogues of jacobi s celebrated theta function identity and of the arithmetic geometric mean iteration of gauss and legendre the iteration in question is a n 1 a n 2b n 3 and b n 1 formula cannot be replicated the limit of this iteration is identified in terms of the hypergeometric function f 1 3 2 3 1 which supports a particularly simple cubic transformation

semi nonparametric maximum likelihood estimation on developpe une approche basee sur une innovation due a phillips 1983 sur les approximations des fonctions de densite

on a general class of semiparametric hazards regression models a general class of semiparametric hazards regression models for survival data is proposed and studied this general class includes some popular classes of models as subclasses such as cox s proportional hazards model the accelerated failure time model and a recently proposed class of models called the accelerated hazards model in the general class of models a covariate s effect is identified as having two separate components namely a time scale change on hazard progression and a relative hazards ratio the new model is flexible in modelling survival data and may yield more accurate prediction of an individual s survival process by way of the nested structure that includes the proportional hazards model the accelerated failure time model and the accelerated hazards model the general class of models may provide a numerical tool for determining which of them is more appropriate for a given dataset

estimation in the cox proportional hazards model with left truncated and interval censored data nous montrons que l estimateur non parametrique du maximum de vraisemblance npmle du coefficient de regression obtenu a partir de la vraisemblance jointe du coefficient de regression et de la survie de base est correct pour le modele de cox a hasards proportionnels avec des donnees tronquees a gauche et censurees par intervalle mais le npmle pent sous estimer la survie de base deux alternatives sont egalement etudiees premierement la vraisemblance marginale en etendant satten 1996 aux donnees tronquees la survie de base etant eliminee comme un parametre nuisible deuxiemement l estimateur monotone du maximum de vraisemblance qui maximise la vraisemblance jointe en supposant que la fonction de hasard est non decroissante pour la distribution de base ceci a ete initialement propose pour resoudre la sous estimation de la survie par le npmle dans le cas de donnees tronquees a gauche sans covariate tsai 1988 le boostrap est utilise a des fins d inference et des simulations sont realisees pour evaluer leur performance les methodes sont appliquees pour evaluer leur performance les methodes sont appliquees aux donnees de l etude du massachusetts health care panel afin de comparer chez les seniors en fonction du sexe les probabilites de perte d independance fonctionnelle

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

mixtures of polya trees for flexible spatial frailty survival modelling mixtures of polya trees offer a very flexible nonparametric approach for modelling time to event data many such settings also feature spatial association that requires further sophistication either at the point level or at the lattice level in this paper we combine these two aspects within three competing survival models obtaining a data analytic approach that remains computationally feasible in a fully hierarchical bayesian framework using markov chain monte carlo methods we illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the surveillance epidemiology and end results program of the national cancer institute our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions ignore spatial association or both

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

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

semiparametric regression analysis of interval censored data summary we propose a semiparametric approach to the proportional hazards regression analysis of interval censored data an em algorithm based on an approximate likelihood leads to an m step that involves maximizing a standard cox partial likelihood to estimate regression coefficients and then using the breslow estimator for the unknown baseline hazards the e step takes a particularly simple form because all incomplete data appear as linear terms in the complete data log likelihood the algorithm of turnbull 1976 journal of the royal statistical society series b38 290 295 is used to determine times at which the hazard can take positive mass we found multiple imputation to yield an easily computed variance estimate that appears to be more reliable than asymptotic methods with small to moderately sized data sets in the right censored survival setting the approach reduces to the standard cox proportional hazards analysis while the algorithm reduces to the one suggested by clayton and cuzick 1985 applied statistics34 148 156 the method is illustrated on data from the breast cancer cosmetics trial previously analyzed by finkelstein 1986 biometrics42 845 854 and several subsequent authors