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

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

soliton solutions of the kadomtsev petviashvili ii equation we study a general class of line soliton solutions of the kadomtsev petviashvili ii kpii equation by investigating the wronskian form of its tau function we show that in addition to the previously known line soliton solutions of kpii this class also contains a large variety of multisoliton solutions many of which exhibit nontrivial spatial interaction patterns we also show that in general such solutions consist of unequal numbers of incoming and outgoing line solitons from the asymptotic analysis of the tau function we explicitly characterize the incoming and outgoing line solitons of this class of solutions we illustrate these results by discussing several examples

a pseudolikelihood method for analyzing interval censored data summary we introduce a method based on a pseudolikelihood ratio for estimating the distribution function of the survival time in a mixed case interval censoring model in a mixed case model an individual is observed a random number of times and at each time it is recorded whether an event has happened or not one seeks to estimate the distribution of time to event we use a poisson process as the basis of a likelihood function to construct a pseudolikelihood ratio statistic for testing the value of the distribution function at a fixed point and show that this converges under the null hypothesis to a known limit distribution that can be expressed as a functional of different convex minorants of a two sided brownian motion process with parabolic drift construction of confidence sets then proceeds by standard inversion the computation of the confidence sets is simple requiring the use of the pool adjacent violators algorithm or a standard isotonic regression algorithm we also illustrate the superiority of the proposed method over competitors based on resampling techniques or on the limit distribution of the maximum pseudolikelihood estimator through simulation studies and illustrate the different methods on a dataset involving time to hiv seroconversion in a group of haemophiliacs

primitive ideals and orbital integrals in complex exceptional groups in 2 two related problems were studied for complex classical groups determination of the primitive spectrum of the enveloping algebra as a set and fourier inversion of unipotent orbital integrals the first of these was solved completely extending work of joseph and others in sl n c and small groups although our techniques presumably solve the second as well up to determination of normalizing constants we carried out the calculations only for special unipotent classes see 181 we had of course tried to apply the same methods to the exceptional groups but they seem to be inadequate since that work was done however brylinski and kashiwara and beilinson and bernstein have established the kazhdan lusztig conjecture giving character formulas for irreducible highest weight modules 3 71 because of a conjecture of joseph proved in 24 this determines in principle the primitive ideals with a fixed regular integral infinitesimal character they are in one to one correspondence with what kazhdan and lusztig call left cells in the weyl group however the algorithm given by kazhdan and lusztig to compute these cells is enormously complicated requiring one to compute roughly 1 i polynomials of degrees on the order of half the number of positive roots this is very unsatisfactory however it

rank invariant tests for interval censored data under the grouped continuous model this paper creates rank invariant score tests for grouped or interval censored data this generalizes finkelstein 1986 biometrics 42 845 854 who derived score tests for interval censored data assuming proportional hazards we frame the problem as a linear rank test of a shift in location with a known error distribution we discuss adjustments to the test that may be required when the number of observation times is large we offer a graphical test of the assumption of the location shift model and discuss an alternative interpretation of the test using the logistic error when the location shift assumption does not hold

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

a two sample test for stochastic ordering with interval censored data a new class of asymptotically nonparametric two sample approximate tests for discrete interval censored data is proposed this class extends the family developed by pepe and fleming 1989 biometrics 45 497 507 for right censored data and is based on an integrated weighted difference in survival function estimates the tests are sensitive to the alternative of stochastic ordering and use turnbull s 1976 journal of the royal statistical society series b 38 290 295 estimator of the survival function the choice of appropriate weight functions is investigated simulation results indicate that for interval censored data the new procedure with an appropriate weight function can be more powerful than an omnibus likelihood ratio test and mantel s 1967 biometrics 23 65 78 test under a broad range of stochastically ordered alternatives for small sample sizes n 50 with moderate censoring 47 and 70 the size of the test is close to the nominal size

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

polynomial splines and their tensor products in extended linear modeling 1994 wald memorial lecture analysis of variance type models are considered for a regression function or for the logarithm of a probability function conditional probability function density function conditional density function hazard function conditional hazard function or spectral density function polynomial splines are used to model the main effects and their tensor products are used to model any interaction components that are included in the special context of survival analysis the baseline hazard function is modeled and nonproportionality is allowed in general the theory involves the l 2 rate of convergence for the fitted model and its components the methodology involves least squares and maximum likelihood estimation stepwise addition of basis functions using rao statistics stepwise deletion using wald statistics and model selection using the bayesian information criterion cross validation or an independent test set publicly available software written in c and interfaced to s s plus is used to apply this methodology to real data

the deodhar decomposition of the grassmannian and the regularity of kp solitons abstract given a point a in the real grassmannian it is well known that one can construct a soliton solution u a x y t to the kp equation the contour plot of such a solution provides a tropical approximation to the solution when the variables x y and t are considered on a large scale and the time t is fixed in this paper we use several decompositions of the grassmannian in order to gain an understanding of the contour plots of the corresponding soliton solutions first we use the positroid stratification of the real grassmannian in order to characterize the unbounded line solitons in the contour plots at y 0 and y 0 next we use the deodhar decomposition of the grassmannian a refinement of the positroid stratification to study contour plots at t 0 more specifically we index the components of the deodhar decomposition of the grassmannian by certain tableaux which we call go diagrams and then use these go diagrams to characterize the contour plots of solitons solutions when t 0 finally we use these results to show that a soliton solution u a x y t is regular for all times t if and only if a comes from the totally non negative part of the grassmannian

complexity reduction for sign configurations through the kp ii equation and its information theoretic aspects we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed we provide a combinatorial setting to explore the information content associated with the fulfillment of the kadomtsev petviashvili kp ii equation we start from a special family of solutions of kp ii namely tau functions of wronskian type a solution in this class can be expressed as a sum of exponentials and we look at combinations of signs signatures for the nonvanishing terms in this sum we prove a characterization of the signatures that return another solution of the kp ii equation they can be represented as choices of signs for columns and rows of a coefficient matrix so we recover a function satisfying the whole kp hierarchy from this single constraint the redundancy of this representation for different choices of the initial solution is investigated enumerative information theoretic and geometric aspects of this construction are discussed

smooth estimation of the survival function for interval censored data interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be observed in some time intervals to estimate the survival function the non parametric maximum likelihood estimator npmle is commonly used which is a step function having some large jumps however in many applications the underlying survival function can be reasonably assumed to be smooth and then the npmle does not efficiently use this information two smooth estimators have been proposed in the literature one is based on the kernel smoothing of the npmle another is the logspline density model however to our knowledge there is no finite sample study yet to assess their performance in the literature in this paper we first show by simulation that both smooth estimators improve over the npmle for smooth survival functions we then apply these estimators to compare two survival curves the test statistics based on the maximum difference between two survival functions kolmogorov smirnov test and on the integrated weighted difference of two survival functions iwdb test are investigated via the bootstrap from our simulation studies the iwdb test seems particularly promising for some stochastically ordered survival functions that do not satisfy the proportional hazards model the methods are illustrated by reanalysing the breast cosmesis study data set copyright 2000 john wiley sons ltd

nonparametric estimation for a form of doubly censored data with application to two problems in aids abstract in many epidemiologic studies of human immunodeficiency virus hiv disease interest focuses on the distribution of the length of the interval of time between two events two such problems are considered here estimation of the distribution of time or number of sexual contacts between infection of an individual an index case and transmission of hiv to their sexual partner and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody data regarding these two problems are available from certain partner studies and the hiv lookback study in both cases the statistical development is complicated by the fact that the times of both events are interval censored so that the length of time between the events is never observed exactly nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution particular attention is paid to

young diagrams and n soliton solutions of the kp equation we consider n soliton solutions of the kp equation an n soliton solution is a solution u x y t which has the same set of n line soliton solutions in both asymptotics y and y the n soliton solutions include all possible resonant interactions among those line solitons we then classify those n soliton solutions by defining a pair of n numbers n n with n n 1 n n n j 1 2n which labels n line solitons in the solution the classification is related to the schubert decomposition of the grassmann manifolds gr n 2n where the solution of the kp equation is defined as a torus orbit then the interaction pattern of n soliton solution can be described by the pair of young diagrams associated with n n we also show that n soliton solutions of the kdv equation obtained by the constraint u y 0 cannot have resonant interaction

a two sample test with interval censored data via multiple imputation interval censored data arise naturally in large scale panel studies where subjects can only be followed periodically and the event of interest can only be recorded as having occurred between two examination times in this paper we consider the problem of comparing two interval censored samples we propose to impute exact failure times from interval censored observations to obtain right censored data then apply existing techniques such as harrington and fleming s g rho tests to imputed right censored data to appropriately account for variability a multiple imputation algorithm based on the approximate bayesian bootstrap abb is discussed through simulation studies we find that it performs well the advantage of our proposal is its simplicity to implement and adaptability to incorporate many existing two sample comparison techniques for right censored data the method is illustrated by reanalysing the breast cosmesis study data set

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

on a family of solutions of the kadomtsev petviashvili equation which also satisfy the toda lattice hierarchy we describe the interaction pattern in the x y plane for a family of soliton solutions of the kadomtsev petviashvili kp equation the solutions considered also satisfy the finite toda lattice hierarchy we determine completely their asymptotic patterns for y and we show that all the solutions except the 1 soliton solution are of resonant type consisting of arbitrary numbers of line solitons in both asymptotics that is arbitrary n incoming solitons for y interact to form arbitrary n outgoing solitons for y we also discuss the interaction process of those solitons and show that the resonant interaction creates a web like structure having n 1 n 1 holes

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

large sample confidence regions based on subsamples under minimal assumptions in this article the construction of confidence regions by approximating the sampling distribution of some statistic is studied the true sampling distribution is estimated by an appropriate normalization of the values of the statistic computed over subsamples of the data in the i i d context the method has been studied by wu in regular situations where the statistic is asymptotically normal the goal of the present work is to prove the method yields asymptotically valid confidence regions under minimal conditions essentially all that is required is that the statistic suitably normalized possesses a limit distribution under the true model unlike the bootstrap the convergence to the limit distribution need not be uniform in any sense the method is readily adapted to parameters of stationary time series or more generally homogeneous random fields for example an immediate application is the construction of a confidence interval for the spectral density function of a homogeneous random field