geometry of exclusion principles in discrete systems abstract using an n species system of difference equations with very general density dependent growth functions we prove that weak dominance and invariance gives the exclusion of all the n 1 dominated species in the system this result is applied to very specific competition models an example of coexistence in a competition model with no invariance is studied a notion of strong dominance is developed in a general setting and shown to imply exclusion of the n 1 dominated species an example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given

on using stratification in the analysis of linear regression models with right censoring we study two modified synthetic data least squares estimation methods for linear regression models with right censored response variables unspecified residual distributions and random censoring variables which may not be i i d these methods are the result of an investigation into the use of stratification we conclude that stratification should be used whether or not the censoring variables are dependent on the covariates we give the asymptotic results of the estimators and numerical results

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

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

analysis of factorial survival experiments several new methodological issues that arise within two way factorial designs for survival experiments are discussed within the framework of asymptotic theory for the proportional hazards model with two binary treatment covariates these issues include the proper formulation of null hypotheses and alternatives the choice among log rank and adjusted or stratified log rank statistics the asymptotic correlation between test statistics for the separate main effects the asymptotic power under the various possible methods of analysis of tests to detect main effects and interactions the comparison of power to detect main effects within a 2 x 2 factorial design with power in a three group trial where no patients are randomized simultaneously to both treatments and the problems of analysis arising when accrual or exposure to one of the treatments is terminated early for ethical reasons

large sample behaviour of the product limit estimator on the whole line weak convergence results are proved for the product limit estimator on the whole line applications are given to confidence band construction estimation of mean lifetime and to the theory of q functions the results are obtained using stochastic calculus and in probability linear bounds for empirical processes

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

whitney continua of curves in this paper we prove several theorems relating shape properties of whitney continua of curves in particular we investigate the fundamental dimension and the shape type of whitney continua of curves

a nonparametric test to compare survival distributions with covariate adjustment summary the analysis of covariance is a technique that is used to improve the power of a k sample test by adjusting for concomitant variables if the end point is the time of survival and some observations are right censored the score statistic from the cox proportional hazards model is the method that is most commonly used to test the equality of conditional hazard functions in many situations however the proportional hazards model assumptions are not satisfied specifically the relative risk function is not time invariant or represented as a log linear function of the covariates we propose an asymptotically valid k sample test statistic to compare conditional hazard functions which does not require the assumption of proportional hazards a parametric specification of the relative risk function or randomization of group assignment simulation results indicate that the performance of this statistic is satisfactory the methodology is demonstrated on a data set in prostate cancer

shape properties of whitney maps for hyperspaces in this paper some shape properties of whitney maps for hyperspaces are investigated in particular the following are proved 1 let x be a continuum and let k be the hyperspace 2x or c x of x with the hausdorff metric then if x is any whitney map for for any 0 s s t w x t is an approximate strong deformation retract of w s t in particular sh w 1 t sh w 1 s t 2 pointed 1 movability is a whitney property 3 for any given n oo the property of cohomological dimension n is a sequential strong whitney reversible property 4 the property of being chainable or circle like is a sequential strong whitneyreversible property 5 the property of being an far is a whitney property for 1 dimensional continua property 2 is an affirmative answer to a problem of j t rogers 16 112 properties 3 and 4 are affirmative answers to problems of s b nadler 20 14 57 and 21 0 introduction by a continuum we mean a compact connected metric space for a given continuum x by the hyperspaces of x we mean 2x a c x i a is a nonempty closed subset of x c x a e 2x i a is connected which have the hausdorff metric pg see 20 the term mapping is a continuous function let a 2xor c x a mapping w 0 o x is called a whitney map for t 20 or 31 provided that the following conditions are satisfied a if a c b and a b then w a w b b o x 0 for each x e x in 1932 h whitney 31 showed that whitney maps always exist the notion of whitney map is a convenient and important tool for hyperspace theory a topological property p is said to be a whitney property 20 or 21 provided that whenever a continuum x has property p so does w f t for each whitney map w for c x and 0 t o x it is well known that connectibility is a whitney property if x is a received by the editors april 9 1985 and in revised form october 16 1985 1980 mathematics subject classification primary 54b20 secondary 54c55 54c56 54f45 kev words anid phrases hyperspaces whitney maps whitney property sequential strong whitneyreversible property approximate strong deformation retract pointed 1 movable far anr chainable circle like e mapping indecomposable 1986 american mathematical society 0002 9947 86 1 00 25 per page

whitney levels in hyperspaces of certain peano continua let x be a peano continuum let 2x resp c x be the space of all nonempty compacta resp subcontinua of x with the hausdorff matric let xo be a whitney map defined on sc 2x or c x such that x is admissible this requires the existence of a certain type of deformation of sc if sc c x assume x contains no free arc then for any to c 0 o x it is proved that w to o to and wf to o x are hilbert cubes this is an analogue of the curtis schori theorem for k a general result for the existance of admissible whitney maps is proved which implies that these maps exist when x is starshaped in a banach space or when x is a dendrite using these results it is shown for example that being an ar an anr an lc space or an lc space is not strongly whitney reversible introduction a continuum is a nonempty compact connected metric space a peano continuum is a locally connected continuum the hyperspaces of a continuum x are the spaces 2x a c x a is nonempty and compact and c x a c 2x a is connected metrized with the hausdorff metric 21 let f1 x x x c x a whitney map for a hyperspace sc of x is a continuous function w sc 0 xo such that o x 0 for each x c f1 x and if a b c c and a c b a then a b intuitively a whitney map is a size function if w is a whitney map for sc and 0 t o x then w l t is called a whitney level if 0 t x then w l t is called a positive whitney level thus a whitney level consists of compacta or continua in x of the same size basic facts about whitney maps and whitney levels are in 21 we note that whitney levels are coverings of x which as t gets close to zero converge to l 0 and consist of compacta of small diameter note that l 0 f1 x and hence l 0 is homeomorphic to x thus as t gets close to zero the whitney levels approximate x it is of interest to obtain information about the structure of positive whitney levels and to determine those properties which are preserved by the convergence of positive whitney levels to the zero level resultsa about this could be used to determine properties of x this is in analogy with the use of nerves of covers the nerves correspond to polyhedra these polyhedra approximate the original space as the mesh of the covers approaches zero and properties of these polyhedra determine various properties of the original space

rank tests for censored randomized block designs summary rank tests are proposed and studied for the hypothesis of equal treatment effects in randomized block experiments the procedures are applicable to samples containing arbitrarily right censored observations as well as uncensored observations in the case of logistic and double exponential rank scores the tests are shown to be censored data extensions of the well known friedman 1937 and brown mood 1951 procedures respectively the application of the techniques to problems in survival analysis is also discussed variate is subjected to arbitrary right censorship in the context of biological assays sampford taylor 1959 have largely dealt with parametric normal theory approaches to both the estimation and testing of treatment effects patel 1975 has discussed a censored data modification of friedman s 1937 statistic for testing the global hypothesis of equal treatment effects while l j wei has in unpublished work proposed a class of test procedures based on gehan s 1965 scoring scheme downton 1976 and morton 1978 have also discussed nonparametric tests for block designs the latter develops a class of rank statistics arising by forming a linear combination of score components from cox s 1975 partial likelihood the present approach is to use the marginal probability of a generalized rank vector rather than a partial likelihood in the formation of a class of tests the resulting rank tests differ from morton s in several respects for example multiple distinct censored values between two consecutive uncensored observations would receive identical scores with the present scheme distinct scores with morton s the specific objective of this paper is to propose a class of linear rank tests derived under optimal local power considerations for the global hypothesis of equal treatment effects to develop this class of tests we exploit the concept of the accumulated rank vector probability of prentice 1978 the principal theoretical results concerning the derivation of the test statistic and its null hypothesis permutation distribution follow in 2 the scores for the test statistic are given in explicit form for selected densities in 3 in 4 the test statistic is shown when dealing with only uncensored data to reduce to friedman s 1937 statistic with logistic scores and to brown mood s 1951 median test with double exponential scores a discussion of the application of the techniques to both the log linear and proportional hazards models in survival analysis is the subject of 5

fully nonparametric hypotheses for factorial designs i multivariate repeated measures designs abstract we introduce nonparametric versions for many of the hypotheses tested in analysis of variance and repeated measures models such as the hypotheses of no main effects no interaction effects and no factor effects these natural extensions of the nonparametric hypothesis of equality of the k distributions in the k sample problem have appealing practical interpretations we concentrate on multivariate repeated measures designs and obtain simple rank statistics for testing these hypotheses these statistics are the rank transform rt versions of the classical statistics for testing hypotheses in repeated measures designs we emphasize that even though recent research has demonstrated the inappropriateness of the rt method for many parametric hypotheses the rt procedure is always valid for testing our nonparametric hypotheses we show that the rank statistics converge in distribution to central chi squared distributions under their respective nonparametric null hypotheses the noncentrality paramet

global behavior of a three dimensional linear fractional system of difference equations we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 a xnb yn yn 1 c ynd zn zn 1 e znf xn n 0 1 where the parameters a b c d e and f are in 0 and the initial conditions x0 y0 and z0 are arbitrary non negative numbers we obtain some global attractivity results for the positive equilibrium of this system for different values of the parameters

a diagnostic for cox regression and general conditional likelihoods abstract diagnostics for changes in the maximum likelihood estimate of due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models for the cox proportional hazards model and in conditional models for arbitrarily matched or stratified data diagnostics derived from augmented regression models are again useful and easy to compute these diagnostics are applicable to different formulations for the multiplicative covariable effects over time or over strata an exact or approximate treatment of tied failure times or multiple case matching and time dependent covariates

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

simultaneous inference on treatment effects in survival studies with factorial designs a clinical trial with a 2 2 factorial design involves randomization of subjects to treatment a or a and within each group further randomization to treatment b or b under this design one can assess the effects of treatments a and b on a clinical endpoint using all patients one may additionally compare treatment a treatment b or combination therapy ab to a b with multiple comparisons however it may be desirable to control the overall type i error especially for regulatory purposes because the subjects overlap in the comparisons the test statistics are generally correlated by accounting for the correlations one can achieve higher statistical power compared to the conventional bonferroni correction herein we derive the correlation between any two stratified or unstratified log rank statistics for a 2 2 factorial design with a survival time endpoint such that the overall type i error for multiple treatment comparisons can be properly controlled in addition we allow for adjustment of prognostic factors in the treatment comparisons and conduct simultaneous inference on the effect sizes we use simulation studies to show that the proposed methods perform well in realistic situations we then provide an application to a recently completed randomized controlled clinical trial on alcohol dependence finally we discuss extensions of our approach to other factorial designs and multiple endpoints

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

an aligned rank test for censored data from randomized block designs summary the aligned rank test of hodges lehmann 1962 is extended to censored survival data collected in matched pairs or randomized blocks the test statistic for matched pairs is a direct extension of the original aligned rank test whereas the test statistic for use with block size k 2 is constructed from the paired data statistics comparing all possible pairs of treatments the efficiency of recovery of interblock information with censored matched pairs is examined by calculating the asymptotic efficiency of the proposed test relative to the sign test under a weibull model with a single overall censoring time the powers of these two tests and two other tests are compared under a more general model in a monte carlo study a numerical example illustrating the technique is included

nonparametric estimation for a scale change with censored observations abstract nonparametric point and interval estimators of the ratio of two scale parameters are given for arbitrarily right censored data based on the idea of hodges and lehmann 1963 these estimators are defined in terms of rank test statistics for testing the equality of two survival distributions the asymptotic properties and efficiencies of estimators corresponding to the tests studied by gill 1980 are investigated

nonparametric inference in factorial designs with censored data a method is proposed for testing the hypotheses of no main effects and no interaction in factorial designs with several observations per cell the method uses the fact that these hypotheses can be expressed in terms of a vector of contrasts it is based on the observation that nonparametric estimation of these contrasts is no more difficult than estimation of the location difference in the two sample problem to implement the method with censored data a new extension of the hodges lehmann estimator is proposed the estimator is simple to compute and its variance is easily evaluated a simulation study examines the performance of the proposed estimation and testing method in the context of a two by two design and a real data set from a three way layout with heavy censoring is analyzed

a class of rank test procedures for censored survival data summary a class of linear rank statistics is proposed for the k sample problem with rightcensored survival data the class contains as special cases the log rank test mantel 1966 cox 1972 and a test essentially equivalent to peto peto s 1972 generalization of the wilcoxon test martingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered and to derive expressions for asymptotic relative efficiencies under contiguous sequences of alternative hypotheses a class of distributions is presented which corresponds to the class of rank statistics in the sense that for each distribution there is a statistic with some optimal properties for detecting location alternatives from that distribution some monte carlo results are displayed which present small sample behaviour

orthogonal bases approach for comparing nonnormal continuous distributions summary we present an orthonormal bases approach for detecting general differences among continuous distributions an unknown density function is represented by a finite vector of its estimated fourier coefficients with respect to a suitable orthonormal basis for a wide class of orthonormal bases we establish asymptotic normality of the vector of estimated fourier coefficients and propose an unbiased and consistent estimator of its asymptotic covariance matrix fourier coefficients are modelled as functions of fixed and possibly random effects this approach allows simultaneous detection of distributional differences attributable to various factors in clustered and correlated data with sufficiently large numbers of observations per each cluster with the same fixed and random effects realisations this work was motivated by multi level clustered non gaussian datasets from genetic studies

a coupled system of rational difference equations abstract we investigate the global stability properties and asymptotic behavior of solutions of the recursive sequence where the parameters a b c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers

least absolute deviations estimation for the censored regression model this paper proposes an alternative to maximum likelihood estimation of the parameters of the censored regression or censored tobit model the proposed estimator is a generalization of least absolute deviations estimation for the standard linear model and unlike estimation methods based on the assumption of normally distributed error terms the estimator is consistent and asymptotically normal for a wide class of error distributions and is also robust to heteroscedasticity the paper gives the regularity conditions and proofs of these large sample results and proposes classes of consistent estimators of the asymptotic covariance matrix for both homoscedastic and heteroscedastic disturbances

weighted kaplan meier statistics large sample and optimality considerations summary we propose a cumulative weighted difference in the kaplan meier estimates as a test statistic for equality of distributions in the two sample censored data survival analysis problem for stability of such a statistic the absolute value of the possibly random weight function must be bounded above by a multiple of c 1 2 6 where 1 c is the left continuous censoring distribution function and 6 0 for these weighted kaplan meier wkm statistics asymptotic distribution theory is presented along with expressions for the efficacy under a sequence of local alternatives a simple censored data generalization of the two sample difference in means test z test is a member of this class and in large samples is seen to be quite efficient relative to the popular log rank test under a range of alternatives including the proportional hazards alternative optimal weight functions are also calculated the optimal wkm statistic is as efficient as the optimal weighted log rank statistic for any particular sequence of local alternatives stratified statistics and trend statistics are also presented

nonparametric hypotheses and rank statistics for unbalanced factorial designs abstract factorial designs are studied with independent observations fixed number of levels and possibly unequal number of observations per factor level combination in this context the nonparametric null hypotheses introduced by akritas and arnold are considered new rank statistics are derived for testing the nonparametric hypotheses of no main effects no interaction and no factor effects in unbalanced crossed classifications the formulation of all results includes tied observations extensions of these procedures to higher way layouts are given and the efficacies of the test statistics against nonparametric alternatives are derived a modification of the test statistics and approximations to their finite sample distributions are also given the small sample performance of the procedures for two factors is examined in a simulation study as an illustration a real dataset with ordinal data is analyzed

box type approximations in nonparametric factorial designs abstract linear rank statistics in nonparametric factorial designs are asymptotically normal and in general heteroscedastic in a comprehensive simulation study the asymptotic chi squared law of the corresponding quadratic forms is shown to be a rather poor approximation of the finite sample distribution motivated by this problem we propose simple finite sample size approximations for the distribution of quadratic forms in factorial designs under a normal heteroscedastic error structure these approximations are based on an f distribution with estimated degrees of freedom that generalizes ideas of patnaik and box simulation studies show that the nominal level is maintained with high accuracy and in most cases the power is comparable to the asymptotic maximin wald test data driven guidelines are given to select the most appropriate test procedure these ideas are finally transferred to nonparametric factorial designs where the same quadratic forms as in the parametric case are applied to the vector

global asymptotic behavior of a two dimensional difference equation modelling competition we investigate the global asymptotic behavior of solutions of the system of difference equations xn 1 xn a cyn yn 1 yn b dxn n 0 1 where the parameters a and b are in 0 1 c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers we show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior in the case where a b we find an explicit equation for the stable manifold

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

nonparametric methods for factorial designs with censored data abstract nonparametric hypotheses of no main effects no simple effects and no interaction effects are considered in the context of factorial designs with censored observations to test these hypotheses the asymptotic distribution of quadratic forms of rank statistics is derived using the methodology of martingales for counting processes the weights used reduce to the usual logistic scores with uncensored data but are different from the weights commonly used for testing the equality of k samples the formulation of all results includes tied observations approximations to the small sample distributions of the test statistics are given the performance of the tests is examined via simulation studies the procedures are illustrated on a real dataset

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

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

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

monotone estimating equations for censored data the monotone class rank test based estimating equations for regression models with right censored data is considered we introduce an estimator which is a solution of a monotone estimating equation that is an extension of the gehan test the estimator is easy to derive sqrt n consistent and asymptotically normal under minimal conditions all monotone estimating equations are characterized and a simulation study which shows that our suggested procedure performs well is included

semiparametric regression functionals abstract a regression method is developed for a general class of functionals a semiparametric linear model is adopted and the regression parameters are estimated by maximizing a profiled nonparametric or empirical likelihood based on a local estimate of the conditional distribution function simulated and real data examples are shown including an application of quantile regression to censored survival data from a clinical trial for myeloma

the theil sen estimator with doubly censored data and applications to astronomy abstract the theil sen estimator of the slope parameter in simple linear regression is extended to data with both the response and the covariate subject to censoring based on inverting a suitable version of kendall s statistic this estimator requires weak assumptions and is simple to compute and a simple estimate of its asymptotic variance is obtained a second extension of the theil sen estimator based on a direct estimation of the median of pairwise slopes is given these estimators are compared numerically with versions of schmitt s estimator and applied to two data sets from the recent astronomical literature

nonparametric models and methods for designs with dependent censored data part i we consider a nonparametric np approach to the analysis of repeated measures designs with censored data using the np model of akritas and arnold 1994 journal of the american statistical association 89 336 343 for marginal distributions we present test procedures for the np hypotheses of no main effects no interaction and no simple effects this extends the existing np methodology for such designs wei and lachin 1984 journal of the american statistical association 79 653 661 the procedures do not require any modeling assumptions and should be useful in cases where the assumptions of proportional hazards or location shift fail to be satisfied the large sample distribution of the test statistics is based on an i i d representation for kaplan meier integrals the testing procedures apply also to ordinal data and to data with ties useful small sample approximations are presented and their performance is examined in a simulation study finally the methodology is illustrated with two real life examples one with censored and one with missing data it is indicated that one of the data sets does not conform to any set of assumptions underlying the available methods and also that the present method provides a useful additional analysis even when data sets conform to modeling assumptions

survival analysis with median regression models abstract the median is a simple and meaningful measure for the center of a long tailed survival distribution to examine the covariate effects on survival a natural alternative to the usual mean regression model is to regress the median of the failure time variable or a transformation thereof on the covariates in this article we propose semiparametric procedures to make inferences for such median regression models with possibly censored observations our proposals can be implemented efficiently using a simulated annealing algorithm numerical studies are conducted to show the advantage of the new procedures over some recently developed methods for the accelerated failure time model a special type of mean regression models in the survival analysis the proposals discussed in the article are illustrated with a lung cancer data set

nonparametric estimation and regression analysis with left truncated and right censored data abstract in many prospective and retrospective studies survival data are subject to left truncation in addition to the usual right censoring for left truncated data without covariates only the conditional distribution of the survival time y given y can be estimated nonparametrically where is the lower boundary of the support of the left truncation variable t if the data are also right censored then the conditional distribution can be consistently estimated only at points not larger than where is the upper boundary of the support of the right censoring variable c in this article we first consider nonparametric estimation of trimmed functionals of the conditional distribution of y with the trimming inside the observable range between and we then extend the approach to regression analysis and curve fitting in the presence of left truncation and right censoring on the response variable y asymptotic normality of m estimators of the regression parameters derived from this approach is