cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

estimation of the ratio of scale parameters in the two sample problem with arbitrary right censorship abstract a two sample version of the cramer von mises statistic for right censored observations is used to obtain an estimator of the ratio of scale parameters of two distributions it is shown that this estimator is consistent for small samples simulations are performed which show the superiority of the estimator over the maximum likelihood estimator for exponential distributions author

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 inference for surrogate endpoints with bivariate censored data considerable attention has been recently paid to the use of surrogate endpoints in clinical research we deal with the situation where the two endpoints are both right censored while proportional hazards analyses are typically used for this setting their use leads to several complications in this article we propose the use of the accelerated failure time model for analysis of surrogate endpoints based on the model we then describe estimation and inference procedures for several measures of surrogacy a complication is that potentially both the independent and dependent variable are subject to censoring we adapt the theil sen estimator to this problem develop the associated asymptotic results and propose a novel resampling based technique for calculating the variances of the proposed estimators the finite sample properties of the estimation methodology are assessed using simulation studies and the proposed procedures are applied to data from an acute myelogenous leukemia clinical trial

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

the use of maximin efficiency robust tests in combining contingency tables and survival analysis abstract a test is the maximin efficiency robust test for a family of possible models underlying the data if no other test has higher minimum efficiency relative to the asymptotically optimum test for each model methods used to examine the efficiency robustness of rank tests for the two sample problem are adapted to obtain maximin efficiency robust procedures for testing the equality of proportions across several 2 2 tables for combining the results of tests for trend in several 2 x j tables in which the dose response function is one of a set of possible monotone functions and to analyze censored survival data when either the wilcoxon or log rank may be appropriate in the survival setting the robust test has maximin efficiency 93 3 relative to the wilcoxon or long rank when each is optimum in contrast to the 75 relative efficiency each statistic has when the other is optimum

modified semiparametric maximum likelihood estimator in linear regression analysis with complete data or right censored data consider a linear regression model where the response variable may be right censored the standard maximum likelihood estimator mle based parametric approach to estimation of regression coefficients requires that the parametric form of the error distribution be known given a dataset we may not be able to find a valid parametric form for the error distribution in such a case the error distribution is unknown and arbitrary and a semiparametric approach is plausible a special modified semiparametric mle msmle of the regression coefficients is proposed simulation suggests that the msmle is consistent is asymptotically normally distributed and may be efficient the new procedure is applied to engineering data

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

a two sample comparison for multiple ordered event data summary a longitudinal study is conducted to compare the process of a particular disease between two groups the process of the disease is monitored according to which of several ordered events occur in the paper the sojourn time between two successive events is considered as the outcome of interest the group effects on the sojourn times of the multiple events are parameterized by scale changes in a semiparametric accelerated failure time model where the dependence structure among the multivariate sojourn times is unspecified suppose that the sojourn times are subject to dependent censoring and the censoring times are observed for all subjects a log rank type estimating approach by rescaling the sojourn times and the dependent censoring times into the same distribution is constructed to estimate the group effects and the corresponding estimators are consistent and asymptotically normal without the dependent censoring the independent censoring times in general are not available for the uncensored data in order to complete the censoring information pseudo censoring times are generated from the corresponding nonparametrically estimated survival function in each group and we can still obtained unbiased estimating functions for the group effects a real application and a simulation study are conducted to illustrate the proposed methods

some scale estimators and lack of fit tests for the censored two sample accelerated life model some new scale estimators for the censored two sample accelerated life model are introduced they are zeros of some integrated weighted difference between the two cumulative hazard estimators these estimators are asymptotically normal the weight is chosen to result in estimators whose asymptotic variances do not involve the destiny functions and can be easily estimated this provides a fast and simple means of statistical inference in the censored two sample accelerated life model through investigating the asymptotic relative efficiency at some important censoring submodels and the finite example behaviors in various numerical studies we obtain some estimators with very competitive performance from the new class of scale estimators some lack of fit tests for the accelerated life model are also derived these tests are related to gill schumacher type tests and require little extra computing time once the estimator is obtained the estimators and tests are illustrated in two applications for a vaginal cancer data set for rats the effect of pretreatment regime was found to be well described by the two sample accelerated life model for a data set on progression of ovarian cancer it was found that the effect of grade of disease could not be described either by the two sample proportional hazards model or the two sample accelerated life model

the variational problems for classical n vector models we prove existence and regularity properties of solutions of the variational problems introduced in the previous paper 1 for classical lattice n vector models these results form a basis of our renormalization group approach to low temperature expansions for the considered models

renormalization and localization expansions ii expectation values of the fluctuation measures this paper is a continuation of 5 the k 1 st renormalization transformation applied to a density k is studied further the new contributions to the effective action obtained in 5 are renormalized and their localization expansions are constructed this completes proofs of theorems 1 and 4 in 5

sequential linear rank tests for two sample censored survival data under extremely general patterns of patient arrival allocation to treatment and loss to follow up in randomized clinical trial settings the sequentially computed logrank statistic mantel 1966 is shown under the null hypothesis of identically distributed lifetimes to have exactly uncorrelated increments and is shown via rebolledo s 1980 martingale invariance principle to satisfy a functional central limit theorem justifying sequential logrank tests of jones and whitehead 1979 generalizations are made to other twosample rank tests for censored survival data and practical applicability to real randomized clinical trials is discussed

tests of independence for bivariate data with random censoring a contingency table approach procedures are proposed for testing the hypothesis of independence between two discrete or discretized random variables one or both of which may be randomly censored the censoring mechanisms can be either independent bivariate censoring or identical univariate censoring the proposed tests reduce to goodness of fit tests for log linear models applied to either complete or incomplete contingency tables three examples are analyzed for illustrative purposes

distribution free methods of estimating location difference with censored paired data abstract nonparametric point and interval estimators of location difference in matched pairs data with arbitrary right censorship are proposed based on a generalized gehan gilbert test wei 1980 the point estimator is shown to be asymptotically normal and strongly consistent the limits of the corresponding interval estimator are readily computable an example is also provided to illustrate the techniques to problems in survival data analysis

two sample multistate accelerated sojourn times model abstract many medical studies involve observations of patients experiencing multiple consecutive states during their follow up since treatments may have differential effects on these states comparison is of interest with respect to individual sojourn times in this article i generalize the univariate accelerated failure time model for multistate processes and model the treatment effects as state specific time scale changes i propose a two sample inference procedure that accommodates incomplete follow up data this semiparametric procedure based on estimating equations yields a class of estimators that are consistent and asymptotically normal sample based consistent variance estimates are derived numerical studies demonstrate that the procedure performs well for practical sample sizes application to a cancer clinical trial is presented for illustration

bounds on net survival probabilities for dependent competing risks bounds on the marginal survival function based on data from a competing risks experiment are obtained these bounds require an investigator to specify a range of possible concordances for the times to occurrences of the competing risks these bounds are tighter than those of peterson 1976 proceedings of the national academy of sciences 73 11 13

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

estimation of a bivariate distribution function under random censorship summary estimators are proposed of the underlying distribution function of independent bivariate random vectors which are subject to random right censorship in each coordinate the estimators satisfy the monotonicity requirements of a distribution function are uniformly strongly consistent at a rate equal to that of the empirical distribution function and are fairly simple to compute

a concordance test for independence in the presence of censoring an extension of the definition of kendall s coefficient of concordance is proposed for testing independence in bivariate censored survival times the test statistic counts the number of known concordances minus the number of known discordances the variance of the statistic is calculated for an random censorship model which however does not require independence of the components of the censoring distribution two examples are given

a low temperature expansion for classical n vector models iii a complete inductive description fluctuation integrals we give a complete inductive description of the effective densities generated by applications of the renormalization transformations to the densities of the classical n vector models described in the paper 1 and we formulate the main theorems of this sequence of papers this description includes now all the large field domains which we ve excluded from the discussions of 1 4 we apply the renormalization transformation to a density satisfying the inductive hypotheses we introduce large field small field partitions and we determine and analyze the fluctuation integrals in the general setting

higgs 2 3 quantum fields in a finite volume we consider a euclidean model of interacting scalar and vector fields in two and three dimensions and prove a lower bound for vacuum energy in a lattice approximation the bound is independent of a lattice spacing it is proved with the help of renormalization transformations in wilson kadanoff form it extends in principal also to generating functional for schwinger functions

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

semiparametric inference for a quantile comparison function with applications to receiver operating characteristic curves summary in studies to compare two samples more information may be available on one treatment than the other when one population is modelled parametrically and the other nonparametrically we study large sample properties of a semiparametric sample quantile comparison function and show that it can have substantially smaller asymptotic variance than its nonparametric counterpart especially near the boundaries we describe applications to both two sample tests and receiver operating characteristic curves

nonparametric bivariate estimation with randomly censored data summary the estimation of a bivariate distribution function with randomly censored data is considered it is assumed that the censoring occurs independently of the lifetimes and that deaths and losses which occur simultaneously can be separated two estimators are developed a reduced sample estimator and a self consistent one it is shown that the latter estimator satisfies a nonparametric likelihood function and is unique up to the final uncensored values in any dimension it jumps at the points of double deaths in both dimensions some key word8 censored data kaplan meier estimator life table product limit estimator survival estimation

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

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

survival analysis with quantile regression models quantile regression offers great flexibility in assessing covariate effects on event times thereby attracting considerable interests in its applications in survival analysis but currently available methods often require stringent assumptions or complex algorithms in this article we develop a new quantile regression approach for survival data subject to conditionally independent censoring the proposed martingale based estimating equations naturally lead to a simple algorithm that involves minimizations only of l1 type convex functions we establish uniform consistency and weak convergence of the resultant estimators we develop inferences accordingly including hypothesis testing second stage inference and model diagnostics we evaluate the finite sample performance of the proposed methods through extensive simulation studies an analysis of a recent dialysis study illustrates the practical utility of our proposals

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

functional censored quantile regression we propose a functional censored quantile regression model to describe the time varying relationship between time to event outcomes and corresponding functional covariates the time varying effect

theory and application of shapelets to the analysis of surface self assembly imaging a method for quantitative analysis of local pattern strength and defects in surface self assembly imaging is presented and applied to images of stripe and hexagonal ordered domains the presented method uses shapelet functions which were originally developed for quantitative analysis of images of galaxies ensuremath propto 10 20 mathrm m in this work they are used instead to quantify the presence of translational order in surface self assembled films ensuremath propto 10 ensuremath 9 mathrm m through reformulation into steerable filters the resulting method is computationally efficient with respect to the number of filter evaluations robust to variation in pattern feature shape and unlike previous approaches is applicable to a wide variety of pattern types an application of the method is presented which uses a nearest neighbor analysis to distinguish between uniform defect free and nonuniform strained defect containing regions within imaged self assembled domains both with striped and hexagonal patterns

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

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

understanding cox s regression model a martingale approach abstract an informal discussion is given of how martingale techniques can be used to extend cox s regression model and to derive its large sample properties

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

validity of the spin wave approximation for the free energy of the heisenberg ferromagnet we consider the quantum ferromagnetic heisenberg model in three dimensions for all spins s 1 2 we rigorously prove the validity of the spin wave approximation for the excitation spectrum at the level of the first non trivial contribution to the free energy at low temperatures our proof comes with explicit constructive upper and lower bounds on the error term it uses in an essential way the bosonic formulation of the model in terms of the holstein primakoff representation in this language the model describes interacting bosons with a hard core on site repulsion and a nearest neighbor attraction this attractive interaction makes the lower bound on the free energy particularly tricky the key idea there is to prove a differential inequality for the two particle density which is thereby shown to be smaller than the probability density of a suitably weighted two particle random process on the lattice

sequential analysis of the proportional hazards model abstract for the proportional hazards model of survival analysis an appropriate large sample theory is developed for cases of staggered entry and sequential analysis the principal techniques involve an approximation of the score process by a suitable martingale and a random rescaling of time based on the observed fisher information as a result we show that the maximum partial likelihood estimator behaves asymptotically like brownian motion author

rank estimation of accelerated lifetime models with dependent censoring under independent censoring estimation of the covariate effects in the accelerated lifetime model may be based on censored data rank tests similar rank methodology has been developed with bivariate accelerated lifetime models for dependent censoring but uses artificial censoring which may lead to substantial information loss we present a new artificial censoring technique using pairwise ranking and establish the asymptotic properties of a pairwise rank estimator simulations show that the pairwise approach achieves large reductions in artificial censoring and large efficiency gains over the existing rank estimator the simulations evidence moderate efficiency gains under independent censoring over a rank estimator that is semiparametric efficient under independent censoring an aids data analysis illustrates the practical utility of the inferential procedures

randomization based interval estimation in randomized clinical trials randomization based interval estimation takes into account the particular randomization procedure in the analysis and preserves the confidence level even in the presence of heterogeneity it is distinguished from population based confidence intervals with respect to three aspects definition computation and interpretation the article contributes to the discussion of how to construct a confidence interval for a treatment difference from randomization tests when analyzing data from randomized clinical trials the discussion covers i the definition of a confidence interval for a treatment difference in randomization based inference ii computational algorithms for efficiently approximating the endpoints of an interval and iii evaluation of statistical properties ie coverage probability and interval length of randomization based and population based confidence intervals under a selected set of randomization procedures when assuming heterogeneity in patient outcomes the method is illustrated with a case study

the large field renormalization operation for classical n vector models a renormalization operation of the large field densities for the classical n vector models is constructed in this paper it allows to improve bounds of these densities and thus to prove all inductive hypotheses this completes the construction and analysis of the full renormalization group flow for these models the results will be used in the next paper to analyze the correlation functions

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

repeated confidence intervals for the median survival time summary we describe methods for the construction of a confidence interval for median survival time based on right censored data these methods are extended to the construction of repeated confidence intervals for the median based on accumulating data here the overall probability that all intervals contain the true median is guaranteed at a fixed level the use of repeated confidence intervals for median survival time in post marketing surveillance is discussed a confidence interval for median survival time provides a useful summary of the survival experience of a group of patients if confidence intervals are calculated repeatedly as data accumulates the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly jennison turnbull 1984 have proposed methods for calculating repeated confidence intervals appropriate to such situations similar ideas have also been discussed by lai 1984 in 2 we propose a new form of single sample nonparametric confidence interval this interval has asymptotically correct coverage probability and monte carlo simulations suggest it is superior to its competitors for small sample sizes repeated confidence intervals for the median are presented in 3 and their stnall sample size performance is assessed by monte carlo simulation an example of their use is given in 4 all the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time

inference for shift functions in the two sample problem with right censored data with applications abstract for two distribution functions f and g the shift function is defined by t g 1 f t t the shift function is the distance from the 45 line and the quantity plotted in q q plots in the analysis of lifetime data a represents the difference between two treatments the shift function can also be used to find crossing points of two distribution functions the large sample distribution theory for estimates of is studied for right censored data it turns out that the asymptotic covariance function depends on the unknown distribution functions f and g hence simultaneous confidence bands cannot be directly constructed a construction of simultaneous confidence bands for is developed via the bootstrap construction and application of such bands are explored for the q q plot

constructive field theory and applications perspectives and open problems in this paper we review many interesting open problems in mathematical physics which may be attacked with the help of tools from constructive field theory they could give work for future mathematical physicists trained with constructive methods well into the 21st century

large sample properties for a general estimator of the treatment effect in the two sample problem with right censoring the estimation of the treatment effect in the two sample problem with right censoring is of interest in survival analysis in this article we consider both the location shift model and the scale change model we establish the large sample properties of a generalized hodges lehmann type estimator the strong consistency is established under the minimal possible conditions the asymptotic normality is also obtained without imposing any conditions on the censoring mechanisms as a by product we also establish a result for the oscillation behavior of the kaplan meier process which extends the bahadur result for the empirical process to the censored case

comparing two failure time distributions in the presence of dependent censoring summary in a randomised clinical trial to compare two groups of patients suppose that the time to disease occurrence the major response variable may be subject to dependent censoring by death or selective patient withdrawal while the patients who have reached the disease endpoint are followed for their secondary endpoints or survival information to adjust for the dependent censoring in assessing the group difference in disease occurrence we assume that on a logarithmic scale the times to disease occurrence and dependent censoring for the two groups satisfy a bivariate location shift model with a completely unspecified underlying distribution rank based procedures are constructed for making inferences about the location shift parameter model checking techniques are also developed numerical studies show that the proposed methods are appropriate for practical use an illustration with data taken from a recent aids clinical trial is provided

nonparametric analysis of an accelerated failure time model summary survival distributions can be characterized by and compared through their hazard functions tests using a proportional hazards model have good power if the two hazards do not cross but without time dependent covariates can have low power if they do the method contained herein is designed to provide a complement to the proportional hazards model differences in survival distributions are parameterized by a scale change and the log rank statistic is used to generate an estimate of the change and a confidence interval based test this approach is fully efficient for the weibull family with no censoring in general it compares favourably with the proportional hazards approach although neither method dominates

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

the renormalization group according to balaban ii large fields this is an expository account of balaban s approach to the renormalization group the method is illustrated with a treatment of the ultraviolet problem for the scalar 4 model on a toroidal lattice in dimension d 3 in this paper we control the large field contribution to the partition function

non parametric tests for distributional treatment effect for randomly censored responses for a binary treatment 0 1 and the corresponding potential response y for the control group 0 and y 1 for the treatment group 1 one definition of no treatment effect is that y and y 1 follow the same distribution given a covariate vector x koul and schick have provided a non parametric test for no distributional effect when the realized response 1 v y y 1 is fully observed and the distribution of x is the same across the two groups this test is thus not applicable to censored responses nor to non experimental i e observational studies that entail different distributions of x across the two groups we propose x matched non parametric tests generalizing the test of koul and schick following an idea of gehan our tests are applicable to non experimental data with randomly censored responses in addition to these motivations the tests have several advantages first they have the intuitive appeal of comparing all available pairs across the treatment and control groups instead of selecting a number of matched controls or treated in the usual pair or multiple matching second whereas most matching estimators or tests have a non overlapping support of x problem across the two groups our tests have a built in protection against the problem third gehan s idea allows the tests to make good use of censored observations a simulation study is conducted and an empirical illustration for a job training effect on the duration of unemployment is provided

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

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

a general estimator of the treatment effect when the data are heavily censored summary a generalized hodges lehmann type estimator for the treatment effect in the twosample problem with right censoring is proposed based on an inverse quantile type idea using truncated versions of the kaplan meier estimators over the subspace where they are consistent its strong consistency and asymptotic normality can be obtained under no conditions on the uninformative censorings and the resulting variance is easily estimable from the data in simulation studies the proposed estimator is superior to existing procedures in the presence of heavy unequal censoring

nonparametric estimation for the difference or ratio of median failure times a simple and purely nonparametric confidence interval procedure for the difference or ratio of two median failure times is proposed with censored observations the new proposal does not involve unstable and complicated nonparametric density estimates and is valid asymptotically even when the two underlying distribution functions differ in shape extensive numerical studies are carried out to examine the appropriateness of the new procedure for practical sample sizes

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

nonparametric methods for analyzing incomplete nondecreasing repeated measurements in comparing the effectiveness of two treatments suppose that nondecreasing repeated measurements of the same characteristic are scheduled to be taken over a common set of time points for each study subject a class of univariate one sided global asymptotically distribution free tests is proposed to test the equality of the two treatments the test procedures allow different patterns of missing observations in the two groups to be compared although the missing data mechanism is required to be independent of the observations in each treatment group test based point and interval estimators of the global treatment difference are given multiple inference procedures are also provided to examine the time trend of treatment differences over the entire study the proposed methods are illustrated by an example from a bladder cancer study

relative efficiency of the log rank test within a multiplicative intensity model summary for large sample clinical trials with independent individuals randomly allocated to two treatment groups in which survival times follow a log linear multiplicative intensity model with treatment group as one covariate this paper calculates the asymptotic relative efficiency of the log rank test for treatment effect as compared with the optimal score test the method is to exhibit the failure hazard intensity not of proportional hazards form obtained by ignoring all covariates other than treatment group the efficiency formulae are illustrated in two examples and estimation from data of the loss of efficiency is illustrated for two clinical trial datasets

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

multiscale formalism for correlation functions of fermions infrared analysis of the tridimensional gross neveu model we present a multiscale formalism for fermionic systems with a smooth uv cutoff establishing a trivial link between the correlation functions and the effective potential flow and study the k point truncated functions of the tridimensional gross neveu model a new efficient method is used to bound these correlation functions and show polynomial tree decay for long distances we are guided by a block lattice mechanism with a property of orthogonality between terms in different scales which leads to simple formulas for the correlations

estimations in homoscedastic linear regression models with censored data an empirical process approach pertaining to the estimating equations proposed by tsiatis based on the linear rank test we show the existence of local confounding between the baseline hazard function and the covariates due to the local confounding an estimating equation in tsiatis family with a larger time point of truncation could contain less information about the regression parameter than the estimating equation with a smaller time point of truncation this phenomenon further indicates significant loss of efficiency of tsiatis estimating equations as well as the power loss of log rank type tests when the baseline hazard function goes up and down along the time scale to take care of this local confounding without using nonparametric estimates of the derivative of the baseline hazard function we propose the empirical process approach epa based on an empirical process constructed from tsiatis log rank estimating equation by varying its truncating time point the epa will provide very tractable estimations of the regression parameters as well as pearson s chi squared statistics for testing the model s assumptions specifically the performance of the epa estimator is shown to be very close to the best estimator in tsiatis family

two sample inference for median survival times based on one sample procedures for censored survival data abstract confidence intervals for median survival times are derived for censored survival data the intervals are obtained by using the quantiles of the kaplan meier product limit estimator and have the same pitman efficiency as the intervals found by inverting the sign test two sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one sample confidence intervals several methods for choosing the confidence coefficients of the corresponding one sample confidence intervals are developed the pitman efficiencies of these two sample tests are the same as that of the median test proposed by brookmeyer and crowley 1982a the procedures can also be used for the accelerated failure time model proportional hazard model and the behrens fisher problem nonparametric two sample inference procedures are useful in comparing the responses of treatment and control groups in medical follow up studies the data are usually subjected to cens

a low temperature expansion for classical n vector models ii renormalization group equations this paper continues the analysis of the low temperature expansions for classicaln vector models started in 1 a main part of it is a derivation of renormalization group equations and a construction of their solutions to do this we have to introduce a fluctuation integral connected with a next renormalization transformation and to make its preliminary analysis the results of the paper are summarized in theorems stating that the renormalization transformation preserves the space of densitites or actions described inductively in 1

long time integration methods for mesoscopic models of pattern forming systems spectral methods for simulation of a mesoscopic diffusion model of surface pattern formation are evaluated for long simulation times backwards differencing time integration coupled with an underlying newton krylov nonlinear solver sundials cvode is found to substantially accelerate simulations without the typical requirement of preconditioning quasi equilibrium simulations of patterned phases predicted by the model are shown to agree well with linear stability analysis simulation results of the effect of repulsive particle particle interactions on pattern relaxation time and short long range order are discussed

approximate methods using ranks for regression with censored data summary an approximation to marginal rank likelihoods is given and used to make inferences for the linear regression model with censored data the approximations involve linear rank statistics adapted for censored data and estimates of their variance various explicit scores are given for right censored data and logistic scores for doubly censored data inferences using the approximate rank analysis are compared with inferences using fully and partially parametric techniques on two data sets

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

interval estimation of slope with right censored data summary a new method for point and interval estimation of a slope that uses randomly right censored data is presented the new method is based on inverting a censored data version of a test for association a simulation study shows that the new method compares favourably with a method due to buckley james 1979 in this paper we consider nonparametric estimation of the slope parameter in a simple linear regression model when the data are randomly right censored the three main nonparametric methods for the estimation of slope in a linear regression model are due to miller 1976 buckley james 1979 and to koul susarla van ryzin 1981 a fourth method due to cox 1972 though used extensively in the regression analysis of right censored data is not directly comparable to the first three methods because it is based on a proportional hazards model miller halpern 1982 compare the four methods and come out generally in favour of the cox and buckley james methods finding that the other two methods have some methodological weaknesses miller halpern conclude that the choice between the cox and buckley james methods must be based on the appropriateness of the proportional hazards model or the linear model in this paper we propose a new method for point and interval estimation of the slope parameter in a simple linear regression model under suitable regularity conditions the

two sample problem with bivariate exchangeable observations on utilise la propriete de symetrie de ce type de probleme et on propose une maniere alternative d analyser les donnees