a nonparametric mixture model for cure rate estimation summary nonparametric methods have attracted less attention than their parametric counterparts for cure rate analysis in this paper we study a general nonparametric mixture model the proportional hazards assumption is employed in modeling the effect of covariates on the failure time of patients who are not cured the em algorithm the marginal likelihood approach and multiple amputations are employed to estimate parameters of interest in the model this model extends models and improves estimation methods proposed by other researchers it also extends cox s proportional hazards regression model by allowing a proportion of event free patients and investigating covariate effects on that proportion the model and its estimation method are investigated by simulations an application to breast cancer data including comparisons with previous analyses using a parametric model and an existing nonparametric model by other researchers confirms the conclusions from the parametric model but not those from the existing nonparametric model

recognising simplicity of black box groups by constructing involutions and their centralisers abstract we investigate the complexity of constructing involutions and their centralisers in groups of lie type over finite fields of odd order and discuss applications to the problem of deciding whether a matrix group or a black box group of known characteristic is simple we show that if the characteristic is odd then simplicity can be recognised in monte carlo polynomial time

a class of semiparametric mixture cure survival models with dependent censoring modern cancer treatments have substantially improved cure rates and have generated a great interest in and need for proper statistical tools to analyze survival data with nonnegligible cure fractions data with cure fractions often are complicated by dependent censoring and the analysis of this type of data typically involves untestable parametric assumptions on the dependence of the censoring mechanism and the true survival times motivated by the analysis of prostate cancer survival trends we propose a class of semiparametric transformation cure models that allows for dependent censoring without making parametric assumptions on the dependence relationship the proposed class of models encompasses a number of common models for the latency survival function including the proportional hazards model and the proportional odds model and also allows for time dependent covariates an inverse censoring probability reweighting scheme is used to derive unbiased estimating equations small sample properties wit

the identifiability of the mixed proportional hazards competing risks model we prove identification of dependent competing risks models in which each risk has a mixed proportional hazard specification with regressors and the risks are dependent by way of the unobserved heterogeneity or frailty components we show that the conditions for identification given by heckman and honore can be relaxed we extend the results to the case in which multiple spells are observed for each subject

analysing competing risks data with transformation models we present a flexible class of marginal models for the cumulative incidence function the semiparametric transformation model is utilized in a decomposition for the marginal failure probabilities which extends previous work on farewell s cure model novel estimation inference and prediction procedures are developed with large sample properties derived from the theory of martingales and u statistics a small simulation study demonstrates that the methods are appropriate for practical use the methods are illustrated with a thorough analysis of a prostate cancer clinical trial simple graphical displays are used to check for the goodness of fit

strong involutions in finite special linear groups of odd characteristic abstract let t be an involution in gl n q whose fixed point space e has dimension k between n 3 and 2 n 3 for each g gl n q such that t t g has even order t t g contains a unique involution z g which commutes with t we prove that with probability at least c log n for some c 0 the restriction z g e is an involution on e with fixed point space of dimension between k 3 and 2 k 3 this result has implications in the analysis of the complexity of recognition algorithms for finite classical groups in odd characteristic we discuss how similar results for involutions in other finite classical groups would solve a major open problem in our understanding of the complexity of constructing involution centralisers in those groups

inference under right censoring for transformation models with a change point based on a covariate threshold we consider linear transformation models applied to right censored survival data with a change point in the regression coefficient based on a covariate threshold we establish consistency and weak convergence of the nonparametric maximum likelihood estimators the change point parameter is shown to be n consistent while the remaining parameters are shown to have the expected root n consistency we show that the procedure is adaptive in the sense that the nonthreshold parameters are estimable with the same precision as if the true threshold value were known we also develop monte carlo methods of inference for model parameters and score tests for the existence of a change point a key difficulty here is that some of the model parameters are not identifiable under the null hypothesis of no change point simulation studies establish the validity of the proposed score tests for finite sample sizes

checking the cox model with cumulative sums of martingale based residuals summary this paper presents a new class of graphical and numerical methods for checking the adequacy of the cox regression model the procedures are derived from cumulative sums of martingale based residuals over follow up time and or covariate values the distributions of these stochastic processes under the assumed model can be approximated by zero mean gaussian processes each observed process can then be compared both visually and analytically with a number of simulated realizations from the approximate null distribution these comparisons enable the data analyst to assess objectively how unusual the observed residual patterns are special attention is given to checking the functional form of a covariate the form of the link function and the validity of the proportional hazards assumption an omnibus test consistent against any model misspecification is also studied the proposed techniques are illustrated with two real data sets

on semiparametric transformation cure models a general class of semiparametric transformation cure models is studied for the analysis of survival data with long term survivors it combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence included as special cases are the proportional hazards cure model farewell 1982 kuk chen 1992 sy taylor 2000 peng dear 2000 and the proportional odds cure model generalised estimating equations are proposed for parameter estimation it is shown that the resulting estimators are asymptotically normal with variance covariance matrix that has a closed form and can be consistently estimated by the usual plug in method simulation studies show that the proposed approach is appropriate for practical use an application to data from a breast cancer study is given to illustrate the methodology

a new bayesian model for survival data with a surviving fraction abstract we consider bayesian methods for right censored survival data for populations with a surviving cure fraction we propose a model that is quite different from the standard mixture model for cure rates we provide a natural motivation and interpretation of the model and derive several novel properties of it first we show that the model has a proportional hazards structure with the covariates depending naturally on the cure rate second we derive several properties of the hazard function for the proposed model and establish mathematical relationships with the mixture model for cure rates prior elicitation is discussed in detail and classes of noninformative and informative prior distributions are proposed several theoretical properties of the proposed priors and resulting posteriors are derived and comparisons are made to the standard mixture model a real dataset from a melanoma clinical trial is discussed in detail

a mixture model combining logistic regression with proportional hazards regression summary a model is proposed for the analysis of censored data which combines a logistic formulation for the probability of occurrence of an event with a proportional hazards specification for the time of occurrence of the event the proposed model is a semiparametric generalization of a parametric model due to farewell 1982 estimates of the regression parameters are obtained by maximizing a monte carlo approximation of a marginal likelihood and the em algorithm is used to estimate the baseline survivor function we present some simulation results to verify the validity of the suggested estimation procedure it appears that the semiparametric estimates are reasonably efficient with acceptable bias whereas the parametric estimates can be highly dependent on the parametric assumptions

constructive recognition of classical groups in even characteristic abstract let g x gl d f be a classical group in its natural representation defined over a finite field f of even characteristic we present las vegas algorithms to construct standard generators for g which permit us to write an element of g as a straight line program in x and to construct an involution as a straight line program in x if f 4 then the algorithms run in time polynomial in the size of the input subject to the existence of a discrete logarithm oracle for f

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

kaplan meier marginal or conditional probability curves in summarizing competing risks failure time data in the context of competing risks the kaplan meier estimator is often unsuitable for summarizing failure time data we discuss some alternative descriptive methods including marginal probability and conditional probability estimators two sample test statistics are also presented

estimating the proportion of immunes in a censored sample summary an estimator for the proportion of immunes in a population is proposed when a sample of censored failure times is available our suggestion is to use one minus the maximum observed value of the kaplan meier empirical distribution function this estimator is shown to be consistent and asymptotically normal under modest conditions on the censoring mechanism simulations suggest that the estimator is approximately normal for quite small sample sizes provided the immune proportion is not too close to zero a simple nonparametric statistic is proposed to test whether the assumptions of the analysis are likely to be valid

the identifiability of the competing risks model summary this paper considers the consequences for identifiability of introducing regressors into the competing risks model of multistate duration analysis we establish conditions under which access to regressors overturns the nonidentification theorem of cox and tsiatis for both proportional and accelerated failure time models

on the linear transformation model for censored data recently cheng wei ying 1995 1997 proposed a class of estimation procedures for semi parametric linear transformation models with censored observations when the support of the censoring variable is shorter than that of the failure time the estimators are asymptotically biased in this paper we present a simple modification of cheng s estimation procedures for the regression parameters through extensive numerical studies with practical sample sizes we find that the new proposals perform well but the original interval estimators may not have correct coverage probabilities when censoring is heavy prediction procedures for the survival probabilities of future subjects are also modified accordingly

semiparametric regression estimation in the presence of dependent censoring summary we propose a semiparametric estimation procedure for estimating the regression of an outcome y measured at the end of a fixed follow up period on baseline explanatory variables x measured prior to start of follow up in the presence of dependent censoring given x the proposed estimators are consistent when the data are missing at random but not missing completely at random rubin 1976 and do not require full specification of the complete data likelihood specifically we assume that the probability of censoring at time t is independent of the outcome y conditional on the recorded history up to t of a vector of time dependent covariates that are correlated with y our estimators can be used to adjust for dependent censoring and nonrandom noncompliance in randomised trials studying the effect of a treatment on the mean of a response variable of interest even with independent censoring our methods allow the investigator to increase efficiency by exploiting the correlation of the outcome with a vector of time dependent covariates

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

analysis of survival data by the proportional odds model a model is presented for the analysis of lifetime data in which the rates of mortality for separate groups of patients converge with time a non parametric estimate is given for the survivor function the theoretical basis for the model assumes that prognostic factors have a multiplicative effect on the odds against survival beyond any given time the model is fitted to data using maximum likelihood estimation and an example of its use in the analysis of a lung cancer trial is given

asymptotic theory for the correlated gamma frailty model the frailty model is a generalization of cox s proportional hazard model where a shared unobserved quantity in the intensity induces a positive correlation among the survival times murphy showed consistency and asymptotic normality of the nonparametric maximum likelihood estimator npmle for the shared gamma frailty model without covariates in this paper we extend this result to the correlated gamma frailty model and we allow for covariates we discuss the definition of the nonparametric likelihood function in terms of a classical proof of consistency for the maximum likelihood estimator which goes back to wald our proof of the consistency for the npmle is essentially the same as the classical proof for the maximum likelihood estimator a new central limit theorem for processes of bounded variation is given furthermore we prove that a consistent estimator for the asymptotic variance of the npmle is given by the inverse of a discrete observed information matrix

two component mixture cure rate model with spline estimated nonparametric components in some survival analysis of medical studies there are often long term survivors who can be considered as permanently cured the goals in these studies are to estimate the noncured probability of the whole population and the hazard rate of the susceptible subpopulation when covariates are present as often happens in practice to understand covariate effects on the noncured probability and hazard rate is of equal importance the existing methods are limited to parametric and semiparametric models we propose a two component mixture cure rate model with nonparametric forms for both the cure probability and the hazard rate function identifiability of the model is guaranteed by an additive assumption that allows no time covariate interactions in the logarithm of hazard rate estimation is carried out by an expectation maximization algorithm on maximizing a penalized likelihood for inferential purpose we apply the louis formula to obtain point wise confidence intervals for noncured probability and hazard rate asymptotic convergence rates of our function estimates are established we then evaluate the proposed method by extensive simulations we analyze the survival data from a melanoma study and find interesting patterns for this study

on the evolution of harmonic maps in higher dimensions on etablit des resultats de regularite partielle et l existence de solutions regulieres globales pour le probleme d evolution pour des applications harmoniques avec des donnees petites

recurrent events analysis in the presence of time dependent covariates and dependent censoring summary recurrent events models have had considerable attention recently the majority of approaches show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates that are included in the model we provide an overview of available recurrent events analysis methods and present an inverse probability of censoring weighted estimator for the regression parameters in the andersen gill model that is commonly used for recurrent event analysis this estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently and it generally improves on the naive estimator for the andersen gill model in the case of independent censoring we illustrate the bias of ad hoc estimators in the presence of informative censoring with a simulation study and provide a data analysis of recurrent lung exacerbations in cystic fibrosis patients when some patients are lost to follow up

analysis of transformation models with censored data summary in this paper we consider a class of semi parametric transformation models under which an unknown transformation of the survival time is linearly related to the covariates with various completely specified error distributions this class of regression models includes the proportional hazards and proportional odds models inference procedures derived from a class of generalised estimating equations are proposed to examine the covariate effects with censored observations numerical studies are conducted to investigate the properties of our proposals for practical sample sizes these transformation models coupled with the new simple inference procedures provide many useful alternatives to the cox regression model in survival analysis

maximum likelihood estimation in semiparametric regression models with censored data summary semiparametric regression models play a central role in formulating the effects of covariates on potentially censored failure times and in the joint modelling of incomplete repeated measures and failure times in longitudinal studies the presence of infinite dimensional parameters poses considerable theoretical and computational challenges in the statistical analysis of such models we present several classes of semiparametric regression models which extend the existing models in important directions we construct appropriate likelihood functions involving both finite dimensional and infinite dimensional parameters the maximum likelihood estimators are consistent and asymptotically normal with efficient variances we develop simple and stable numerical techniques to implement the corresponding inference procedures extensive simulation experiments demonstrate that the inferential and computational methods proposed perform well in practical settings applications to three medical studies yield important new insights we conclude that there is no reason theoretical or numerical not to use maximum likelihood estimation for semiparametric regression models we discuss several areas that need further research

estimation of the time dependent accelerated failure time model in the presence of confounding factors summary cox oakes 1984 p 66 introduced the strong version of the accelerated failure time model with time dependent exposures we provide conditions under which this model could be used to estimate from observational data the causal effect of a time varying exposure or treatment on time to an event of interest in the presence of time dependent confounding variables we propose a class of semiparametric tests and estimators for the model parameters this class contains an estimator that is semipara metric efficient in the sense of begun et al 1983 the purpose of this paper is first to provide conditions under which it would be possible to estimate from observational data the causal effect of a time dependent treatment or exposure on time to an event of interest in the presence of time dependent confounding covariates and then to construct estimators for the treatment effect under these condi tions our approach will be based on the semiparametric estimation of the parameters of the strong version of the accelerated failure time model with time dependent exposures or treatments introduced by cox oakes 1984 p 66 the usual approach to the estimation of the effect of a time varying treatment on survival is to model the hazard of failure at t as a function of past treatment history using a time dependent proportional hazards model we show that the usual approach may be biased whether or not one further adjusts for past confounder history in the analysis when a there exists a time dependent risk factor for or predictor of the event of interest that also predicts subsequent treatment and b past treatment history predicts subsequent risk factor level the following four examples demonstrate conditions a and b will often be true in an observational study in which there is treatment by indication the drug zidovudine formerly azt used in the treatment of the acquired immunodeficiency syndrome is a direct red blood cell toxin that is contra indicated in anaemic subjects i e subjects with depressed red cell counts since the toxic effects of zidovudine can worsen the anaemia further anaemic patients are at increased risk of death thus in an observational study of the effect of zidovudine on survival of patients with the acquired immunodeficiency syndrome anaemia is both a risk factor for death

mixture cure survival models with dependent censoring summary the paper is motivated by cure detection among the prostate cancer patients in the national institutes of health surveillance epidemiology and end results programme wherein the main end point e g deaths from prostate cancer and the censoring causes e g deaths from heart diseases may be dependent although many researchers have studied the mixture survival model to analyse survival data with non negligible cure fractions none has studied the mixture cure model in the presence of dependent censoring to account for such dependence we propose a more general cure model that allows for dependent censoring we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time by using a class of archimedean copula models within this framework we consider the parameter estimation the cure detection and the two sample comparison of latency distributions in the presence of dependent censoring when a proportion of patients is deemed cured large sample results by using martingale theory are obtained we examine the finite sample performance of the proposed methods via simulation and apply them to analyse the surveillance epidemiology and end results prostate cancer data