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

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

bootstrap for the case cohort design the case cohort design facilitates economical investigation of risk factors in a large survival study with covariate data collected only from the cases and a simple random subset of the full cohort methods that accommodate the design have been developed for various semiparametric models but most inference procedures are based on asymptotic distribution theory such inference can be cumbersome to derive and implement and does not permit confidence band construction while bootstrap is an obvious alternative how to resample is unclear because of complications from the two stage sampling design we establish an equivalent sampling scheme and propose a novel and versatile nonparametric bootstrap for robust inference with an appealingly simple single stage resampling theoretical justification and numerical assessment are provided for a number of procedures under the proportional hazards model

censored linear regression for case cohort studies summary right censored data from a classical case cohort design and a stratified case cohort design are considered in the classical case cohort design the subcohort is obtained as a simple random sample of the entire cohort whereas in the stratified design this subcohort is elected by independent bernoulli sampling with arbitrary selection probabilities for each design and under a linear regression model methods for estimating the regression parameters are proposed and analysed these methods are derived by modifying the linear ranks tests and estimating equations that arise from full cohort data using methods that are similar to the pseudolikelihood estimating equation that has been used in relative risk regression for these models the estimators so obtained are shown to be consistent and asymptotically normal variance estimation and numerical illustrations are also provided

information bounds for cox regression models with missing data we derive information bounds for the regression parameters in cox models when data are missing at random these calculations are of interest for understanding the behavior of efficient estimation in case cohort designs a type of two phase design often used in cohort studies the derivations make use of key lemmas appearing in robins rotnitzky and zhao j amer statist assoc 89 1994 846 866 and robins hsieh and newey j roy statist soc ser b 57 1995 409 424 but in a form suited for our purposes here we begin by summarizing the results of robins rotnitzky and zhao in a form that leads directly to the projection method which will be of use for our model of interest we then proceed to derive new information bounds for the regression parameters of the cox model with data missing at random mar in the final section we exemplify our calculations with several models of interest in cohort studies including an i i d version of the classical case cohort design of prentice biometrika 73 1986 1 11 and self and prentice ann statist 16 1988 64 81

accelerated failure time models for counting processes summary we present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events a class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model in addition a nelson aalen type estimator for the mean function of the counting process is constructed which is consistent and properly normalised converges weakly to a zeromean gaussian process we assess the finite sample properties of the proposed estimators and the associated inference procedures through monte carlo simulation and provide an application to a well known bladder cancer study

a case cohort design for epidemiologic cohort studies and disease prevention trials summary suppose that a cohort of individuals is to be followed in order to relate failure rates to preceding covariate histories a design is proposed which involves covariate data only for cases experiencing failure and for members of a randomly selected subcohort odds ratio and relative risk estimation procedures are presented for such a case cohort design a small simulation study compares case cohort relative risk estimation procedures to full cohort and synthetic case control analyses relevance to epidemiologic cohort studies and disease prevention trials is discussed

efficient estimation of semiparametric transformation models for two phase cohort studies under two phase cohort designs such as case cohort and nested case control sampling information on observed event times event indicators and inexpensive covariates is collected in the first phase and the first phase information is used to select subjects for measurements of expensive covariates in the second phase inexpensive covariates are also used in the data analysis to control for confounding and to evaluate interactions this article provides efficient estimation of semiparametric transformation models for such designs accommodating both discrete and continuous covariates and allowing inexpensive and expensive covariates to be correlated the estimation is based on the maximization of a modified nonparametric likelihood function through a generalization of the expectation maximization algorithm the resulting estimators are shown to be consistent asymptotically normal and asymptotically efficient with easily estimated variances simulation studies demonstrate that the asymptotic approximati

large subgroups of simple groups abstract let g be a finite group a proper subgroup h of g is said to be large if the order of h satisfies the bound h 3 g in this note we determine all the large maximal subgroups of finite simple groups and we establish an analogous result for simple algebraic groups in this context largeness is defined in terms of dimension an application to triple factorisations of simple groups both finite and algebraic 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

adjusted regression estimation for time to event data with differential measurement error differential measurement error data plausibly arise in epidemiology and biomedical studies but have been rarely dealt with explicitly especially for time to event data we propose an estimation equation correction method in semiparametric censored linear regression to deal with differential measurement error for time to event data with validation samples the method does not require explicit modelling of the error prone covariates and leads to unbiased estimation copyright 2013 oxford university press

modules with small loewy length a module of complexity c for e z p r in characteristic p has loewy length at least p 1 r c 1 we study the case of equality if p is odd the only rank varieties possible are finite unions of linear subspaces of dimension c and every such rank variety occurs if p 2 the variety has to be equidimensional if such a variety is a finite union of set theoretic complete intersections then it occurs for such a module but otherwise the situation is unclear exterior algebras in any characteristic are also treated and follow the same behaviour as the case p 2 above

semiparametric accelerated failure time modeling for clustered failure times from stratified sampling clustered failure times often arise from studies with stratified sampling designs where it is desired to reduce both cost and sampling error semiparametric accelerated failure time aft models have not been used as frequently as cox relative risk models in such settings due to lack of efficient and reliable computing routines for inferences the challenge roots in the nonsmoothness of the rank based estimating functions and for clustered data the asymptotic properties of the estimator from the weighted version have not been available the recently proposed induced smoothing approach which provides fast and accurate rank based inferences for aft models is generalized to incorporate weights to accommodate stratified sampling designs the estimator from the induced smoothing weighted estimating equations are shown to be consistent and have the same asymptotic distribution as that from the nonsmooth version which has not been developed before the variance of the estimator is estimated by computational

estimation in the semiparametric accelerated failure time model with missing covariates improving efficiency through augmentation abstractthis article considers linear regression with missing covariates and a right censored outcome we first consider a general two phase outcome sampling design where full covariate information is only ascertained for subjects in phase two and sampling occurs under an independent bernoulli sampling scheme with known subject specific sampling probabilities that depend on phase one information e g survival time failure status and covariates the semiparametric information bound is derived for estimating the regression parameter in this setting we also introduce a more practical class of augmented estimators that is shown to improve asymptotic efficiency over simple but inefficient inverse probability of sampling weighted estimators estimation for known sampling weights and extensions to the case of estimated sampling weights are both considered the allowance for estimated sampling weights permits covariates to be missing at random according to a monotone but unknown mechanism the asymptotic pr

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

case cohort and case control analysis with cox s model prentice 1986 proposed the case cohort design and studied a pseudolikelihood estimator of regression parameters in cox s model we derive a class of estimating equations for case cohort sampling each depending on a different estimator of the population distribution which lead naturally to simple estimators that improve on prentice s pseudolikelihood estimator we also discuss an equivalence between case control and case cohort sampling in terms of the estimation of regression parameters in cox s model

calibration regression of censored lifetime medical cost analysis of lifetime medical cost is challenged by its irregular distribution and by incomplete follow up particularly the latter with limited study duration as is typical in medical research this article proposes the so called calibration regression to address these issues by modeling not only lifetime medical cost but also survival time in a semiparametric fashion it is postulated that both outcomes on possibly transformed scales linearly relate to the covariates however the bivariate model error distribution is completely unspecified whereas this conceptually simple model is a natural multivariate generalization of the accelerated failure time model this article proposes an inference procedure by extending the weighted log rank estimating function to the marked point process framework the resulting estimators are consistent and asymptotically normal in addition robustness and efficiency issues are discussed furthermore a novel sample based variance estimation procedure is proposed for es

triple factorisations of the general linear group and their associated geometries abstract triple factorisations of finite groups g of the form g p q p are essential in the study of lie theory as well as in geometry geometrically each triple factorisation g p q p corresponds to a g flag transitive point line geometry such that each pair of points is incident with at least one line we call such a geometry collinearly complete and duality interchanging the roles of points and lines gives rise to the notion of concurrently complete geometries in this paper we study triple factorisations of the general linear group gl v as pqp where the subgroups p and q either fix a subspace or fix a decomposition of v as v 1 v 2 with dim v 1 dim v 2

regression calibration in semiparametric accelerated failure time models summary in large cohort studies it often happens that some covariates are expensive to measure and hence only measured on a validation set on the other hand relatively cheap but error prone measurements of the covariates are available for all subjects regression calibration rc estimation method prentice 1982 biometrika 69 331 342 is a popular method for analyzing such data and has been applied to the cox model by wang et al 1997 biometrics 53 131 145 under normal measurement error and rare disease assumptions in this article we consider the rc estimation method for the semiparametric accelerated failure time model with covariates subject to measurement error asymptotic properties of the proposed method are investigated under a two phase sampling scheme for validation data that are selected via stratified random sampling resulting in neither independent nor identically distributed observations we show that the estimates converge to some well defined parameters in particular unbiased estimation is feasible under additive normal measurement error models for normal covariates and under berkson error models the proposed method performs well in finite sample simulation studies we also apply the proposed method to a depression mortality study

additive hazards regression for case cohort studies summary the case cohort design is a common means of reducing cost in large epidemiological cohort studies under this design covariates are measured only on the cases and a subcohort randomly selected from the entire cohort in this paper we demonstrate how to use the case cohort data to estimate the regression parameter of the additive hazards model which specifies that the conditional hazard function given a set of covariates is the sum of an arbitrary baseline hazard function and a regression function of the covariates the proposed estimator is shown to be consistent and asymptotically normal with an easily estimated variance the subcohort may be selected by independent bernoulli sampling with arbitrary selection probabilities or by stratified simple random sampling the efficiencies of various sampling schemes are investigated both analytically and by simulation a real example is provided