semiparametric inference in a model for association in bivanate survival data summary clayton s 1978 model for association in bivariate survival data is both of intrinsic importance and an interesting example of a semiparametric estimation problem that is a problem where inference about a parameter is required in the presence of nuisance functions we derive the asymptotic variance of clayton s estimator obtaining a simple explicit formula for uncensored data and indicating the modification required when the survival times are subject to arbitrary random censorship some comparisons are made with results derived by oakes 1982 for other estimators within this model in the absence of censoring the exact null variance of the score statistic corresponding to clayton s estimator is derived and compared with that of the locally most powerful rank test given by cuzick 1982

estimating treatment effects of longitudinal designs using regression models on propensity scores we derive regression estimators that can compare longitudinal treatments using only the longitudinal propensity scores as regressors these estimators which assume knowledge of the variables used in the treatment assignment are important for reducing the large dimension of covariates for two reasons first if the regression models on the longitudinal propensity scores are correct then our estimators share advantages of correctly specified model based estimators a benefit not shared by estimators based on weights alone second if the models are incorrect the misspecification can be more easily limited through model checking than with models based on the full covariates thus our estimators can also be better when used in place of the regression on the full covariates we use our methods to compare longitudinal treatments for type ii diabetes mellitus

fundamental properties of infinite trees infinite trees naturally arise in the formalization and the study of the semantics of programming languages this paper investigates some of their combinatorial and algebraic properties that are especially relevant to semantics

a semiparametric estimation procedure of dependence parameters in multivariate families of distributions summary this paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions the proposed estimator obtained as a solution of a pseudo likelihood equation is shown to be consistent asymptotically normal and fully efficient at independence a natural estimator of its asymptotic variance is proved to be consistent comparisons are made with alternative semiparametric estimators in the special case of clayton s model for association in bivariate data

on strong normalization and type inference in the intersection type discipline we introduce a new unification procedure for the type inference problem in the intersection type discipline it is well known that type inference in this case should succeed exactly for the strongly normalizing expressions we give a proof for the strong normalization result in the intersection type discipline which we obtain by putting together some well known results and proof techniques our proof uses a variant of klop s extended l calculus for which it is shown that strong normalization is equivalent to weak normalization this is proved here by means of a finiteness of developments theorem obtained following de vrijer s combinatory technique the main property of this extended calculus is uniformity i e weak and strong normalizabilities coincide the strong normalizability result is therefore a consequence of the fact first established by coppo and dezani for the l calculus that typability implies weak normalizability we then show that the unification process which is the basis for type inference exactly corresponds to reduction in the extended l calculus finally we show that our notion of unification allows us to compute a principal typing for any typable l expression

finitary pcf is not decidable the question of the decidability of the observational ordering of finitary pcf was raised jung and stoughton in m bezem j f groote eds typed lambda calculi and applications lecture notes in computer science vol 664 springer berlin 1993 pp 230 244 to give mathematical content to the full abstraction problem for pcf milner theoret comput sci 4 1977 1 22 we show that the ordering is in fact undecidable this result places limits on how explicit a representation of the fully abstract model can be it also gives a slight strengthening of the author s earlier result on typed ability loader in a anderson m zeleny eds church memorial volume kluwer academic press dordrecht to appear copyright 2001 elsevier science b v

adaptation of bivariate frailty models for prediction with application to biological markers as prognostic indicators serial biological markers are often used in medicine as prognostic indicators for example elevated tumour antigen tests presage tumour recurrence rapid decrease in the cd4 cell counts of hiv individuals indicate high risk for developing aids methods for evaluating the usefulness of markers should address how the prediction of future risk is revised in a way that assists the making of decisions at the time such an indicator is observed proportional hazards modelling with time varying covariates a common approach seems unnatural for this purpose because its orientation is explanatory it addresses the question is the individual suffering a failure more likely to have had the marker and allows use of all information prior to the failure rather than the more relevant predictive question does the appearance of the marker alter the individual s subsequent risk enough to warrant intervention today frailty models do address this question but available methods for their analysis make censoring assumptions which are inappropriate in the predictive setting we adapt frailty models to relevant censoring processes and propose a predictively oriented test statistic and a related estimation procedure based on summing concurrent martingales each representing a landmark analysis

bivariate survival models induced by frailties abstract when two observed survival times depend via a proportional hazards model on the same unobserved variable called a frailty this common dependence induces an association between the observed times this article considers the class of bivariate survival distributions that can arise in this way extends it to allow negative association and shows that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter a cross ratio function easily estimated even from censored data is the key to both the characterization results and inferential procedures and diagnostic plots that are introduced and illustrated by real examples the models considered are the natural counterpart for survival data of the latent variable models that have long been used in factor analysis for continuous data or in latent structure analysis for binary data the main distinguishing feature of survival data is the possibility of censoring which makes the standard methods difficu

semiclassical behaviour of expectation values in time evolved lagrangian states for large times we study the behaviour of time evolved quantum mechanical expectation values in lagrangian states in the limit 0 and t we show that it depends strongly on the dynamical properties of the corresponding classical system if the classical system is strongly chaotic i e anosov then the expectation values tend to a universal limit this can be viewed as an analogue of mixing in the classical system if the classical system is integrable then the expectation values need not converge and if they converge their limit depends on the initial state an additional difference occurs in the timescales for which we can prove this behaviour in the chaotic case we get up to ehrenfest time t ln 1 whereas for integrable system we have a much larger time range

a goodness of fit test for association in a bivariate survival model summary we propose a simple test of constant conditional hazard ratio in the clayton model 1978 by comparing the unweighted and weighted concordance estimators of the association parameter if the clayton model holds the difference of these two estimates converges to zero the proposed test is consistent against alternatives under which the two concordance estimators converge to different values we derive an explicit formula for the asymptotic variance and derive the asymptotic distribution of the test statistic under the clayton model then we extend the test statistic to incorporate censoring the proposed test is expected to perform well for a general class of alternatives with monotone conditional hazard ratio we examine the finite sample properties of the test statistic through simulations

complete restrictions of the intersection type discipline abstract in this paper the intersection type discipline as defined in barendregt 1983 is studied we will present two different and independent complete restrictions of the intersection type discipline the first restricted system the strict type assignment system is presented in section 2 its major feature is the absence of the derivation rule and it is based on a set of strict types we will show that these together give rise to a strict filter lambda model that is essentially different from the one presented in barendregt we will show that the strict type assignment system is the nucleus of the full system i e for every derivation in the intersection type discipline there is a derivation in which is used only at the very end finally we will prove that strict type assignment is complete for inference semantics the second restricted system is presented in section 3 its major feature is the absence of the type we will show that this system gives rise to a filter i model and that type assignment without is complete for the i calculus finally we will prove that a lambda term is typeable in this system if and only if it is strongly normalizable

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

a bayesian view of doubly robust causal inference in causal inference the effect of confounding may be controlled using regression adjustment in an outcome model propensity score adjustment inverse probability of treatment weighting or a combination of these approaches based on modelling the treatment assignment mechanism along with their doubly robust extensions have been difficult to motivate using formal likelihood based or bayesian arguments as the treatment assignment model plays no part in inferences concerning the expected outcomes on the other hand forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness in this paper we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood based arguments as an alternative to bayesian propensity score analysis we propose a bayesian posterior predictive method for constructing doubly robust estimation procedures by incorporating the inverse treatment assignment probabilities as importance sampling weights in monte carlo integration

estimators and confidence intervals for the marginal odds ratio using logistic regression and propensity score stratification propensity score methods are widely used to estimate treatment or exposure effects in observational studies in studies with binary response the effect can be described as an odds ratio and the mantel haenszel estimator is traditionally used for stratified data although propensity score methods are designed for marginal treatment effects it has been shown that the mantel haenszel estimator stratified for propensity score is a questionable estimator for the marginal odds ratio which describes the change in odds of response if everybody versus nobody were treated we studied recently proposed alternative estimators for the marginal odds ratio one stratified for propensity score the other derived from logistic regression additionally we adapted the methodology of the logistic regression based estimator for the derivation of a marginal odds ratio estimator to covariate adjustment by the propensity score we also derived corresponding variance estimators using the delta method the estimators were illustrated and compared to the inverse probability weighted estimator and the stratified mantel haenszel estimator in a study dealing with respiratory tract infections in children in germany furthermore simulation studies that were carried out to investigate relative bias variance and coverage probability showed reasonable performance of marginal odds ratio estimators if response rates or regression based approaches were used their variances were accurately estimated in contrast the stratified mantel haenszel estimator was substantially biased in some situations due to problems of non collapsibility and thus it is generally inappropriate for a reliable estimation of the marginal odds ratio

estimation of the causal effect of a time varying exposure on the marginal mean of a repeated binary outcome abstract we provide sufficient conditions for estimating from longitudinal data the causal effect of a time dependent exposure or treatment on the marginal probability of response for a dichotomous outcome we then show how one can estimate this effect under these conditions using the g computation algorithm of robins we also derive the conditions under which some current approaches to the analysis of longitudinal data such as the generalized estimating equations gee approach of zeger and liang the feedback model techniques of liang and zeger and within subject conditional methods can provide valid tests and estimates of causal effects we use our methods to estimate the causal effect of maternal stress on the marginal probability of a child s illness from the mothers stress and children s morbidity data and compare our results with those previously obtained by zeger and liang using a gee approach

stratification and weighting via the propensity score in estimation of causal treatment effects a comparative study estimation of treatment effects with causal interpretation from observational data is complicated because exposure to treatment may be confounded with subject characteristics the propensity score the probability of treatment exposure conditional on covariates is the basis for two approaches to adjusting for confounding methods based on stratification of observations by quantiles of estimated propensity scores and methods based on weighting observations by the inverse of estimated propensity scores we review popular versions of these approaches and related methods offering improved precision describe theoretical properties and highlight their implications for practice and present extensive comparisons of performance that provide guidance for practical use

dependent competing risks and summary survival curves summary in many contexts where there is interest in inferring the marginal distribution of a survival time t subject to censoring embodied in a latent waiting time c the times t and c may not be independent this paper presents a new class of nonparametric assumptions on the conditional distribution of t given c and shows how they lead to consistent generalizations of the kaplan meier 1958 survival curve estimator the new survival curve estimators are used under weak assumptions to construct bounds on the marginal survival which can be much narrower than those of peterson 1976 in stratified populations where t and c are independent only within strata examples indicate that the kaplan meier estimator is often approximately consistent

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

inferences on the association parameter in copula models for bivariate survival data we investigate two stage parametric and two stage semi parametric estimation procedures for the association parameter in copula models for bivariate survival data where censoring in either or both components is allowed we derive asymptotic properties of the estimators and compare their performance by simulations both parametric and semi parametric estimators of the association parameter are efficient at independence and the parameter estimates in the margins have high efficiency and are robust to misspecification of dependency structures in addition we propose a consistent variance estimator for the semi parametric estimator of the association parameter we apply the proposed methods to an aids data set for illustration

on semi competing risks data summary we consider a variation of the competing risks problem in which a terminal event censors a non terminal event but not vice versa the joint distribution of the events is formulated via a gamma frailty model in the upper wedge where data are observable day et al 1997 with the marginal distributions unspecified an estimator for the association parameter is obtained from a concordance estimating function a novel plug in estimator for the marginal distribution of the non terminal event is shown to be uniformly consistent and to converge weakly to a gaussian process the assumptions on the joint distribution outside the upper wedge are weaker than those usually made in competing risks analyses simulations demonstrate that the methods work well with practical sample sizes the proposals are illustrated with data on morbidity and mortality in leukaemia patients

variance estimation for stratified propensity score estimators propensity score methods are increasingly used to estimate the effect of a treatment or exposure on an outcome in non randomised studies we focus on one such method stratification on the propensity score comparing it with the method of inverse probability weighting by the propensity score the propensity score the conditional probability of receiving the treatment given observed covariates is usually an unknown probability estimated from the data estimators for the variance of treatment effect estimates typically used in practice however do not take into account that the propensity score itself has been estimated from the data by deriving the asymptotic marginal variance of the stratified estimate of treatment effect correctly taking into account the estimation of the propensity score we show that routinely used variance estimators are likely to produce confidence intervals that are too conservative when the propensity score model includes variables that predict cause the outcome but only weakly predict the treatment in contrast a comparison with the analogous marginal variance for the inverse probability weighted ipw estimator shows that routinely used variance estimators for the ipw estimator are likely to produce confidence intervals that are almost always too conservative because exact calculation of the asymptotic marginal variance is likely to be complex particularly for the stratified estimator we suggest that bootstrap estimates of variance should be used in practice

a syntactic approach to type soundness we present a new approach to proving type soundness for hindley milner style polymorphic type systems the keys to our approach are 1 an adaptation of subject reduction theorems from combinatory logic to programming languages and 2 the use of rewriting techniques for the specification of the language semantics the approach easily extends from polymorphic functional languages to imperative languages that provide references exceptions continuations and similar features we illustrate the technique with a type soundness theorem for the core of standard ml which includes the first type soundness proof for polymorphic exceptions and continuations

an automata theoretic approach to branching time model checking translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear time model checking and for obtaining many extensions and improvements to this verification method on the other hand for branching temporal logic automata theoretic techniques have long been thought to introduce an exponential penalty making them essentially useless for model checking recently bernholtz and grumberg 1993 have shown that this exponential penalty can be avoided though they did not match the linear complexity of non automata theoretic algorithms in this paper we show that alternating tree automata are the key to a comprehensive automata theoretic framework for branching temporal logics not only can they be used to obtain optimal decision procedures as was shown by muller et al but as we show here they also make it possible to derive optimal model checking algorithms moreover the simple combinatorial structure that emerges from the automata theoretic approach opens up new possibilities for the implementation of branching time model checking and has enabled us to derive improved space complexity bounds for this long standing problem

the role of the propensity score in estimating dose response functions summary estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large standard covariance adjustment methods are often inadequate rosenbaum rubin 1983 propose an alternative method for adjusting for pre treatment variables for the binary treatment case based on the so called propensity score here an extension of the propensity score methodology is proposed that allows for estimation of average casual effects with multi valued treatments estimation of average treatment effects in observational studies often requires adjustment for differences in pre treatment variables if the number of pre treatment variables is large and their distribution varies substantially with treatment status standard adjustment methods such as covari ance adjustment are often inadequate rosenbaum rubin 1983 1984 propose an alternative method for adjusting for pre treatment variables based on the propensity score the conditional probability of receiving the treatment given pre treatment variables they demonstrate that adjusting solely for the propensity score removes all bias associated with differences in the pre treatment variables the rosenbaum rubin proposals deal exclusively with binary valued treat ments in many cases of interest however treatments take on more than two values here an extension of the propensity score methodology is proposed that allows for estimation of average causal effects with multi valued treatments the key insight is that for estimation of average causal effects it is not necessary to divide the population into subpopulations where causal comparisons are valid as the propensity score does it is sufficient to divide the population into subpopulations where average potential outcomes can be estimated

estimates of marginal survival for dependent competing risks based on an assumed copula summary when time to death and time to censoring are associated one may be appreciably misled when the marginal survival functions are estimated using the product limit estimators which assume independent censoring if no assumption about the relationship between the two times is made the marginal survival functions are not identifiable a natural function that defines the association between the two random variables is the copula we show that if this function is known then the competing risks data are sufficient to identify the marginal survival functions and construct a suitable estimator this estimator is consistent and reduces to the kaplan meier estimator when death and censoring times are independent this statistic can be used to provide bounds on the marginal survival functions based on a range of possible associations between the competing risks

stability of wave packet dynamics under perturbations we introduce a method to investigate the stability of wave packet dynamics under perturbations of the hamiltonian our approach relies on semiclassical approximations but is nonperturbative two separate contributions to the quantum fidelity are identified one factor derives from the dispersion of the wave packets whereas the other factor is determined by the separation of a trajectory of the perturbed classical system away from a corresponding unperturbed trajectory we furthermore estimate both contributions in terms of classical lyapunov exponents and find a decay of fidelity that is generically at least exponential but may also be doubly exponential the latter case is shown to be realized for inverted harmonic oscillators

a simple proof of a theorem of statman abstract in this note we reprove a theorem of statman that deciding the equality of two first order typable terms is not elementary recursive statman 1982 the basic idea of our proof like that of statman s is the henkin quantifier elimination procedure henkin 1963 however our coding is much simpler and easy to understand

regression analysis based on semicompeting risks data summary semicompeting risks data are commonly seen in biomedical applications in which a terminal event censors a non terminal event possible dependent censoring complicates statistical analysis we consider regression analysis based on a non terminal event say disease progression which is subject to censoring by death the methodology proposed is developed for discrete covariates under two types of assumption first separate copula models are assumed for each covariate group and then a flexible regression model is imposed on the progression time which is of major interest model checking procedures are also proposed to help to choose a best fitted model under a two sample setting lin and co workers proposed a competing method which requires an additional marginal assumption on the terminal event and implicitly assumes that the dependence structures in the two groups are the same using simulations we compare the two approaches on the basis of their finite sample performances and robustness properties under model misspecification the method proposed is applied to a bone marrow transplant data set

an alternative approach to confidence interval estimation for the win ratio statistic summary pocock et al 2012 european heart journal 33 176 182 proposed a win ratio approach to analyzing composite endpoints comprised of outcomes with different clinical priorities in this article we establish a statistical framework for this approach we derive the null hypothesis and propose a closed form variance estimator for the win ratio statistic in all pairwise matching situation our simulation study shows that the proposed variance estimator performs well regardless of the magnitude of treatment effect size and the type of the joint distribution of the outcomes

stratification for the propensity score compared with linear regression techniques to assess the effect of treatment or exposure stratifying and matching by the propensity score are increasingly popular approaches to deal with confounding in medical studies investigating effects of a treatment or exposure a more traditional alternative technique is the direct adjustment for confounding in regression models this paper discusses fundamental differences between the two approaches with a focus on linear regression and propensity score stratification and identifies points to be considered for an adequate comparison the treatment estimators are examined for unbiasedness and efficiency this is illustrated in an application to real data and supplemented by an investigation on properties of the estimators for a range of underlying linear models we demonstrate that in specific circumstances the propensity score estimator is identical to the effect estimated from a full linear model even if it is built on coarser covariate strata than the linear model as a consequence the coarsening property of the propensity score adjustment for a one dimensional confounder instead of a high dimensional covariate may be viewed as a way to implement a pre specified richly parametrized linear model we conclude that the propensity score estimator inherits the potential for overfitting and that care should be taken to restrict covariates to those relevant for outcome

the central role of the propensity score in observational studies for causal effects abstract the results of observational studies are often disputed because of nonrandom treatment assignment for example patients at greater risk may be overrepresented in some treatment group this paper discusses the central role of propensity scores and balancing scores in the analysis of observational studies the propensity score is the estimated conditional probability of assignment to a particular treatment given a vector of observed covariates both large and small sample theory show that adjustment for the scalar propensity score is sufficient to remove bias due to all observed covariates applications include matched sampling on the univariate propensity score which is equal percent bias reducing under more general conditions than required for discriminant matching multivariate adjustment by subclassification on balancing scores where the same subclasses are used to estimate treatment effects for all outcome variables and in all subpopulations and visual representation of multivariate adjustment by a two dimensional plot author

semiparametric regression for repeated outcomes with nonignorable nonresponse abstract we consider inference about the parameter indexing the conditional mean of a vector of correlated outcomes given a vector of explanatory variables when some of the outcomes are missing in a subsample of the study and the probability of response depends on both observed and unobserved data values that is nonresponse is nonignorable we propose a class of augmented inverse probability of response weighted estimators that are consistent and asymptotically normal can for estimating when the response probabilities can be parametrically modeled and a can estimator exists the proposed estimators do not require full specification of a parametric likelihood and their computation does not require numerical integration our estimators can be viewed as an extension of generalized estimating equation estimators that allows for nonignorable nonresponse we show that our class essentially consists of all can estimators of we also show that the asymptotic variance of the optimal estimator in our

model checking higher order programs we propose a novel verification method for higher order functional programs based on higher order model checking or more precisely model checking of higher order recursion schemes recursion schemes for short the most distinguishing feature of our verification method for higher order programs is that it is sound complete and automatic for the simply typed calculus with recursion and finite base types and for various program verification problems such as reachability flow analysis and resource usage verification we first show that a variety of program verification problems can be reduced to model checking problems for recursion schemes by transforming a program into a recursion scheme that generates a tree representing all the interesting possible event sequences of the program we then develop a new type based model checking algorithm for recursion schemes and implement a prototype recursion scheme model checker to our knowledge this is the first implementation of a recursion scheme model checker experiments show that our model checker is reasonably fast despite the worst case time complexity of recursion scheme model checking being hyperexponential in general altogether the results provide a new promising approach to verification of higher order functional programs

a weibull model for dependent censoring a bivariate weibull model is proposed for censored survival data when there may be dependence between the survival and censoring random variables the model is based on marginal transformations of the pickands class of bivariate exponential distributions assuming the model to hold the joint distribution of survival and censoring times is shown to be identifiable and the maximum likelihood estimator of the parameters is shown to be consistent

the io and oi hierarchies abstract an analysis of recursive procedures in algol 68 with finite modes shows that a denotational semantics of this language can be described on the level of program schemes using a typed calculus with fixed point operators in the first part of this paper we derive classical schematological theorems for the resulting class of level n schemes in part two we investigate the language families obtained by call by value and call by name interpretation of level n schemes over the algebra of formal languages it is proved that differentiating according to the functional level of recursion leads to two infinite hierarchies of recursive languages the io and oi hierarchies which can be characterized as canonical extensions of the regular context free and io and oi macro languages respectively sufficient conditions are derived to establish strictness of io like hierarchies finally we derive that recursion on higher types induces an infinite hierarchy of control structures by proving that level n schemes are strictly less powerful than level n 1 schemes

principal type schemes for an extended type theory we consider the extension of curry s basic functionality theory presented by barendregt et al to appear and we define for any term x a principal type scheme p t s we prove that all and the only type schemes deducible for x can be obtained from the p t s of x by suitable operations

principality and type inference for intersection types using expansion variables principality of typings is the property that for each typable term there is a typing from which all other typings are obtained via some set of operations type inference is the problem of finding a typing for a given term if possible we define an intersection type system which has principal typings and types exactly the strongly normalizable terms more interestingly every finite rank restriction of this system using leivant s first notion of rank has principal typings and also has decidable type inference this is in contrast to system f where the finite rank restriction for every finite rank at 3 and above has neither principal typings nor decidable type inference furthermore the notion of principal typings for our system involves only one operation substitution rather than several operations not all substitution based as in earlier presentations of principality for intersection types without rank restrictions in our system the earlier notion of expansion is integrated in the form of expansion variables which are subject to substitution as are ordinary variables a unification based type inference algorithm is presented using a new form of unification unification

a model for association in bivariate survival data summary a reparameterization of a model introduced by d g clayton for association in bivariate life tables is discussed inference for the parameter governing the association is con sidered when the marginal distributions are specified up to lehmann alternatives the information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters the likelihood proposed by clayton for the case that the marginal distributions are completely unknown is criticized an alternative non parametric estimator based on kendall s coefficient of concordance is proposed and its asymptotic variance evaluated if g s pr s s and h t pr t t are continuous univariate survivor functions with g o h o 1 and 0 1 then the function f s t pr s s t t given by f s t g h 1 1 is a bivariate survivor function with g and h as marginals this paper considers inference about the parameter 0 governing the association between s and t given a sample of size n from their bivariate distribution we suppose first that the marginals g s and h t are known up to lehmann alternatives and secondly that they are completely unknown the model 1 is a reparameterization of a model introduced by clayton 1978 for association in bivariate life tables section 2 describes some properties of the family including the limits as 0 1 and 0 oo a simple interpretation of 0 in terms of hazard functions and a random effects derivation of the model this section leans heavily on clayton s work section 3 discusses parametric inference for 0 including tests of the hypothesis 0 1 of independence between s and t we assume that the marginal survivor functions g s and h t are specified up to lehmann alternatives asymptotic variance formulae are derived in section 4 which also explores the extent to which the parameterization achieves orthogonality clayton 1978 proposed an ingenious method for estimating 0 in the absence of knowledge of the marginal distributions unfortunately there are difficulties with his proposed con ditional likelihood function in particular the estimated variance from the second derivative appears to be incorrect clayton s derivation is described and criticized in our section 5 in principle rank invariance properties of 1 when g s and h t are completely unknown yield a marginal likelihood for 0 although this likelihood appears to be intractable in general in section 6 it is evaluated when n 3 and shown to differ from clayton s likelihood a simpler non parametric estimator of 0 based on the coefficient of concordance is proposed in section

reducing bias in observational studies using subclassification on the propensity score abstract the propensity score is the conditional probability of assignment to a particular treatment given a vector of observed covariates previous theoretical arguments have shown that subclassification on the propensity score will balance all observed covariates subclassification on an estimated propensity score is illustrated using observational data on treatments for coronary artery disease five subclasses defined by the estimated propensity score are constructed that balance 74 covariates and thereby provide estimates of treatment effects using direct adjustment these subclasses are applied within sub populations and model based adjustments are then used to provide estimates of treatment effects within these sub populations two appendixes address theoretical issues related to the application the effectiveness of subclassification on the propensity score in removing bias and balancing properties of propensity scores with incomplete data

estimating parsimonious models of longitudinal causal effects using regressions on propensity scores parsimony is important for the interpretation of causal effect estimates of longitudinal treatments on subsequent outcomes one method for parsimonious estimates fits marginal structural models by using inverse propensity scores as weights this method leads to generally large variability that is uncommon in more likelihood based approaches a more recent method fits these models by using simulations from a fitted g computation but requires the modeling of high dimensional longitudinal relations that are highly susceptible to misspecification we propose a new method that first uses longitudinal propensity scores as regressors to reduce the dimension of the problem and then uses the approximate likelihood for the first estimates to fit parsimonious models we demonstrate the methods by estimating the effect of anticoagulant therapy on survival for cancer and non cancer patients who have inferior vena cava filters

a simple nonparametric estimator of the bivariate survival function under univariate censoring summary in the presence of univariate censoring the bivariate survival function of paired failure times can be expressed as the ratio of the bivariate at risk probability to the survival function of the censoring time the use of this natural representation yields a very simple nonparametric estimator for the bivariate survival curve the estimator is strongly consistent and upon proper normalization converges weakly to a zero mean gaussian process with an easily estimated covariance function numerical studies demonstrate that both the survival curve estimator and its covariance function estimator perform markedly well for practical sample sizes applications to the correlation problem and to the interval estimation of the difference in median survival times are also studied

semiparametric model for bivariate survival data subject to biased sampling to better understand the relationship between patient characteristics and their residual survival after an intermediate event such as the local cancer recurrence it is of interest to identify patients with the intermediate event and then analyze their residual survival data one challenge in analyzing such data is that the observed residual survival times tend to be longer than those in the target population since patients who die before experiencing the intermediate event are excluded from the identified cohort we propose to jointly model the ordered bivariate survival data using a copula model and appropriately adjusting for the sampling bias we develop an estimating procedure to simultaneously estimate the parameters for the marginal survival functions and the association parameter in the copula model and use a two stage expectation maximization algorithm using empirical process theory we prove that the estimators have strong consistency and asymptotic normality we conduct simulations studies to evaluate the finite sample performance of the proposed method we apply the proposed method to two cohort studies to evaluate the association between patient characteristics and residual survival

semiparametric regression analysis of interval censored data with informative dropout interval censored data arise when the event time of interest can only be ascertained through periodic examinations in medical studies subjects may not complete the examination schedule for reasons related to the event of interest in this article we develop a semiparametric approach to adjust for such informative dropout in regression analysis of interval censored data specifically we propose a broad class of joint models under which the event time of interest follows a transformation model with a random effect and the dropout time follows a different transformation model but with the same random effect we consider nonparametric maximum likelihood estimation and develop an em algorithm that involves simple and stable calculations we prove that the resulting estimators of the regression parameters are consistent asymptotically normal and asymptotically efficient with a covariance matrix that can be consistently estimated through profile likelihood in addition we show how to consistently estimate the survival function when dropout represents voluntary withdrawal and the cumulative incidence function when dropout is an unavoidable terminal event furthermore we assess the performance of the proposed numerical and inferential procedures through extensive simulation studies finally we provide an application to data on the incidence of diabetes from a major epidemiological cohort study

quantile regression adjusting for dependent censoring from semicompeting risks in this work we study quantile regression when the response is an event time subject to potentially dependent censoring we consider the semi competing risks setting where time to censoring remains observable after the occurrence of the event of interest while such a scenario frequently arises in biomedical studies most of current quantile regression methods for censored data are not applicable because they generally require the censoring time and the event time be independent by imposing rather mild assumptions on the association structure between the time to event response and the censoring time variable we propose quantile regression procedures which allow us to garner a comprehensive view of the covariate effects on the event time outcome as well as to examine the informativeness of censoring an efficient and stable algorithm is provided for implementing the new method we establish the asymptotic properties of the resulting estimators including uniform consistency and weak convergence the theoretical development may serve as a useful template for addressing estimating settings that involve stochastic integrals extensive simulation studies suggest that the proposed method performs well with moderate sample sizes we illustrate the practical utility of our proposals through an application to a bone marrow transplant trial

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