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

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

a proportional hazards model for interval censored failure time data this paper develops a method for fitting the proportional hazards regression model when the data contain left right or interval censored observations results given for testing the hypothesis of a zero regression coefficient lead to a generalization of the log rank test for comparison of several survival curves the method is used to analyze data from an animal tumorigenicity study and also a clinical trial

a semiparametric regression cure model with current status data summary this paper considers the analysis of current status data with a cured proportion in the population using a mixture model that combines a logistic regression formulation for the probability of cure with a semiparametric regression model for the time to occurrence of the event the semiparametric regression model belongs to the flexible class of partly linear models that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable a sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed under some mild conditions the estimators are shown to be strongly consistent the convergence rate of the estimator for the unknown smooth function is obtained and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method and the model is fitted to a dataset from a study of calcification of the hydrogel intraocular lenses a complication of cataract treatment

semiparametric analysis of zero inflated count data medical and public health research often involve the analysis of count data that exhibit a substantially large proportion of zeros such as the number of heart attacks and the number of days of missed primary activities in a given period a zero inflated poisson regression model which hypothesizes a two point heterogeneity in the population characterized by a binary random effect is generally used to model such data subjects are broadly categorized into the low risk group leading to structural zero counts and high risk or normal group so that the counts can be modeled by a poisson regression model the main aim is to identify the explanatory variables that have significant effects on i the probability that the subject is from the low risk group by means of a logistic regression formulation and ii the magnitude of the counts given that the subject is from the high risk group by means of a poisson regression where the effects of the covariates are assumed to be linearly related to the natural logarithm of the mean of the counts in this article we consider a semiparametric zero inflated poisson regression model that postulates a possibly nonlinear relationship between the natural logarithm of the mean of the counts and a particular covariate a sieve maximum likelihood estimation method is proposed asymptotic properties of the proposed sieve maximum likelihood estimators are discussed under some mild conditions the estimators are shown to be asymptotically efficient and normally distributed simulation studies were carried out to investigate the performance of the proposed method for illustration purpose the method is applied to a data set from a public health survey conducted in indonesia where the variable of interest is the number of days of missed primary activities due to illness in a 4 week period

partially monotone tensor spline estimation of the joint distribution function with bivariate current status data the analysis of the joint cumulative distribution function cdf with bivariate event time data is a challenging problem both theoretically and numerically this paper develops a tensor spline based sieve maximum likelihood estimation method to estimate the joint cdf with bivariate current status data the i splines are used to approximate the joint cdf in order to simplify the numerical computation of a constrained maximum likelihood estimation problem the generalized gradient projection algorithm is used to compute the constrained optimization problem based on the properties of b spline basis functions it is shown that the proposed tensor spline based nonparametric sieve maximum likelihood estimator is consistent with a rate of convergence potentially better than n 1 3 under some mild regularity conditions the simulation studies with moderate sample sizes are carried out to demonstrate that the finite sample performance of the proposed estimator is generally satisfactory

regression analysis for current status data using the em algorithm we propose new expectation maximization algorithms to analyze current status data under two popular semiparametric regression models the proportional hazards ph model and the proportional odds po model monotone splines are used to model the baseline cumulative hazard function in the ph model and the baseline odds function in the po model the proposed algorithms are derived by exploiting a data augmentation based on poisson latent variables unlike previous regression work with current status data our ph and po model fitting methods are fast flexible easy to implement and provide variance estimates in closed form these techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy copyright 2013 john wiley sons ltd

linear regression with current status data abstract in survival analysis a linear model often provides an adequate approximation after a suitable transformation of the survival times and possibly of the covariates this article proposes a semiparametric regression method for estimating the regression parameter in the linear model without specifying the distribution of the random error where the response variable is subject to so called case 1 interval censoring the method uses a constructed random sieve likelihood and constraints combining the benefits of semiparametric likelihood with estimating equations the estimation procedure is implemented and the asymptotic distributions for the estimated regression parameter and for the profile likelihood ratio statistic are obtained in addition some model diagnostics aspects are described finally the small sample operating characteristics of the proposed method is examined via simulations and its usefulness is illustrated on datasets from an animal tumorigenicity study and from a hiv study

asymptotics of likelihood ratio derivative estimators in simulations of highly reliable markovian systems we discuss the estimation of derivatives of a performance measure using the likelihood ratio method in simulations of highly reliable markovian systems we compare the difficulties of estimating the performance measure and of estimating its partial derivatives with respect to component failure rates as the component failure rates tend to 0 and the component repair rates remain fixed we first consider the case when the quantities are estimated using naive simulation i e when no variance reduction technique is used in particular we prove that in the limit some of the partial derivatives can be estimated as accurately as the performance measure itself this result is of particular interest in light of the somewhat pessimistic empirical results others have obtained when applying the likelihood ratio method to other types of systems however the result only holds for certain partial derivatives of the performance measure when using naive simulation more specifically we can estimate a certain partial

semi parametric accelerated failure time regression analysis with application to interval censored hiv aids data this paper demonstrates a way to investigate a potentially non linear relationship between an interval censored response variable and a continuously distributed explanatory variable a potentially non linear effect of a continuous explanatory variable on the response is incorporated into an accelerated failure time model forming a partial linear model a sieve maximum likelihood estimator mle is suggested to simultaneously estimate all the parameters the sieve mle is shown to be asymptotically efficient and normally distributed simulation studies show that the proposed estimators for the scale and regression parameters are robust and efficient and the estimator for the non linear function is able to capture the shape of a variety of smooth non linear functions the model is applied to observational hiv data where the response variable is the time to suppression of hiv viral load after initiation of antiretroviral therapy and baseline viral load is investigated as a potentially non linear effect

semiparametric estimation methods for panel count data using monotone b splines we study semiparametric likelihood based methods for panel count data with proportional mean model e t z 0 t exp 0tz where z is a vector of covariates and 0 t is the baseline mean function we propose to estimate 0 t and 0 jointly with 0 t approximated by monotone b splines and to compute the estimators using generalized rosen algorithm proposed by jamshidian 2004 we show that the proposed spline based likelihood estimators of 0 t are consistent with a possibly better than n1 3 convergence rate if 0 t is sufficiently smooth the normality of the estimators of 0 is also established comparisons between the proposed estimators and their alternatives studied in wellner and zhang 2007 are made through simulations studies regarding their finite sample performance and computational complexity a real example from a bladder tumor clinical trial is used to illustrate the methods

the profile sampler we consider frequentist inference for the parametric component separately from the nuisance parameter in semiparametric models based on sampling from the posterior of the profile likelihood we prove that this procedure gives a first order correct approximation to the maximum likelihood estimator and consistent estimation of the efficient fisher information for without computing derivatives or using complicated numerical approximations an exact bayesian interpretation is established under a certain data dependent prior the sampler is useful in particular when the nuisance parameter is not estimable at the rate where neither bootstrap validity nor general automatic variance estimation has been theoretically justified even when the nuisance parameter is consistent and the bootstrap is known to be valid the proposed markov chain monte carlo procedure can yield computational savings because maximization of the likelihood is not required the theory is verified for three examples the methods are

inference based on imputed failure times for the proportional hazards model with interval censored data abstract we propose an approach to the proportional hazards model for interval censored data in which parameter estimates are obtained by solving estimating equations that are the partial likelihood score equations for the full data proportional hazards model averaged over all rankings of imputed failure times consistent with the observed censoring intervals imputed failure times are generated using a parametric estimate of the baseline distribution the parameters of the baseline distribution are estimated simultaneously with the proportional hazards regression parameters although a parametric form for the baseline distribution must be specified simulation studies show that the method performs well even when the baseline distribution is misspecified the estimating equations are solved using monte carlo techniques we present a recursive stochastic approximation scheme that converges to the zero of the estimating equations the solution has a random error that is asymptotically normally distributed w

semiparametric regression analysis of length biased interval censored data in prevalent cohort design subjects who have experienced an initial event but not the failure event are preferentially enrolled and the observed failure times are often length biased moreover the prospective follow up may not be continuously monitored and failure times are subject to interval censoring we study the nonparametric maximum likelihood estimation for the proportional hazards model with length biased interval censored data direct maximization of likelihood function is intractable thus we develop a computationally simple and stable expectation maximization algorithm through introducing two layers of data augmentation we establish the strong consistency asymptotic normality and efficiency of the proposed estimator and provide an inferential procedure through profile likelihood we assess the performance of the proposed methods through extensive simulations and apply the proposed methods to the massachusetts health care panel study

assessing age at onset risk factors with incomplete covariate current status data under proportional odds models motivated by an epidemiological survey of fracture in elderly women we develop a semiparametric regression analysis of current status data with incompletely observed covariate under the proportional odds model to accommodate both the interval censored nature of current status failure time data and the incompletely observed covariate data we propose an analysis based on the validation likelihood vl which is derived from likelihood pertaining to the validation sample namely the subset of the sample where the data are completely observed the missing data mechanism is assumed to be missing at random and is explicitly modeled and estimated in the vl approach we propose implementing the vl method by integrating self consistency and newton raphson algorithms asymptotic normality and standard error estimation for the proposed estimator of the regression parameter are guaranteed simulation results reveal good performance of the vl estimator the vl method has some gain in efficiency compared with the naive complete case method but the vl method leads to unbiased estimators whereas the complete case method does not when missing covariates are not missing completely at random application of the vl approach to the fracture data confirms that osteoporosis low bone density is a strong risk factor for the age at onset of fracture in elderly women copyright 2012 john wiley sons ltd

importance sampling for stochastic simulations importance sampling is one of the classical variance reduction techniques for increasing the efficiency of monte carlo algorithms for estimating integrals the basic idea is to replace the original random mechanism in the simulation by a new one and at the same time modify the function being integrated in this paper the idea is extended to problems arising in the simulation of stochastic systems discrete time markov chains continuous time markov chains and generalized semi markov processes are covered applications are given to a gi g 1 queueing problem and response surface estimation computation of the theoretical moments arising in importance sampling is discussed and some numerical examples given

hellinger consistency of certain nonparametric maximum likelihood estimators consider a class mathscr p p theta theta in theta of probability measures on a measurable space mathscr x mathscr a dominated by a sigma finite measure mu let f theta dp theta d mu theta in theta and let theta n be a maximum likelihood estimator based on n independent observations from p theta 0 theta 0 in theta we use results from empirical process theory to obtain convergence for the hellinger distance h f hat theta n f theta 0 under certain entropy conditions on the class of densities f theta theta in theta the examples we present are a model with interval censored observations smooth densities monotone densities and convolution models in most examples the convexity of the class of densities is of special importance

penalized log likelihood estimation for partly linear transformation models with current status data we consider partly linear transformation models applied to current status data the unknown quantities are the transformation function a linear regression parameter and a nonparametric regression effect it is shown that the penalized mle for the regression parameter is asymptotically normal and efficient and converges at the parametric rate although the penalized mle for the transformation function and nonparametric regression effect are only n 1 3 consistent inference for the regression parameter based on a block jack knife is investigated we also study computational issues and demonstrate the proposed methodology with a simulation study the transformation models and partly linear regression terms coupled with new estimation and inference techniques provide flexible alternatives to the cox model for current status data analysis

variance estimation of a survival function for interval censored survival data interval censored survival data often occur in medical studies especially in clinical trials in this case many authors have considered estimation of a survival function there is however relatively little discussion on estimating the variance of estimated survival functions for right censored data a special case of interval censored data the most commonly used method for variance estimation is to use the greenwood formula in this paper we propose a generalization of the greenwood formula for variance estimation of a survival function based on interval censored data also a simple bootstrap approach is presented the two methods are evaluated and compared using simulation studies and a real data set the simulation results suggest that the methods work well

computationally simple accelerated failure time regression for interval censored data summary an approach is presented for fitting the accelerated failure time model to interval censored data that does not involve computing the nonparametric maximum likelihood estimate of the distribution function at the residuals the approach involves estimating equations computed with the examination times from the same individual treated as if they had actually been obtained from different individuals the dependence between different measurements obtained from the same individual is then accounted for in the calculation of the standard error of the regression coefficients the approach is applicable to interval censored data in settings in which examinations continue to occur regardless of whether the failure time has occurred simulations are presented to assess the behaviour of the approach and the methodology is illustrated through an application to data from an aids clinical trial

a nonparametric test for panel count data summary panel count data arise when a recurrent event is under investigation and each study subject is observed only at discrete time points in this situation observed data include only the numbers of occurrences of the event of interest between observation time points and no information is available on subjects between their observation time points we propose a nonparametric test for comparing the point processes characterising the recurrent event when only panel count data are available the asymptotic distribution of the test statistic is derived and a simulation study is conducted to evaluate its performance the method is illustrated using data from a medical follow up study

locally efficient estimation with current status data and time dependent covariates abstract in biostatistical applications interest often focuses on the estimation of the distribution of a failure time variable t if one observes only whether or not t exceeds an observed monitoring time c then the data structure is called current status data also known as interval censored data case i we extend the data structure by allowing the presence of a possibly time dependent covariate process which is observed up till the monitoring time c we follow the approach of robins and rotnitzky by modeling the hazard of c conditional on the failure time variable and the covariate process i e the missingness or censoring process under the restriction that the missingness monitoring process satisfies coarsening at random because of the curse of dimensionality no globally efficient nonparametric estimators with a good practical performance at moderate sample sizes exist we introduce an inverse probability of censoring weighted estimator of the distribution and of smooth functionals of this di

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

maximum likelihood estimation for the proportional hazards model with partly interval censored data summary the maximum likelihood estimator mle for the proportional hazards model with partly interval censored data is studied under appropriate regularity conditions the mles of the regression parameter and the cumulative hazard function are shown to be consistent and asymptotically normal two methods to estimate the variance covariance matrix of the mle of the regression parameter are considered based on a generalized missing information principle and on a generalized profile information procedure simulation studies show that both methods work well in terms of the bias and variance for samples of moderate size an example illustrates the methods

a semiparametric pseudolikelihood estimation method for panel count data in this paper we study panel count data with covariates a semiparametric pseudolikelihood estimation method is proposed based on the assumption that given a covariate vector z the underlying counting process is a nonhomogeneous poisson process with the conditional mean function given by e n t z 0 t exp 0 z the proposed estimation method is shown to be robust in the sense that the estimator converges to its true value regardless of whether or not n t is a conditional poisson process given z an iterative numerical algorithm is devised to compute the semiparametric maximum pseudolikelihood estimator of 0 0 the algorithm appears to be attractive especially when 0 is a high dimensional regression parameter some simulation studies are conducted to validate the method finally the method is applied to a real dataset from a bladder tumour study

a local likelihood proportional hazards model for interval censored data we discuss the use of local likelihood methods to fit proportional hazards regression models to right and interval censored data the assumed model allows for an arbitrary smoothed baseline hazard on which a vector of covariates operates in a proportional manner and thus produces an interpretable baseline hazard function along with estimates of global covariate effects for estimation we extend the modified em algorithm suggested by betensky lindsey ryan and wand we illustrate the method with data on times to deterioration of breast cosmeses and hiv 1 infection rates among haemophiliacs

efficient estimation in additive hazards regression with current status data summary current status data arise when the exact timing of an event is unobserved and it is only known at a given point in time whether or not the event has occurred recently lin et al 1998 studied the additive semiparametric hazards model for current status data they showed that the analysis of current status data under the additive hazards model reduces to ordinary cox regression under the assumption that a proportional hazards model may be used to describe the monitoring intensity this analysis does not make efficient use of data and in some cases it may not be appropriate to assume a proportional hazards model for the monitoring times we study the semiparametric hazards model for current status data but make use of the semiparametric efficient score function the suggested approach has the advantages that it is efficient in that it reaches the semiparametric information bound and it does not involve any modelling of the monitoring times

on asymptotically optimal tests under loss of identifiability in semiparametric models we consider tests of hypotheses when the parameters are not identifiable under the null in semiparametric models where regularity conditions for profile likelihood theory fail exponential average tests based on integrated profile likelihood are constructed and shown to be asymptotically optimal under a weighted average power criterion with respect to a prior on the nonidentifiable aspect of the model these results extend existing results for parametric models which involve more restrictive assumptions on the form of the alternative than do our results moreover the proposed tests accommodate models with infinite dimensional nuisance parameters which either may not be identifiable or may not be estimable at the usual parametric rate examples include tests of the presence of a change point in the cox model with current status data and tests of regression parameters in odds rate models with right censored data optimal tests have not previously been studied for these scenarios we study the asymptotic distribution of the proposed tests under the null fixed contiguous alternatives and random contiguous alternatives we also propose a weighted bootstrap procedure for computing the critical values of the test statistics the optimal tests perform well in simulation studies where they may exhibit improved power over alternative tests

on pseudolikelihood inference for semiparametric models with boundary problems consider a semiparametric model indexed by a euclidean parameter of interest and an infinite dimensional nuisance parameter in many applications pseudolikelihood provides a convenient way to infer the parameter of interest where the nuisance parameter is replaced by a consistent estimator the purpose of this paper is to establish the asymptotic behaviour of the pseudolikelihood ratio statistic under semiparametric models in particular we consider testing the hypothesis that the parameter of interest lies on the boundary of its parameter space under regularity conditions we establish the equivalence between the asymptotic distributions of the pseudolikelihood ratio statistic and a likelihood ratio statistic for a normal mean problem with a misspecified covariance matrix this result holds when the nuisance parameter is estimated at a rate slower than the usual rate in parametric models we study three examples in which the asymptotic distributions are shown to be mixtures of chi squared variables we conduct simulation studies to examine the finite sample performance of the pseudolikelihood ratio test

ensemble estimation and variable selection with semiparametric regression models we consider scenarios in which the likelihood function for a semiparametric regression model factors into separate components with an efficient estimator of the regression parameter available for each component an optimal weighted combination of the component estimators named an ensemble estimator may be employed as an overall estimate of the regression parameter and may be fully efficient under uncorrelatedness conditions this approach is useful when the full likelihood function may be difficult to maximize but the components are easy to maximize it covers settings where the nuisance parameter may be estimated at different rates in the component likelihoods as a motivating example we consider proportional hazards regression with prospective doubly censored data in which the likelihood factors into a current status data likelihood and a left truncated right censored data likelihood variable selection is important in such regression modelling but the applicability of existing techniques is unclear in the ensemble approach we propose ensemble variable selection using the least squares approximation technique on the unpenalized ensemble estimator followed by ensemble re estimation under the selected model the resulting estimator has the oracle property such that the set of nonzero parameters is successfully recovered and the semiparametric efficiency bound is achieved for this parameter set simulations show that the proposed method performs well relative to alternative approaches analysis of an aids cohort study illustrates the practical utility of the method

hazard regression with interval censored data in a recent paper kooperberg stone and truong 1995a introduced hazard regression hare in which linear splines and their tensor products are used to estimate the conditional log hazard function based on possibly censored positive response data and one or more covariates model selection is carried out in an adaptive fashion using maximum likelihood estimation of the unknown coefficients rao and wald statistics to carry out stepwise addition and deletion of basis functions and the bayesian information criterion bic to select the final model in the present paper the hare methodology is extended to accommodate interval censored data time dependent covariates and cubic splines the presence of interval censored data means that the log likelihood function may no longer be concave presenting additional numerical challenges the extended methodology is applied to a data set containing both interval censoring and time dependent covariates the new software will be available in a future release of s plus

modelling tumour biology progression relationships in screening trials there has been some recent work in the statistical literature for modelling the relationship between tumour biology properties and tumour progression in screening trials while non parametric methods have been proposed for estimation of the tumour size distribution at which metastatic transition occurs their asymptotic properties have not been studied in addition no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for we develop a unified approach to non parametric and semi parametric analysis of modelling tumour size metastasis data in this article an association between the models considered by previous authors with survival data structures is discussed based on this relationship we develop non parametric testing procedures and semi parametric regression methodology of modelling the effect of size of tumour on the probability at which metastatic transitions occur in two situations asymptotic properties of these estimators are provided the proposed methodology is applied to data from a screening study in lung cancer

semiparametric analysis of incomplete current status outcome data under transformation models summary this work motivated by an osteoporosis survey study considers regression analysis with incompletely observed current status data here the current status data including an examination time and an indicator for whether or not the event of interest has occurred by the examination time is not observed for all subjects instead a surrogate outcome subject to misclassification of the current status is available for all subjects we focus on semiparametric regression under transformation models including the proportional hazards and proportional odds models as special cases under the missing at random mechanism where the missingness of the current status outcome can depend only on the observed surrogate outcome and covariates we propose an approach of validation likelihood based on the likelihood from the validation subsample where the data are fully observed with adjustments of the probability of observing the current status outcome as well as the distribution of the surrogate outcome in the validation subsample we propose an efficient computation algorithm for implementation and derive consistency and asymptotic normality for inference with the proposed estimator the application to the osteoporosis survey data and simulations reveal that the validation likelihood performs well it removes the bias from the complete case analysis discarding subjects with missing data and achieves higher efficiency than the inverse probability weighting analysis

a unified approach to the calculation of information operators in semiparametric models the infinite dimensional information operator for the nuisance parameter plays a key role in semiparametric inference as it is closely related to the regular estimability of the target parameter calculation of information operators has traditionally proceeded in a case by case manner and has often entailed lengthy derivations with complicated arguments we develop a unified framework for this task by exploiting commonality in the form of semiparametric likelihoods the general formula developed allows one to derive information operators with simple calculus and if necessary at all a minimal amount of probabilistic evaluation this streamlined approach shows its simplicity and versatility in application to a number of existing models as well as a new model of practical interest

weighted likelihood estimation under two phase sampling we develop asymptotic theory for weighted likelihood esti mators wle under two phase stratied sampling without replacement we also consider several variants of wle s involving estimated weights and calibration a set of empirical process tools are developed including a glivenko cantelli theorem a theorem for rates of convergence of z estimators and a donsker theorem for the inverse probability weighted em pirical processes under two phase sampling and sampling without replace ment at the second phase using these general results we derive asymptotic distributions of the wle of a nite dimensional parameter in a general semiparametric model where an estimator of a nuisance parameter is es timable either at regular or non regular rates we illustrate these results and methods in the cox model with right censoring and interval censor ing we compare the methods via their asymptotic variances under both sampling without replacement and the more usual and easier to analyze assumption of bernoulli sampling at the second phase ams 2000 subject classications primary 62e20 secondary 62g20 62d99 62n01

additive hazards regression with current status data current status data arise when the only knowledge about the failure time of interest is whether the failure occurs before or after a random monitoring time we propose to analyse such data by the semiparametric additive hazards model which specifies that the hazard function for the failure time associated with a set of possibly time dependent covariates is the sum of an arbitrary baseline hazard function and a regression function of covariates under certain conditions on the monitoring time one can make inferences about the regression parameters of the additive hazards model by using the familiar asymptotic theory and software for the proportional hazards model with right censored data an application to a carcinogenicity experiment is provided

sieve estimation for the proportional odds failure time regression model with interval censoring abstract estimation of the proportional odds failure time regression model with interval censoring is considered conditions that allow for positive information for the regression parameter are discussed the efficient score is characterized by a fredholm equation of the second kind the sieve maximum likelihood estimator for the finite dimensional regression parameter is shown to be asymptotically normal with n convergence rate and to achieve the information bound data analysis and simulations assist in clarifying our thoughts regarding the choice of sieve for finite sample problems

linear regression with interval censored data i occurred in reliability studies destructive tests are often used to find whether an item e g fire extinguisher has failed in rodent bioassay experiments the presence or absence of a tumor may only be detected through sacrifices for certain designs of experiments t are i i d random variables with a i known probability density in general t and z are associated in case 2 ii interval censoring two censoring variables t t are observed with the ii knowledge that y is inside the interval t t in both cases of interval ii i

likelihood ratio sensitivity analysis for markovian models of highly dependable systems this paper discusses the application of the likelihood ratio gradient estimator to simulations of large markovian models of highly dependable systems extensive empirical work as well as some mathematical analysis of small dependability models suggests that in this model setting the gradient estimators are not significantly more noisy than the estimates of the performance measures themselves the paper also discusses implementation issues associated with likelihood ratio gradient estimation as well as some theoretical complements associated with application of the technique to continuous time markov chains

nonparametric estimation for a form of doubly censored data with application to two problems in aids abstract in many epidemiologic studies of human immunodeficiency virus hiv disease interest focuses on the distribution of the length of the interval of time between two events two such problems are considered here estimation of the distribution of time or number of sexual contacts between infection of an individual an index case and transmission of hiv to their sexual partner and estimation of the distribution of time between infectiousness as a blood donor and the development of detectable antibody data regarding these two problems are available from certain partner studies and the hiv lookback study in both cases the statistical development is complicated by the fact that the times of both events are interval censored so that the length of time between the events is never observed exactly nonparametric methods for estimation of the interval length distribution are developed by casting the problem in terms of nonparametric estimation of a mixing distribution particular attention is paid to

on maximum likelihood estimation in infinite dimensional parameter spaces an approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions in this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter we provide conditions under which the rate of convergence can be established this rate is essentially governed by the size of the space of score functions as measured by an entropy index we also show that for a large class of smooth functionals the plug in maximum likelihood estimate is asymptotically efficient that is it achieves the minimal fisher information bound the theory is illustrated by several nonparametric or semiparametric examples

asymptotically self similar global solutions of a general semilinear heat equation we consider the general nonlinear heat equation partial t u delta u a u p 1 1 u g u u 0 varphi on 0 infty times i r n where a in i r p 1 1 2 n and g satisfies certain growth conditions we prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation we also prove that some of those global solutions are asymptotic for large time to self similar solutions of the single power nonlinear heat equation i e with g equiv 0

maximum likelihood estimation for semiparametric transformation models with interval censored data interval censoring arises frequently in clinical epidemiological financial and sociological studies where the event or failure of interest is known only to occur within an interval induced by periodic monitoring we formulate the effects of potentially time dependent covariates on the interval censored failure time through a broad class of semiparametric transformation models that encompasses proportional hazards and proportional odds models we consider nonparametric maximum likelihood estimation for this class of models with an arbitrary number of monitoring times for each subject we devise an em type algorithm that converges stably even in the presence of time dependent covariates and show that the estimators for the regression parameters are consistent asymptotically normal and asymptotically efficient with an easily estimated covariance matrix finally we demonstrate the performance of our procedures through simulation studies and application to an hiv aids study conducted in thailand

a sieve m theorem for bundled parameters in semiparametric models with application to the efficient estimation in a linear model for censored data in many semiparametric models that are parameterized by two types of parameters a euclidean parameter of interest and an infinite dimensional nuisance parameter the two parameters are bundled together i e the nuisance parameter is an unknown function that contains the parameter of interest as part of its argument for example in a linear regression model for censored survival data the unspecified error distribution function involves the regression coefficients motivated by developing an efficient estimating method for the regression parameters we propose a general sieve m theorem for bundled parameters and apply the theorem to deriving the asymptotic theory for the sieve maximum likelihood estimation in the linear regression model for censored survival data the numerical implementation of the proposed estimating method can be achieved through the conventional gradient based search algorithms such as the newton raphson algorithm we show that the proposed estimator is consistent and asymptotically normal and achieves the semiparametric efficiency bound simulation studies demonstrate that the proposed method performs well in practical settings and yields more efficient estimates than existing estimating equation based methods illustration with a real data example is also provided

a semiparametric regression cure model for interval censored data motivated by medical studies in which patients could be cured of disease but the disease event time may be subject to interval censoring we present a semiparametric nonmixture cure model for the regression analysis of interval censored time to event data we develop semiparametric maximum likelihood estimation for the model using the expectation maximization method for interval censored data the maximization step for the baseline function is nonparametric and numerically challenging we develop an efficient and numerically stable algorithm via modern convex optimization techniques yielding a self consistency algorithm for the maximization step we prove the strong consistency of the maximum likelihood estimators under the hellinger distance which is an appropriate metric for the asymptotic property of the estimators for interval censored data we assess the performance of the estimators in a simulation study with small to moderate sample sizes to illustrate the method we also analyze a real dataset

semiparametric probit models with univariate and bivariate current status data summary multivariate current status data are frequently encountered in biomedical and public health studies semiparametric regression models have been extensively studied for univariate current status data but most existing estimation procedures are computationally intensive involving either penalization or smoothing techniques it becomes more challenging for the analysis of multivariate current status data in this article we study the maximum likelihood estimations for univariate and bivariate current status data under the semiparametric probit regression models we present a simple computational procedure combining the expectation maximization algorithm with the pool adjacent violators algorithm for solving the monotone constraint on the baseline function asymptotic properties of the maximum likelihood estimators are investigated including the calculation of the explicit information bound for univariate current status data as well as the asymptotic consistency and convergence rate for bivariate current status data extensive simulation studies showed that the proposed computational procedures performed well under small or moderate sample sizes we demonstrate the estimation procedure with two real data examples in the areas of diabetic and hiv research

case cohort studies with interval censored failure time data the case cohort design has been widely used as a means of cost reduction in assembling or measuring expensive covariates in large cohort studies the existing literature on the case cohort design is mainly focused on right censored data in practice however the failure time is often subject to interval censoring it is known only to fall within some random time interval in this paper we consider the case cohort study design for interval censored failure time and develop a sieve semiparametric likelihood approach for analyzing data from this design under the proportional hazards model we construct the likelihood function using inverse probability weighting and build the sieves with bernstein polynomials the consistency and asymptotic normality of the resulting regression parameter estimator are established and a weighted bootstrap procedure is considered for variance estimation simulations show that the proposed method works well for practical situations and an application to real data is provided

regression analysis of case k interval censored failure time data in the presence of informative censoring summary interval censored failure time data occur in many fields such as demography economics medical research and reliability and many inference procedures on them have been developed sun 2006 chen sun and peace 2012 however most of the existing approaches assume that the mechanism that yields interval censoring is independent of the failure time of interest and it is clear that this may not be true in practice zhang et al 2007 ma hu and sun 2015 in this article we consider regression analysis of case k interval censored failure time data when the censoring mechanism may be related to the failure time of interest for the problem an estimated sieve maximum likelihood approach is proposed for the data arising from the proportional hazards frailty model and for estimation a two step procedure is presented in the addition the asymptotic properties of the proposed estimators of regression parameters are established and an extensive simulation study suggests that the method works well finally we apply the method to a set of real interval censored data that motivated this study

two likelihood based semiparametric estimation methods for panel count data with covariates we consider estimation in a particular semiparametric regression model for the mean of a counting process with panel count data the basic model assumption is that the conditional mean function of the counting process is of the form efn t jzg exp fl t z 0 t where z is a vector of covariates and 0 is the baseline mean function the panel count observation scheme involves observation of the counting processn for an individual at a random number k of random time points both the number and the locations of these time points may difier across individuals we study semiparametric maximum pseudo likelihood and maximum likelihood estimators of the unknown parameters fl0 0 derived on the basis of a nonhomogeneous poisson process assumption the pseudo likelihood estimator is fairly easy to compute while the maximum likelihood estimator poses more challenges from the computational perspective we study asymptotic properties of both estimators assuming that the proportional mean model holds but dropping the poisson process assumption used to derive the estimators in particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses the results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process

semiparametric bayes proportional odds models for current status data with underreporting current status data are a type of interval censored event time data in which all the individuals are either left or right censored for example our motivation is drawn from a cross sectional study which measured whether or not fibroid onset had occurred by the age of an ultrasound exam for each woman we propose a semiparametric bayesian proportional odds model in which the baseline event time distribution is estimated nonparametrically by using adaptive monotone splines in a logistic regression model and the potential risk factors are included in the parametric part of the mean structure the proposed approach has the advantage of being straightforward to implement using a simple and efficient gibbs sampler whereas alternative semiparametric bayes event time models encounter problems for current status data the model is generalized to allow systematic underreporting in a subset of the data and the methods are applied to an epidemiologic study of uterine fibroids

on derivative estimation of the mean time to failure in simulations of highly reliable markovian system the mean time to failure mttf of a markovian system can be expressed as a ratio of two expectations for highly reliable markovian systems the resulting ratio formula consists of one expectation that cannot be estimated with bounded relative error when using standard simulation while the other which we call a nonrare expectation can be estimated with bounded relative error we show that some derivatives of the nonrare expectation cannot be estimated with bounded relative error when using standard simulation which in turn may lead to an estimator of the derivative of the mttf that has unbounded relative error however if particular importance sampling methods e g balanced failure biasing are used then the estimator of the derivative of the nonrare expectation will have bounded relative error which under certain conditions will yield an estimator of the derivative of the mttf with bounded relative error

sieve maximum likelihood regression analysis of dependent current status data current status data occur in contexts including demographic studies and tumorigenicity experiments in such cases each subject is observed only once and the failure time of interest is either left or right censored kalbfleisch prentice 2002 many methods have been developed for the analysis of such data huang 1996 sun 2006 most of which assume that the failure time and the observation time are independent completely or given covariates in this paper we present a sieve maximum likelihood approach for current status data when independence does not hold a copula model and monotone i splines are used and the asymptotic properties of the resulting estimators are established in particular the estimated regression parameters are shown to be semiparametrically efficient an illustrative example is provided

sieve maximum likelihood estimator for semiparametric regression models with current status data in a randomized controlled clinical trial study where the response variable of interest is the time to occurrence of a certain event it is often too expensive or even impossible to observe the exact time however the current status of the subject at a random time of inspection is much more natural feasible and practical in terms of cost effectiveness this article considers a semiparametric regression model that consists of parametric and nonparametric regression components a sieve maximum likelihood estimator mle is proposed to estimate the regression parameter allowing exploration of the nonlinear relationship between a certain covariate and the response function asymptotic properties of the proposed sieve mles are discussed under some mild conditions the estimators are shown to be strongly consistent moreover the estimators of the unknown parameters are asymptotically efficient and normally distributed and the estimator of the nonparametric function has an optimal convergence rate simula

pseudo and conditional score approach to joint analysis of current count and current status data we develop a joint analysis approach for recurrent and nonrecurrent event processes subject to case i interval censorship which are also known in literature as current count and current status data respectively we use a shared frailty to link the recurrent and nonrecurrent event processes while leaving the distribution of the frailty fully unspecified conditional on the frailty the recurrent event is assumed to follow a nonhomogeneous poisson process and the mean function of the recurrent event and the survival function of the nonrecurrent event are assumed to follow some general form of semiparametric transformation models estimation of the models is based on the pseudo likelihood and the conditional score techniques the resulting estimators for the regression parameters and the unspecified baseline functions are shown to be consistent with rates of square and cubic roots of the sample size respectively asymptotic normality with closed form asymptotic variance is derived for the estimator of the regression parameters we apply the proposed method to a fracture osteoporosis survey data to identify risk factors jointly for fracture and osteoporosis in elders while accounting for association between the two events within a subject

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

likelihood based inference for monotone response models the behavior of maximum likelihood estimates mles and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied this class of problems differs radically from the usual parametric or semiparametric situations in that the mle of the monotone function at a point converges to the truth at rate n 1 3 slower than the usual n rate with a non gaussian limit distribution a framework for likelihood based estimation of monotone functions is developed and limit theorems describing the behavior of the mles and the likelihood ratio statistic are established in particular the likelihood ratio statistic is found to be asymptotically pivotal with a limit distribution that is no longer 2 but can be explicitly characterized in terms of a functional of brownian motion applications of the main results are presented and potential extensions discussed

maximum likelihood estimation for semiparametric regression models with multivariate interval censored data interval censored multivariate failure time data arise when there are multiple types of failure or there is clustering of study subjects and each failure time is known only to lie in a certain interval we investigate the effects of possibly time dependent covariates on multivariate failure times by considering a broad class of semiparametric transformation models with random effects and we study nonparametric maximum likelihood estimation under general interval censoring schemes we show that the proposed estimators for the finite dimensional parameters are consistent and asymptotically normal with a limiting covariance matrix that attains the semiparametric efficiency bound and can be consistently estimated through profile likelihood in addition we develop an em algorithm that converges stably for arbitrary datasets finally we assess the performance of the proposed methods in extensive simulation studies and illustrate their application using data derived from the atherosclerosis risk in communities study

a nonparametric test for current status data with unequal censoring nonparametric tests for the comparison of different treatments based on current status data are proposed for this problem most methods proposed in the literature require that observation times on all subjects follow the same distribution in other words censoring distributions are identical between the treatment groups in this paper we focus on the situation where the censoring distributions may be different for subjects in different treatment groups and the test that can take this unequal censoring into account is given the asymptotic distribution of the test proposed is derived the method proposed is applied to data arising from a tumorigenicity experiment

well posedness global existence and large time behavior for hardy henon parabolic equations in this paper we study the nonlinear parabolic equation tu u a x u u tu u a x u u t 0 x rn 0 n 1 a r 0 0 min 2 n and with initial value u 0 u 0 we establish local well posedness in lq rn lq rn and in c0 rn c0 rn in particular the value q n 2 q n 2 plays a critical role for 2 n 2 n we show the existence of global self similar solutions with initial values x x x 2 x x x 2 where l rn l rn is homogeneous of degree 00 and is sufficiently small we then prove that if x x x 2 x x x 2 for x x large then the solution is global and is asymptotic in the l l norm to a self similar solution of the nonlinear equation while if x x x x x x for x x large with 2 n 2 n then the solution is global but is asymptotic in the l l norm to et x x et x x the equation with more general potential tu u v x u u v x x l rn is also studied in particular for initial data x x x 2 x x x 2 x x large we show that the large time behavior is linear if vv is compactly supported near the origin while it is nonlinear if vv is compactly supported near infinity

a sieve semiparametric maximum likelihood approach for regression analysis of bivariate interval censored failure time data abstractinterval censored failure time data arise in a number of fields and many authors have discussed various issues related to their analysis however most of the existing methods are for univariate data and there exists only limited research on bivariate data especially on regression analysis of bivariate interval censored data we present a class of semiparametric transformation models for the problem and for inference a sieve maximum likelihood approach is developed the model provides a great flexibility in particular including the commonly used proportional hazards model as a special case and in the approach bernstein polynomials are employed the strong consistency and asymptotic normality of the resulting estimators of regression parameters are established and furthermore the estimators are shown to be asymptotically efficient extensive simulation studies are conducted and indicate that the proposed method works well for practical situations supplementary materials for this article are

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

a method for analyzing clustered interval censored data based on cox s model methods for analyzing interval censored data are well established unfortunately these methods are inappropriate for the studies with correlated data in this paper we focus on developing a method for analyzing clustered interval censored data our method is based on cox s proportional hazard model with piecewise constant baseline hazard function the correlation structure of the data can be modeled by using clayton s copula or independence model with proper adjustment in the covariance estimation we establish estimating equations for the regression parameters and baseline hazards and a parameter in copula simultaneously simulation results confirm that the point estimators follow a multivariate normal distribution and our proposed variance estimations are reliable in particular we found that the approach with independence model worked well even when the true correlation model was derived from clayton s copula we applied our method to a family based cohort study of pandemic h1n1 influenza in taiwan during 2009 2010 using the proposed method we investigate the impact of vaccination and family contacts on the incidence of ph1n1 influenza

regression analysis of a disease onset distribution using diagnosis data we consider methods for estimating the effect of a covariate on a disease onset distribution when the observed data structure consists of right censored data on diagnosis times and current status data on onset times amongst individuals who have not yet been diagnosed dunson and baird 2001 biometrics 57 306 403 approached this problem using maximum likelihood under the assumption that the ratio of the diagnosis and onset distributions is monotonic nondecreasing as an alternative we propose a two step estimator an extension of the approach of van der laan jewell and petersen 1997 biometrika 84 539 554 in the single sample setting which is computationally much simpler and requires no assumptions on this ratio a simulation study is performed comparing estimates obtained from these two approaches as well as that from a standard current status analysis that ignores diagnosis data results indicate that the dunson and baird estimator outperforms the two step estimator when the monotonicity assumption holds but the reverse is true when the assumption fails the simple current status estimator loses only a small amount of precision in comparison to the two step procedure but requires monitoring time information for all individuals in the data that motivated this work a study of uterine fibroids and chemical exposure to dioxin the monotonicity assumption is seen to fail here the two step and current status estimators both show no significant association between the level of dioxin exposure and the hazard for onset of uterine fibroids the two step estimator of the relative hazard associated with increasing levels of exposure has the least estimated variance amongst the three estimators considered

a semiparametric model for regression analysis of interval censored failure time data left right and interval censored response time data arise in a variety of settings including the analyses of data from laboratory animal carcinogenicity experiments clinical trials and longitudinal studies for such incomplete data the usual regression techniques such as the cox 1972 journal of the royal statistical society series b 34 187 220 proportional hazards model are inapplicable in this paper we present a method for regression analysis which accommodates interval censored data we present applications of this methodology to data sets from a study of breast cancer patients who were followed for cosmetic response to therapy a small animal tumorigenicity study and a clinical trial

a partially linear proportional hazards model for current status data for analyzing current status data a flexible partially linear proportional hazards model is proposed modeling flexibility is attained through using monotone splines to approximate the baseline cumulative hazard function as well as b splines to accommodate nonlinear covariate effects to facilitate model fitting a computationally efficient and easy to implement expectation maximization algorithm is developed through a two stage data augmentation process involving carefully structured latent poisson random variables asymptotic normality and the efficiency of the spline estimator of the regression coefficients are established and the spline estimators of the nonparametric components are shown to possess the optimal rate of convergence under suitable regularity conditions the finite sample performance of the proposed approach is evaluated through monte carlo simulation and it is further illustrated using uterine fibroid data arising from a prospective cohort study on early pregnancy