Catálogo de publicaciones - libros

In many survival studies one is interested not only in the duration time to some terminal event, but also in repeated measurements made on a time-dependent covariate. In these studies, subjects often drop out of the study before the occurrence of the terminal event and the problem of interest then becomes modelling the relationship between the time to dropout and the internal covariate. Dupuy and Mesbah (2002) (DM) proposed a model that described this relationship when the value of the covariate at the dropout time is unobserved. This model combined a first-order Markov model for the longitudinally measured covariate with a time-dependent Cox model for the dropout process. Parameters were estimated using the EM algorithm and shown to be consistent and asymptotically normal. In this paper, we propose a test statistic to test the validity of Dupuy and Mesbah’s model. Using the techniques developed by Lin (1991), we develop a class of estimators of the regression parameters using weight functions. The test statistic is a function of the standard maximum likelihood estimators and the estimators based on the weight function. Its asymptotic distribution and some related results are presented.

Some aspects of statistics of inverse gamma process as a model of wear are considered. Formulae for finite-dimensional distribution densities of the process are given. Partial derivatives with respect to parameters of one-dimensional densities of both the direct, and inverse processes with independent positive increments are derived. Methods for estimation of parameters of the inverse gamma process are investigated.

It is often of interest to effectively use the information on a large number of covariates in predicting response or outcome. Various statistical tools have been developed to overcome the difficulties caused by the high-dimensionality of the covariate space in the setting of a linear regression model. This paper focuses on the situation where the outcomes of interest are subjected to right censoring. We implement the extended partial least squares method along with other commonly used approaches for analyzing the high dimensional covariates to a data set from AIDS clinical trials (ACTG333). Predictions were computed on the covariate effect and the response for a future subject with a set of covariates. Simulation studies were conducted to compare our proposed methods with other prediction procedures for different numbers of covariates, different correlations among the covariates and different failure time distributions. Mean squared prediction error and mean absolute distance were used to measure the accuracy of prediction on the covariate effect and the response, respectively. We also compared the prediction performance of different approaches using numerical studies. The results show that the Buckley-James based partial least squares, stepwise subset model selection and principal components regression have similar predictive power and the partial least squares method has several advantages in terms of interpretability and numerical computation.

We consider survival data that are both interval censored and truncated. Turnbull [Tur76] proposed in 1976 a nice method for nonparametric maximum likelihood estimation of the distribution function in this case, which has been used since by many authors. But, to our knowledge, the consistency of the resulting estimate was never proved. We prove here the consistency of Turnbull’s NPMLE under appropriate conditions on the involved distributions: the censoring, truncation and survival distributions.

The applicability of purely lifetime based statistical analysis is limited due to several reasons. If the random event is the result of an underlying observable degradation process then it is possible to estimate the parameters of the resulting lifetime from observations of these process. In this paper we describe the degradation by a position-dependent marked doubly stochastic Poisson process. The intensity of such processes is a product of a deterministic function and a random variable Y which leads to an individual intensity for each realization. Our main interest consists in estimating the parameters of the distribution of Y under the assumption that the realization of Y is not observable.

This paper deals with the joint modeling and simultaneous analysis of failure time data and degradation and covariate data. Many failure mechanisms can be traced to an underlying degradation process and stochastically changing covariates. We consider a general class of reliability models in which failure is due to the competing causes of degradation and trauma and express the failure time in terms of degradation and covariates. We compute the survival function of the resulting failure time and derive the likelihood function for the joint observation of failure time data and degradation data at discrete times.

We investigate the properties of several statistical tests for comparing treatment groups with respect to multivariate survival data, based on the marginal analysis approach introduced by Wei, Lin and Weissfeld [WLW89]. We consider two types of directional tests, based on a constrained maximization and on linear combinations of the unconstrained maximizer of the working likelihood function, and the omnibus test arising from the same working likelihood. The directional tests are members of a larger class of tests, from which an asymptotically optimal test can be found. We compare the asymptotic powers of the tests under general contiguous alternatives for a variety of settings, and also consider the choice of the number of survival times to include in the multivariate outcome. We illustrate the results with two simulations and with the results from a clinical trial examining recurring opportunistic infections in persons with HIV.