Catálogo de publicaciones - libros

The aim of this study, corresponding to a research project on functional decline and mortality of frail elderly patients, is to build a predictive survival process that takes into account the functional and nutritional evolution of the patients over time. We deal with both survival data and repeated measures, but the usual statistical methods for the joint analysis of longitudinal and survival data are not appropriate in this case. As an alternative, we use the multistate survival model approach to evaluate the association between mortality and the recovery, or not, of normal functional and nutritional levels. Once the model is estimated and the prognostic factors of mortality identified, a predictive process is computed that allows predictions to be made of a patient’s survival based on his or her history at a given time. This provides a more exact estimate of the prognosis for each group of patients that may be very helpful to clinicians in the making of decisions.

We propose an approach for analysis of survivorship data from observational and/or experimental studies that allows comparison of survival in the control and several experimental groups. Our approach is based on the model of heterogeneous mortality (frailty model), and we also assume that the difference between survivals for the control and experimental groups is in both the frailty distribution and baseline hazard. We explore the variety of survival patterns that can be captured by different specifications of the proposed model and illustrate the approach with an example of the model application to the analysis of data from stress-experiment with nematodes Caenorhabditis elegans . We show that the proposed model gives a good fit to the data and helps to advance our understanding of biological phenomena as they appear at both individual and population levels.

We define nonparametric kernel-type estimators of the conditional distribution of a lifetime, in a random censorship framework. We show that these estimators have closed-form expressions, and establish their strong uniform consistency under minimal assumptions.

In this chapter, we investigate the asymptotic behavior of the sequential version of the regression parameter estimator for the additive hazard model. We mainly establish that the Lin and Ying (1994) nonsequential estimator is strongly consistent (in the sense of complete convergence) and that this estimator, indexed by any regular sequence (sequential estimator), has the same asymptotic behavior as the nonsequential estimator. An example of a fixed-width confidence-type sequential estimator is illustrated by simulations.

Doubly censored failure time data often occur in epidemiological or disease progression studies. In this situation, several authors have investigated the problem of estimating a survival function and proposed methods for the problem. However, there appears to be no existing research studying variance estimation of an estimated survival function. This chapter discusses pointwise estimation of variances of an estimated survival function and several methods are presented. The evaluation and comparison of the methods are conducted using numerical studies and a set of real doubly censored failure time data. The results suggest that the proposed methods work well under practical situations.

It is well known that any statistical model for supervised or unsupervised classification can be realized as a neural network. This discussion is devoted to supervised classification and therefore the essential framework is the family of feedforward nets. Ciampi and Lechevallier have studied two- and three-hidden-layer feedforward neural nets that are equivalent to trees, characterized by neurons with “hard” thresholds. Softening the thresholds has led to more general models. Also, neural nets that realize additive models have been studied, as well as networks of networks that represent a “mixed” classifier (predictor) consisting of a tree component and an additive component. Various “dependent” variables have been studied, including the case of censored survival times. A new development has recently been proposed: the soft tree. A soft tree can be represented as a particular type of hierarchy of experts. This representation can be shown to be equivalent to that of Ciampi and Lechevallier. However, it leads to an appealing interpretation, to other possible generalizations and to a new approach to training. Soft trees for classification and prediction of a continuous variable will be presented. Comparisons between conventional trees (trees with hard thresholds) and soft trees will be discussed and it will be shown that the soft trees achieve better predictions than the hard tree.

Standard clustering methods do not handle truly large data sets and fail to take into account multilevel data structures. This work outlines an approach to clustering that integrates the Kohonen Self-Organizing Map (SOM) with other clustering methods. Moreover, in order to take into account multilevel structures, a statistical model is proposed, in which a mixture of distributions may have mixing coefficients depending on higher-level variables. Thus, in a first step, the SOM provides a substantial data reduction, whereby a variety of ascending and divisive clustering algorithms becomes accessible. As a second step, statistical modeling provides both a direct means to treat multilevel structures and a framework for model-based clustering. The interplay of these two steps is illustrated on an example of nutritional data from a multicenter study on nutrition and cancer, known as EPIC.

Smear negative pulmonary tuberculosis (SNPT) accounts for 30% of pulmonary tuberculosis (PT) cases reported yearly. Rapid and accurate diagnosis of SNPT could provide lower morbidity and mortality, and case detection at a less contagious status. The main objective of this work is to evaluate a prediction model for diagnosis of SNPT, useful for outpatients who are attended in settings with limited resources. The data used for developing the proposed models werecomprised of 136 patients from health care units. They were referred to the University Hospital in Rio de Janeiro, Brazil, from March 2001 to September 2002, with clinical-radiological suspicion of SNPT. Only symptoms and physical signs were used for constructing the neural network (NN) modelling, which was able to correctly classify 77% of patients from a test sample. The achievements of the NN model suggest that mathematical modelling, developed for classifying SNPT cases could be a useful tool for optimizing application of more expensive tests, and to avoid costs of unnecessary anti-PT treatment. In addition, the main features extracted by the neural model are shown to agree with current analysis from experts in the field.

In this chapter, we have assessed the time to development of drug resistance in HIV-infected individuals treated with antiviral drugs by using longitudinal viral load HIV-1 counts. Through log-transformed data of HIV virus counts over time, we have assumed a linear changing-point model and developed procedures to estimate the unknown parameters by using the Bayesian approach. We have applied the method and procedure to the data generated by the ACTG 315 involving treatment by the drug combination (3TC, AZT, and Ritonavir). Our analysis showed that the mean time to the first changing point (i.e., the time the macrophage and long-lived cells began to release HIV particles) was around 15 days whereas the time to development of drug resistance by HIV was around 75 days. The Bayesian HPD intervals for these changing points are given by (8.7, 21.3) and (42, 108), respectively. This analysis indicated that if we use the combination of three drugs involving two NRTI inhibitors (3TC and AZT) and one PI inhibitor (Ritonavir) to treat HIV-infected individuals, in about two and half months, it would be beneficial to change drugs to avoid the problem of drug resistance.

In this chapter, we have developed a method to estimate the efficiency of the drugs and the numbers of infectious and noninfectious HIV in HIV-infected individuals treated with antiretroviral drugs. As an illustration, we have applied the method to some clinical and laboratory data of an AIDS patient treated with various antiviral drugs. For this individual, the estimates show that the HAART protocol has effectively controlled the number of infectious HIV virus to below 400/ml copies although the total number of HIV copies was very high in some intervals.