A multiple time scale survival model with a cure fraction

Many recent survival studies propose modeling data with a cure fraction, i.e., data in which part of the population is not susceptible to the event of interest. This event may occur more than once for the same individual (recurrent event). We then have a scenario of recurrent event data in the presence of a cure fraction, which may appear in various areas such as oncology, finance, industries, among others. This paper proposes a multiple time scale survival model to analyze recurrent events using a cure fraction. The objective is analyzing the efficiency of certain interventions so that the studied event will not happen again in terms of covariates and censoring. All estimates were obtained using a sampling-based approach, which allows information to be input beforehand with lower computational effort. Simulations were done based on a clinical scenario in order to observe some frequentist properties of the estimation procedure in the presence of small and moderate sample sizes. An application of a well-known set of real mammary tumor data is provided.

A new long-term lifetime distribution induced by a latent complementary risk framework

In this paper, we proposed a new three-parameter long-term lifetime distribution induced by a latent complementary risk framework with decreasing, increasing and unimodal hazard function, the long-term complementary exponential geometric distribution. The new distribution arises from latent competing risk scenarios, where the lifetime associated scenario, with a particular risk, is not observable, rather we observe only the maximum lifetime value among all risks, and the presence of long-term survival. The properties of the proposed distribution are discussed, including its probability density function and explicit algebraic formulas for its reliability, hazard and quantile functions and order statistics. The parameter estimation is based on the usual maximum-likelihood approach. A simulation study assesses the performance of the estimation procedure. We compare the new distribution with its particular cases, as well as with the long-term Weibull distribution on three real data sets, observing its potential and competitiveness in comparison with some usual long-term lifetime distributions.

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.