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.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

The negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Effects of arterial oxygen tension and cardiac output on venous saturation: a mathematical modeling approach

OBJECTIVES: Hemodynamic support is aimed at providing adequate O-2 delivery to the tissues; most interventions target O-2 delivery increase. Mixed venous O-2 saturation is a frequently used parameter to evaluate the adequacy of O-2 delivery. METHODS: We describe a mathematical model to compare the effects of increasing O-2 delivery on venous oxygen saturation through increases in the inspired O-2 fraction versus increases in cardiac output. The model was created based on the lungs, which were divided into shunted and non-shunted areas, and on seven peripheral compartments, each with normal values of perfusion, optimal oxygen consumption, and critical O-2 extraction rate. O-2 delivery was increased by changing the inspired fraction of oxygen from 0.21 to 1.0 in steps of 0.1 under conditions of low (2.0 L.min(-1)) or normal (6.5 L.min(-1)) cardiac output. The same O-2 delivery values were also obtained by maintaining a fixed O-2 inspired fraction value of 0.21 while changing cardiac output. RESULTS: Venous oxygen saturation was higher when produced through increases in inspired O-2 fraction versus increases in cardiac output, even at the same O-2 delivery and consumption values. Specifically, at high inspired O-2 fractions, the measured O-2 saturation values failed to detect conditions of low oxygen supply. CONCLUSIONS: The mode of O-2 delivery optimization, specifically increases in the fraction of inspired oxygen versus increases in cardiac output, can compromise the capability of the "venous O-2 saturation" parameter to measure the adequacy of oxygen supply. Consequently, venous saturation at high inspired O-2 fractions should be interpreted with caution.

Survival Analysis of Patients with Heart Failure: Implications of Time-Varying Regression Effects in Modeling Mortality

Background: Several models have been designed to predict survival of patients with heart failure. These, while available and widely used for both stratifying and deciding upon different treatment options on the individual level, have several limitations. Specifically, some clinical variables that may influence prognosis may have an influence that change over time. Statistical models that include such characteristic may help in evaluating prognosis. The aim of the present study was to analyze and quantify the impact of modeling heart failure survival allowing for covariates with time-varying effects known to be independent predictors of overall mortality in this clinical setting. Methodology: Survival data from an inception cohort of five hundred patients diagnosed with heart failure functional class III and IV between 2002 and 2004 and followed-up to 2006 were analyzed by using the proportional hazards Cox model and variations of the Cox's model and also of the Aalen's additive model. Principal Findings: One-hundred and eighty eight (188) patients died during follow-up. For patients under study, age, serum sodium, hemoglobin, serum creatinine, and left ventricular ejection fraction were significantly associated with mortality. Evidence of time-varying effect was suggested for the last three. Both high hemoglobin and high LV ejection fraction were associated with a reduced risk of dying with a stronger initial effect. High creatinine, associated with an increased risk of dying, also presented an initial stronger effect. The impact of age and sodium were constant over time. Conclusions: The current study points to the importance of evaluating covariates with time-varying effects in heart failure models. The analysis performed suggests that variations of Cox and Aalen models constitute a valuable tool for identifying these variables. The implementation of covariates with time-varying effects into heart failure prognostication models may reduce bias and increase the specificity of such models.

Drag reduction phenomenon in viscous oil-water dispersed pipe flow: Experimental investigation and phenomenological modeling

An experimental study on drag-reduction phenomenon in dispersed oil-water flow has been performed in a 26-mm-i.d. Twelve meter long horizontal glass pipe. The flow was characterized using a novel wire-mesh sensor based on capacitance measurements and high-speed video recording. New two-phase pressure gradient, volume fraction, and phase distribution data have been used in the analysis. Drag reduction and slip ratio were detected at oil volume fractions between 10 and 45% and high mixture Reynolds numbers, and with water as the dominant phase. Phase-fraction distribution diagrams and cross-sectional imaging of the flow suggested the presence of a higher amount of water near to the pipe wall. Based on that, a phenomenology for explaining drag reduction in dispersed flow in a flow situation where slip ratio is significant is proposed. A simple phenomenological model is developed and the agreement between model predictions and data, including data from the literature, is encouraging. (c) 2011 American Institute of Chemical Engineers AIChE J, 2012

A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data

In this article, we propose a new Bayesian flexible cure rate survival model, which generalises the stochastic model of Klebanov et al. [Klebanov LB, Rachev ST and Yakovlev AY. A stochastic-model of radiation carcinogenesis - latent time distributions and their properties. Math Biosci 1993; 113: 51-75], and has much in common with the destructive model formulated by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)]. In our approach, the accumulated number of lesions or altered cells follows a compound weighted Poisson distribution. This model is more flexible than the promotion time cure model in terms of dispersion. Moreover, it possesses an interesting and realistic interpretation of the biological mechanism of the occurrence of the event of interest as it includes a destructive process of tumour cells after an initial treatment or the capacity of an individual exposed to irradiation to repair altered cells that results in cancer induction. In other words, what is recorded is only the damaged portion of the original number of altered cells not eliminated by the treatment or repaired by the repair system of an individual. Markov Chain Monte Carlo (MCMC) methods are then used to develop Bayesian inference for the proposed model. Also, some discussions on the model selection and an illustration with a cutaneous melanoma data set analysed by Rodrigues et al. [Rodrigues J, de Castro M, Balakrishnan N and Cancho VG. Destructive weighted Poisson cure rate models. Technical Report, Universidade Federal de Sao Carlos, Sao Carlos-SP. Brazil, 2009 (accepted in Lifetime Data Analysis)] are presented.