On estimation and influence diagnostics for log-Birnbaum-Saunders Student-t regression models: Full Bayesian analysis

The purpose of this paper is to develop a Bayesian approach for log-Birnbaum-Saunders Student-t regression models under right-censored survival data. Markov chain Monte Carlo (MCMC) methods are used to develop a Bayesian procedure for the considered model. In order to attenuate the influence of the outlying observations on the parameter estimates, we present in this paper Birnbaum-Saunders models in which a Student-t distribution is assumed to explain the cumulative damage. Also, some discussions on the model selection to compare the fitted models are given and case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback-Leibler divergence. The developed procedures are illustrated with a real data set. (C) 2010 Elsevier B.V. All rights reserved.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Regression analysis of mean quality-adjusted survival time based on pseudo-observations

Regression models for the mean quality-adjusted survival time are specified from hazard functions of transitions between two states and the mean quality-adjusted survival time may be a complex function of covariates. We discuss a regression model for the mean quality-adjusted survival (QAS) time based on pseudo-observations, which has the advantage of directly modeling the effect of covariates in the QAS time. Both Monte Carlo Simulations and a real data set are studied. Copyright (C) 2009 John Wiley & Sons, Ltd.

Robust Inferences For Covariate Effects On Survival Time With Censored Linear Regression Models

Various inference procedures for linear regression models with censored failure times have been studied extensively. Recent developments on efficient algorithms to implement these procedures enhance the practical usage of such models in survival analysis. In this article, we present robust inferences for certain covariate effects on the failure time in the presence of "nuisance" confounders under a semiparametric, partial linear regression setting. Specifically, the estimation procedures for the regression coefficients of interest are derived from a working linear model and are valid even when the function of the confounders in the model is not correctly specified. The new proposals are illustrated with two examples and their validity for cases with practical sample sizes is demonstrated via a simulation study.

Mixture Cure Survival Models with Dependent Censoring

A number of authors have studies the mixture survival model to analyze survival data with nonnegligible cure fractions. A key assumption made by these authors is the independence between the survival time and the censoring time. To our knowledge, no one has studies the mixture cure model in the presence of dependent censoring. To account for such dependence, we propose a more general cure model which allows for dependent censoring. In particular, we derive the cure models from the perspective of competing risks and model the dependence between the censoring time and the survival time using a class of Archimedean copula models. Within this framework, we consider the parameter estimation, the cure detection, and the two-sample comparison of latency distribution in the presence of dependent censoring when a proportion of patients is deemed cured. Large sample results using the martingale theory are obtained. We applied the proposed methodologies to the SEER prostate cancer data.

SURVIVAL PREDICTION FOR BRAIN TUMOR PATIENTS USING GENE EXPRESSION DATA

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. In order to evaluate this hypothesis, the general goal of this research is to build models for survival prediction of glioma patients using DNA molecular profiles (U133 Affymetrix gene expression microarrays) along with clinical information. First, a predictive Random Forest model is built for binary outcomes (i.e. short vs. long-term survival) and a small subset of genes whose expression values can be used to predict survival time is selected. Following, a new statistical methodology is developed for predicting time-to-death outcomes using Bayesian ensemble trees. Due to a large heterogeneity observed within prognostic classes obtained by the Random Forest model, prediction can be improved by relating time-to-death with gene expression profile directly. We propose a Bayesian ensemble model for survival prediction which is appropriate for high-dimensional data such as gene expression data. Our approach is based on the ensemble "sum-of-trees" model which is flexible to incorporate additive and interaction effects between genes. We specify a fully Bayesian hierarchical approach and illustrate our methodology for the CPH, Weibull, and AFT survival models. We overcome the lack of conjugacy using a latent variable formulation to model the covariate effects which decreases computation time for model fitting. Also, our proposed models provides a model-free way to select important predictive prognostic markers based on controlling false discovery rates. We compare the performance of our methods with baseline reference survival methods and apply our methodology to an unpublished data set of brain tumor survival times and gene expression data, selecting genes potentially related to the development of the disease under study. A closing discussion compares results obtained by Random Forest and Bayesian ensemble methods under the biological/clinical perspectives and highlights the statistical advantages and disadvantages of the new methodology in the context of DNA microarray data analysis.

Functional analysis of the ATM-p53-p21 pathway in the LRF CLL4 trial: blockade at the level of p21 is associated with short response duration.

PURPOSE: This study sought to establish whether functional analysis of the ATM-p53-p21 pathway adds to the information provided by currently available prognostic factors in patients with chronic lymphocytic leukemia (CLL) requiring frontline chemotherapy. EXPERIMENTAL DESIGN: Cryopreserved blood mononuclear cells from 278 patients entering the LRF CLL4 trial comparing chlorambucil, fludarabine, and fludarabine plus cyclophosphamide were analyzed for ATM-p53-p21 pathway defects using an ex vivo functional assay that uses ionizing radiation to activate ATM and flow cytometry to measure upregulation of p53 and p21 proteins. Clinical endpoints were compared between groups of patients defined by their pathway status. RESULTS: ATM-p53-p21 pathway defects of four different types (A, B, C, and D) were identified in 194 of 278 (70%) samples. The type A defect (high constitutive p53 expression combined with impaired p21 upregulation) and the type C defect (impaired p21 upregulation despite an intact p53 response) were each associated with short progression-free survival. The type A defect was associated with chemoresistance, whereas the type C defect was associated with early relapse. As expected, the type A defect was strongly associated with TP53 deletion/mutation. In contrast, the type C defect was not associated with any of the other prognostic factors examined, including TP53/ATM deletion, TP53 mutation, and IGHV mutational status. Detection of the type C defect added to the prognostic information provided by TP53/ATM deletion, TP53 mutation, and IGHV status. CONCLUSION: Our findings implicate blockade of the ATM-p53-p21 pathway at the level of p21 as a hitherto unrecognized determinant of early disease recurrence following successful cytoreduction.

A review on reliability models with covariates

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-to-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and industry applications, the lifetime of assets is influenced by different risk factors, which are called covariates. The fundamental notion in reliability theory is the failure time of a system and its covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. An extensive amount of literature on hazard models with covariates (also termed covariate models), including theory and practical applications, has emerged. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesise these models from both industrial reliability and biomedical fields and then contextually group them into non-parametric and semi-parametric models. Comments on their merits and limitations are also presented. Another main purpose of this paper is to comprehensively review and summarise the current research on the development of the covariate models so as to facilitate the application of more covariate modelling techniques into prognostics and asset health management.

Incorporating weather into regionwide safety planning prediction models

Predicting safety on roadways is standard practice for road safety professionals and has a corresponding extensive literature. The majority of safety prediction models are estimated using roadway segment and intersection (microscale) data, while more recently efforts have been undertaken to predict safety at the planning level (macroscale). Safety prediction models typically include roadway, operations, and exposure variables—factors known to affect safety in fundamental ways. Environmental variables, in particular variables attempting to capture the effect of rain on road safety, are difficult to obtain and have rarely been considered. In the few cases weather variables have been included, historical averages rather than actual weather conditions during which crashes are observed have been used. Without the inclusion of weather related variables researchers have had difficulty explaining regional differences in the safety performance of various entities (e.g. intersections, road segments, highways, etc.) As part of the NCHRP 8-44 research effort, researchers developed PLANSAFE, or planning level safety prediction models. These models make use of socio-economic, demographic, and roadway variables for predicting planning level safety. Accounting for regional differences - similar to the experience for microscale safety models - has been problematic during the development of planning level safety prediction models. More specifically, without weather related variables there is an insufficient set of variables for explaining safety differences across regions and states. Furthermore, omitted variable bias resulting from excluding these important variables may adversely impact the coefficients of included variables, thus contributing to difficulty in model interpretation and accuracy. This paper summarizes the results of an effort to include weather related variables, particularly various measures of rainfall, into accident frequency prediction and the prediction of the frequency of fatal and/or injury degree of severity crash models. The purpose of the study was to determine whether these variables do in fact improve overall goodness of fit of the models, whether these variables may explain some or all of observed regional differences, and identifying the estimated effects of rainfall on safety. The models are based on Traffic Analysis Zone level datasets from Michigan, and Pima and Maricopa Counties in Arizona. Numerous rain-related variables were found to be statistically significant, selected rain related variables improved the overall goodness of fit, and inclusion of these variables reduced the portion of the model explained by the constant in the base models without weather variables. Rain tends to diminish safety, as expected, in fairly complex ways, depending on rain frequency and intensity.

Forecasting crashes at the planning level: Simultaneous negative binomial crash model applied in Tucson, Arizona

At least two important transportation planning activities rely on planning-level crash prediction models. One is motivated by the Transportation Equity Act for the 21st Century, which requires departments of transportation and metropolitan planning organizations to consider safety explicitly in the transportation planning process. The second could arise from a need for state agencies to establish incentive programs to reduce injuries and save lives. Both applications require a forecast of safety for a future period. Planning-level crash prediction models for the Tucson, Arizona, metropolitan region are presented to demonstrate the feasibility of such models. Data were separated into fatal, injury, and property-damage crashes. To accommodate overdispersion in the data, negative binomial regression models were applied. To accommodate the simultaneity of fatality and injury crash outcomes, simultaneous estimation of the models was conducted. All models produce crash forecasts at the traffic analysis zone level. Statistically significant (p-values < 0.05) and theoretically meaningful variables for the fatal crash model included population density, persons 17 years old or younger as a percentage of the total population, and intersection density. Significant variables for the injury and property-damage crash models were population density, number of employees, intersections density, percentage of miles of principal arterial, percentage of miles of minor arterials, and percentage of miles of urban collectors. Among several conclusions it is suggested that planning-level safety models are feasible and may play a role in future planning activities. However, caution must be exercised with such models.

Impact of traffic oscillations on freeway crash occurrences

Traffic oscillations are typical features of congested traffic flow that are characterized by recurring decelerations followed by accelerations (stop-and-go driving). The negative environmental impacts of these oscillations are widely accepted, but their impact on traffic safety has been debated. This paper describes the impact of freeway traffic oscillations on traffic safety. This study employs a matched case-control design using high-resolution traffic and crash data from a freeway segment. Traffic conditions prior to each crash were taken as cases, while traffic conditions during the same periods on days without crashes were taken as controls. These were also matched by presence of congestion, geometry and weather. A total of 82 cases and about 80,000 candidate controls were extracted from more than three years of data from 2004 to 2007. Conditional logistic regression models were developed based on the case-control samples. To verify consistency in the results, 20 different sets of controls were randomly extracted from the candidate pool for varying control-case ratios. The results reveal that the standard deviation of speed (thus, oscillations) is a significant variable, with an average odds ratio of about 1.08. This implies that the likelihood of a (rear-end) crash increases by about 8% with an additional unit increase in the standard deviation of speed. The average traffic states prior to crashes were less significant than the speed variations in congestion.