Generalizing the standardized hazard ratio to multivariate proportional hazards regression,with an application to clinical~genomic studies

The standardized hazard ratio for univariate proportional hazards regression is generalized as a scalar to multivariate proportional hazards regression. Estimators of the standardized log hazard ratio are developed, with corrections for bias and for regression to the mean in high-dimensional analyses. Tests of point and interval null hypotheses and confidence intervals are constructed. Cohort sampling study designs, commonly used in prospective–retrospective clinical genomic studies, are accommodated.     

Risk Perception, Federal Spending, and the Savannah River Site: Attitudes of Hunters and Fishermen

This paper examines the attitudes of 285 hunters and fishermen from South Carolina about hunting and fishing, risk, environmental issues, and future land use of the Savannah River Site. We test the null hypothesis that there is no difference in hunting and fishing rates, attitudes toward the safety of fish and deer obtained from SRS, attitudes toward future land use at SRS, and perceptions of the severity of environmental problems as a function of how far respondents lived from the site. Respondents hunted or fished an average of over 40 days a year, and only half felt that the fish and deer from SRS were safe to eat. Willingness to expend federal funds was correlated with perceptions of the severity of the problem. Preferences for future land use at SRS fell into three categories: high (environmental research park, hunting, fishing, camping), medium (nuclear production, factories, preserve only), and low (nuclear waste storage, residential). There were no differences in hunting and fishing rates, ranking of the severity of environmental problems, and willingness to expend federal funds as a function of distance of residence from SRS, but attitudes toward future land use differed significantly as a function of location of residence. Those living close to SRS were more willing to have the site used for factories, residential, nuclear material production and to store nuclear wastes than those living farther from the site. Our data on recreational rates, attitudes toward future land use, and willingness to expend federal funds to solve environmental problems reiterate the importance of assessing stakeholder attitudes toward decisions regarding future land use at DOE sites     

Exponential tilt models for two-group comparison with censored data

We study application of the Exponential Tilt Model (ETM) to compare survival distributions in two groups. The ETM assumes a parametric form for the density ratio of the two distributions. It accommodates a broad array of parametric models such as the log-normal and gamma models and can be sufficiently flexible to allow for crossing hazard and crossing survival functions. We develop a nonparametric likelihood approach to estimate ETM parameters in the presence of censoring and establish related asymptotic results. We compare the ETM to the Proportional Hazards Model (PHM) in simulation studies. When the proportional hazards assumption is not satisfied but the ETM assumption is, the ETM has better power for testing the hypothesis of no difference between the two groups. And, importantly, when the ETM relation is not satisfied but the PHM assumption is, the ETM can still have power reasonably close to that of the PHM. Application of the ETM is illustrated by a gastrointestinal tumor study.     

A Bayesian approach to Weibull survival models—Application to a cancer clinical trial

In this paper we outline a class of fully parametric proportional hazards models, in which the baseline hazard is assumed to be a power transform of the time scale, corresponding to assuming that survival times follow a Weibull distribution. Such a class of models allows for the possibility of time varying hazard rates, but assumes a constant hazard ratio. We outline how Bayesian inference proceeds for such a class of models using asymptotic approximations which require only the ability to maximize the joint log posterior density. We apply these models to a clinical trial to assess the efficacy of neutron therapy compared to conventional treatment for patients with tumors of the pelvic region. In this trial there was prior information about the log hazard ratio both in terms of elicited clinical beliefs and the results of previous studies. Finally, we consider a number of extensions to this class of models, in particular the use of alternative baseline functions, and the extension to multi-state data.     

A Discrete Time Parametric Model for the Analysis of Failure Time Data

This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.     

A Weibull Regression Model with Gamma Frailties for Multivariate Survival Data

Frequently in the analysis of survival data, survival times within the same group are correlated due to unobserved co-variates. One way these co-variates can be included in the model is as frailties. These frailty random block effects generate dependency between the survival times of the individuals which are conditionally independent given the frailty. Using a conditional proportional hazards model, in conjunction with the frailty, a whole new family of models is introduced. By considering a gamma frailty model, often the issue is to find an appropriate model for the baseline hazard function. In this paper a flexible baseline hazard model based on a correlated prior process is proposed and is compared with a standard Weibull model. Several model diagnostics methods are developed and model comparison is made using recently developed Bayesian model selection criteria. The above methodologies are applied to the McGilchrist and Aisbett (1991) kidney infection data and the analysis is performed using Markov Chain Monte Carlo methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Elicitation of Decision-Makers'Preferences for Management of Major Hazards

A survey has been conducted among decision-makers from the urban area of Lyon (France). It aimed at elicitating attitudes toward industrial risk, with an emphasis on major hazards. The sample was quite small (23 individuals), but most of the actual decision-makers of the area belonged to it. A questionnaire allowed to look at the weights that are given to "catastrophic accidents," when compared to more usual ones. It showed that decision-makers are strongly "adverse to catastrophes." The findings support many risk management approaches that are based on assigning an "extra weight" to potential accidents that may cause a high number of casualties.     

Some recent developments for regression analysis of multivariate failure time data

Cox's seminal 1972 paper on regression methods for possibly censored failure time data popularized the use of time to an event as a primary response in prospective studies. But one key assumption of this and other regression methods is that observations are independent of one another. In many problems, failure times are clustered into small groups where outcomes within a group are correlated. Examples include failure times for two eyes from one person or for members of the same family.This paper presents a survey of models for multivariate failure time data. Two distinct classes of models are considered: frailty and marginal models. In a frailty model, the correlation is assumed to derive from latent variables (frailties) common to observations from the same cluster. Regression models are formulated for the conditional failure time distribution given the frailties. Alternatively, marginal models describe the marginal failure time distribution of each response while separately modelling the association among responses from the same cluster.We focus on recent extensions of the proportional hazards model for multivariate failure time data. Model formulation, parameter interpretation and estimation procedures are considered.     

Dynamic Simulation as an Approach to Understanding Hurricane Risk Response: Insights from the Stormview Lab

This article investigates the use of dynamic laboratory simulations as a tool for studying decisions to prepare for hurricane threats. A prototype web‐based simulation named Stormview is described that allows individuals to experience the approach of a hurricane in a computer‐based environment. In Stormview participants can gather storm information through various media, hear the opinions of neighbors, and indicate intentions to take protective action. We illustrate how the ability to exert experimental control over the information viewed by participants can be used to provide insights into decision making that would be difficult to gain from field studies, such as how preparedness decisions are affected by the nature of news coverage of prior storms, how a storm's movement is depicted in graphics, and the content of word‐of‐mouth communications. Data from an initial application involving a sample of Florida residents reveal a number of unexpected findings about hurricane risk response. Participants who viewed forecast graphics, which contained track lines depicting the most likely path of the storm, for example, had higher levels of preparation than those who saw graphics that showed only uncertainty cones—even among those living far from the predicted center path. Similarly, the participants who were most likely to express worry about an approaching storm and fastest to undertake preparatory action were those who, ironically, had never experienced one. Finally, external validity is evidenced by a close rank‐order correspondence between patterns of information use revealed in the lab and that found in previous cross‐sectional field studies.