Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data

Summary In many instances, a subject can experience both a nonterminal and terminal event where the terminal event (e.g., death) censors the nonterminal event (e.g., relapse) but not vice versa. Typically, the two events are correlated. This situation has been termed semicompeting risks (e.g., Fine, Jiang, and Chappell, 2001 , Biometrika 88, 907–939; Wang, 2003 , Journal of the Royal Statistical Society, Series B 65, 257–273), and analysis has been based on a joint survival function of two event times over the positive quadrant but with observation restricted to the upper wedge. Implicitly, this approach entertains the idea of latent failure times and leads to discussion of a marginal distribution of the nonterminal event that is not grounded in reality. We argue that, similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We note that semicompeting risks have more classically been described as an illness–death model and this formulation avoids any reference to latent times. We consider an illness–death model with shared frailty, which in its most restrictive form is identical to the semicompeting risks model that has been proposed and analyzed, but that allows for many generalizations and the simple incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference and resulting estimates for the correlation parameter are compared with other proposed approaches. Asymptotic properties, simulations studies, and application to a randomized clinical trial in nasopharyngeal cancer evaluate and illustrate the methods. A simple and fast algorithm is developed for its numerical implementation.     

具有反馈控制的Schoner模型的渐近性

本文讨论了具有反馈控制的非自治Schoner系统的持续生存性条件以及该系统为周期系统时，存在唯一严格正的全局稳定的周期解的条件。     

Public health risk analysis for ambient polycyclic aromatic hydrocarbon exposure surrounding a petrochemical complex in Curaçao

Abstract

Antiquated petroleum refining methods may exacerbate polycyclic aromatic hydrocarbons (PAHs) in ambient air. There is currently an aging, yet active refinery on the island of Curaçao that has been the subject of public health concern. The objective of this study was to determine if ambient PAHs surrounding this refinery exceeded public health guidelines and investigate potential public health risks by calculating risk probability estimates. A number of recommended guidelines for the protection of public health from ambient PAHs were exceeded in Curaçao. Cumulative lifetime risk estimates for carcinogenic effects exceeded the upper bound level of acceptable risk at sites located both upwind and downwind of the petrochemical complex in 2011 and decreased to within the range considered acceptable in 2014. Risk probability estimates were highest for children and either exceeded or were approaching the upper bound advisory levels in 2011. Results indicate inhalation risks are higher at sites located downwind from the petrochemical complex compared to those upwind. This emphasizes the potential for higher risk probability estimates for residents that may have higher susceptibility, warranting the need for further health assessments in these populations and underscores the importance for continued monitoring of PAH sources and levels in Curaçao.