Sample size calculation for logrank test and prediction of number of events over time

We review and compare existing methods for sample size calculation based on the logrank statistic and recommend the method of Lakatos for its accuracy and flexibility in allowing time-dependent rates of event, loss to follow-up, and noncompliance. We extend the Lakatos method to allow a general follow-up scheme, to handle non-inferiority tests, and to predict the number of events over calendar time. We apply the Lakatos method to the simple nonproportional hazard situation of delayed treatment effect to facilitate the comparison of different weighting methods and to evaluate the performance of the maximum combination tests. We use simulation studies to confirm the validity of the Lakatos method and its extensions.     

论环境公害的民事救济——以民事诉讼制度为视角

我国虽然制定了十几部环境法律法规,但环境程序法的研究和立法仍显滞后,导致环境实体法无法得到有效执行。本文针对我国传统环境诉讼与环境保护现实需求和理论研究极不协调的现状,从完善民事诉讼制度的角度,提出应当建立环境公害民事救济制度。具体化为通过建立健全环境公益诉讼制度,以期对我国的环境公害诉讼的发展提供一种研究进路。     

Precedence tests and Lehmann alternatives

G = F ^k (k > 1); G = 1 − (1−F) ^k (k < 1); G = F ^k (k < 1); and G = 1 − (1−F) ^k (k > 1), where F and G are two continuous cumulative distribution functions. If an optimal precedence test (one with the maximal power) is determined for one of these four classes, the optimal tests for the other classes of alternatives can be derived. Application of this is given using the results of Lin and Sukhatme (1992) who derived the best precedence test for testing the null hypothesis that the lifetimes of two types of items on test have the same distibution. The test has maximum power for fixed κ in the class of alternatives G = 1 − (1−F) ^k , with k < 1. Best precedence tests for the other three classes of Lehmann-type alternatives are derived using their results. Finally, a comparison of precedence tests with Wilcoxon's two-sample test is presented. Received: February 22, 1999; revised version: June 7, 2000     

Cox regression analysis in presence of collinearity: an application to assessment of health risks associated with occupational radiation exposure

This paper considers the analysis of time to event data in the presence of collinearity between covariates. In linear and logistic regression models, the ridge regression estimator has been applied as an alternative to the maximum likelihood estimator in the presence of collinearity. The advantage of the ridge regression estimator over the usual maximum likelihood estimator is that the former often has a smaller total mean square error and is thus more precise. In this paper, we generalized this approach for addressing collinearity to the Cox proportional hazards model. Simulation studies were conducted to evaluate the performance of the ridge regression estimator. Our approach was motivated by an occupational radiation study conducted at Oak Ridge National Laboratory to evaluate health risks associated with occupational radiation exposure in which the exposure tends to be correlated with possible confounders such as years of exposure and attained age. We applied the proposed methods to this study to evaluate the association of radiation exposure with all-cause mortality.     

Vulnerabilities and risks in population and environment studies

In the study of risks , different sciences use the same category in different ways, each related to its own ontological assumptions. But many of these fields communicate very little with one another. This article seeks to approximate two of these areas of study that have shown similar concerns and that can mutually strengthen one another, namely, geography and demography. Geography was one of the first disciplines to include risk in its environmental dimension and has had broad experience in simultaneously focusing on social and natural dynamics. Demography, on the other hand, faces greater difficulties because only recently has it incorporated the environmental dimension into its scientific scope. Both have brought the concept of vulnerability into their conceptual framework as complementary to that of risk. Geographers understand vulnerability as a more symbiotic form of the relationship between society and nature, whereas demographers give it a strong socioeconomic component. In this regard, the conceptual discussion on risks and vulnerabilities, in its attempt at approximating these two fields, is a way of conceptually advancing and strengthening the different approaches to empirical work, especially in population–environment studies which is the common ground for the dialogue between the two disciplines.

Professional quality of life of adult protective service workers

Adult Protective Services (APS) workers are exposed to substantial occupational hazards and job stress, but these stressors are underdocumented. Therefore, we sought to describe APS workers’ work environments and responses to occupational hazards and stressors, including compassion fatigue, burnout, and secondary traumatic stress. Survey data were gathered with closed-ended questionnaires administered to APS workers in an urban setting. Virtually all workers (97%) reported exposure to one or more environmental hazards in their work, and 80% reported hazard exposure in the past month. Workers also reported mixed responses to their work environment and to experiences with supervision. A sizable minority (22.7%) was at high risk for burnout, 24.6% were at risk for secondary traumatic stress, and 19.9% reported low compassion satisfaction. The results document multiple stressors in APS work. The APS partner is committed to ongoing efforts to better support its staff, and these findings can inform future efforts to enhance supervisor support and worker self-care, to minimize burnout and secondary traumatic stress.     

Bayesian partial likelihood approach for tied observations

The Bayesian analysis based on the partial likelihood for Cox's proportional hazards model is frequently used because of its simplicity. The Bayesian partial likelihood approach is often justified by showing that it approximates the full Bayesian posterior of the regression coefficients with a diffuse prior on the baseline hazard function. This, however, may not be appropriate when ties exist among uncensored observations. In that case, the full Bayesian and Bayesian partial likelihood posteriors can be much different. In this paper, we propose a new Bayesian partial likelihood approach for many tied observations and justify its use.     

Use of log−log survival function in modeling time-covariate interactions in Cox regression

Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.     

Variable selection for semiparametric proportional hazards model under progressive Type-II censoring

Variable selection is an effective methodology for dealing with models with numerous covariates. We consider the methods of variable selection for semiparametric Cox proportional hazards model under the progressive Type-II censoring scheme. The Cox proportional hazards model is used to model the influence coefficients of the environmental covariates. By applying Breslow’s “least information” idea, we obtain a profile likelihood function to estimate the coefficients. Lasso-type penalized profile likelihood estimation as well as stepwise variable selection method are explored as means to find the important covariates. Numerical simulations are conducted and Veteran’s Administration Lung Cancer data are exploited to evaluate the performance of the proposed method.     

Additive hazards regression of current status data with auxiliary covariates

This paper discusses the regression analysis of current status failure time data arising from the additive hazards model with auxiliary covariates. As often occurs in practice, it is impossible or impractical to measure the exact magnitude of covariates for all subjects in a study. To compensate the missing information, some auxiliary covariates are utilized instead. We propose two easy-to-implement procedures for estimation of regression parameters by making use of auxiliary information. The asymptotic properties of the resulting estimators are established and extensive numerical studies indicate that both procedures work well in practice.