Malcolm H. Ray

Abstract With explanatory covariates, the standard analysis for competing risks data involves modeling the cause-specific hazard functions via a proportional hazards assumption. Unfortunately, the cause-specific hazard function does not have a direct interpretation in terms of survival probabilities for the particular failure type. In recent years many clinicians have begun using the cumulative incidence function, the marginal failure probabilities for a particular cause, which is intuitively appealing and more easily explained to the nonstatistician. The cumulative incidence is especially relevant in cost-effectiveness analyses in which the survival probabilities are needed to determine treatment utility. Previously, authors have considered methods for combining estimates of the cause-specific hazard functions under the proportional hazards formulation. However, these methods do not allow the analyst to directly assess the effect of a covariate on the marginal probability function. In this article we propose a novel semiparametric proportional hazards model for the subdistribution. Using the partial likelihood principle and weighting techniques, we derive estimation and inference procedures for the finite-dimensional regression parameter under a variety of censoring scenarios. We give a uniformly consistent estimator for the predicted cumulative incidence for an individual with certain covariates; confidence intervals and bands can be obtained analytically or with an easy-to-implement simulation technique. To contrast the two approaches, we analyze a dataset from a breast cancer clinical trial under both models. Key Words: Hazard of subdistributionMartingalePartial likelihoodTransformation model

In this paper, for right censored competing risks data, a class of tests developed for comparing the cumulative incidence of a particular type of failure among different groups. The tests are based on comparing weighted averages of the hazards of the subdistribution for the failure type of interest. Asymptotic results are derived by expressing the statistics in terms of counting processes and using martingale central limit theory. It is proposed that weight functions very similar to those for the $G^p$ tests from ordinary survival analysis be used. Simulation results indicate that the asymptotic distributions provide adequate approximations in moderate sized samples.

An elasto-plastic damage model with rate effects was developed for concrete and implemented into LS-DYNA, a commercially available finite element code. This manual documents the theory of the concrete material model, describes the required input format, and includes example problems for use as a learning tool. A default material property input option is provided for normal strength concrete. The model was developed for roadside safety applications, such as concrete bridge rails and portable barriers impacted by vehicles, but it should also be applicable to other dynamic applications.\nThe companion report to this manual is entitled Evaluation of LS-DYNA Concrete Material Model 159, FHWA-HRT-05-063.\n

An elastoplastic damage model with rate effects was developed for concrete and implemented into LS-DYNA, a commercially available finite element code. This manual documents the evaluation of the concrete material model, including the selection of the concrete model input parameters. The model is evaluated through correlations with test data: drop tower impact of 1/3-scale beams (plain and reinforced), bogie vehicle impact of full-scale reinforced beams, pendulum impact of bridge rails, and quasi-static loading of a safety-shaped barrier. Although the model was developed and evaluated for roadside safety applications, it should also be applicable to many dynamic problems.