Accelerated life tests under competing weibull causes of failure

Accelerated life testing of a product under more severe than normal conditions is cawiionly used to reduce test time and cost. Data collected at such accelerated conditions is used to obtain estimates of parameters of a stress translation function which is then used to make inference about the product's, per" formance under normal conditions. This problem is considered when the product is a p component series system with WeibuH distributed component lifetimes liaving a caimon shape parameter. A general stress translation function is used and estimates of model parameters are obtained for various censoring schemes.     

Approximate variance formulas and asymptotic joint sampling distributions of standardized risk ratios in the presence of competing risks in cohort studies

The present paper is concerned with some results in cohort studies, in which the individuals in two study population are exposed simultaneously to several risks of death, which compete for their lives.

The morality experience of individuals in the two study populations is compared with respect to the morality experience of individuals in a well-defined and fixed population called the standard population.

Under some reasonable assumptions, not only simple variance formulas are-developed for the standardized risk ratio statistics (S[Rcirc]R_i) but also their joint asymptotic sampling distribution. It is demonstrated that these SRcirc;R_i's have asymptotically a multivariate normal distribtion corresponding to any given number of competing risks of death, These results are utilized to construct Scheffé-type and Sidak-type simultaneous confidence intervals for the SRR_i parameters which hold regardless of any covariance structure among the competing risks of death. The corresponding results for the cause-specific SMR and the externally standardized risk ratio parameters follow as special cases.

The present paper generalizes the available results in the literature in two directions, namely, to obtain simple variance formulas for the S[Rcirc]R_i, statistics and to treat the situation in the presence of competing risks to which individuals in a study are simultaneously exposed.

An empirical evaluation of these results is discussed in the last section utilizing some real cohort data from two recent occupational epidemiologic cohort studies.     

Asymptotic efficiency of a competing risks model: A two-sample case

A generalized Cox regression model is studied for the covariance analysis of competing risks data subject to independent random censoring. The information of the maximum partial likelihood estimates is compared with that of maximum likelihood estimates assuming a log linear hazard function.The method of generalized variance is used to define the efficiency of estimation between the two models. This is then applied to two-sample problems with two exponentially censoring rates. Numerical results are summarized ane presented graphically.The detailed results indicate that the semi-parametric model wrks well for a higher rate of censoring. A method of generalizing the result to type 1 censoring and the efficiency of estimating the coefficient of the covariate are discussecd. A brief account of using the results to help design experiments is also given.     

Latent cure rate model under repair system and threshold effect

In this paper, we formulate a simple latent cure rate model with repair mechanism for a cell exposed to radiation. This latent approach is a flexible alternative to the models proposed by Klebanov et al. [A stochastic model of radiation carcinogenesis: latent time distributions and their properties. Math Biosci. 1993;18:51–75], Kim et al. [A new threshold regression model for survival data with a cure fraction. Lifetime Data Anal. 2011;17:101–122], and is along the lines of the destructive cure rate model formulated recently by Rodrigues et al. [Destructive weighted Poisson cure rate model. Lifetime Data Anal. 2011b;17:333–346]. A new version of the modified Gompertz model and the promotion cure rate model that takes into account the first passage time of reaching the critical point are discussed, and the estimation of tumor size at detection is then addressed from the Bayesian viewpoint. In addition, a simulation study and an application to real data set illustrate the usefulness of the proposed cure rate model.     

Generalized Supremum Tests for the Equality of Cause Specific Hazard Rates

In this paper we propose two new classes of asymptotically distribution-free Renyi-type tests for testing the equality of two risks in a competing risk model with possible censoring. This work extends the work of Aly, Kochar and McKeague [1994, Journal of American Statistical Association, 89, 994–999] and many of the existing tests for this problem belong to these newly proposed classes. The asymptotic properties of the proposed tests are investigated. Simulation studies are done to compare the performance with existing tests. A competing risks data set is analyzed to demonstrate the usefulness of the procedure.     

Modeling Event Times with Multiple Outcomes Using the Wiener Process with Drift

Length of stay in hospital (LOS) is a widely used outcome measure in Health Services research, often acting as a surrogate for resource consumption or as a measure of efficiency. The distribution of LOS is typically highly skewed, with a few large observations. An interesting feature is the presence of multiple outcomes (e.g. healthy discharge, death in hospital, transfer to another institution). Health Services researchers are interested in modeling the dependence of LOS on covariates, often using administrative data collected for other purposes, such as calculating fees for doctors. Even after all available covariates have been included in the model, unexplained heterogeneity usually remains. In this article, we develop a parametric regression model for LOS that addresses these features. The model is based on the time, T, that a Wiener process with drift (representing an unobserved health level process) hits one of two barriers, one representing healthy discharge and the other death in hospital. Our approach to analyzing event times has many parallels with competing risks analysis (Kalbfleisch and Prentice, The Statistical Analysis of Failure Time Data, New York: John Wiley and Sons, 1980)), and can be seen as a way of formalizing a competing risks situation. The density of T is an infinite series, and we outline a proof that the density and its derivatives are absolutely and uniformly convergent, and regularity conditions are satisfied. Expressions for the expected value of T, the conditional expectation of T given outcome, and the probability of each outcome are available in terms of model parameters. The proposed regression model uses an approximation to the density formed by truncating the series, and its parameters are estimated by maximum likelihood. An extension to allow a third outcome (e.g. transfers out of hospital) is discussed, as well as a mixture model that addresses the issue of unexplained heterogeneity. The model is illustrated using administrative data.     

Saddlepoint p-values for a class of tests for comparing competing risks with censored data

One of the general problems in clinical trials and mortality rates is the comparison of competing risks. Most of the test statistics used for independent and dependent risks with censored data belong to the class of weighted linear rank tests in its multivariate version. In this paper, we introduce the saddlepoint approximations as accurate and fast approximations for the exact p-values of this class of tests instead of the asymptotic and permutation simulated calculations. Real data examples and extensive simulation studies showed the accuracy and stability performance of the saddlepoint approximations over different scenarios of lifetime distributions, sample sizes and censoring.     

Marginal and Conditional Distribution Estimation from Double‐sampled Semi‐competing Risks Data

Informative dropout is a vexing problem for any biomedical study. Most existing statistical methods attempt to correct estimation bias related to this phenomenon by specifying unverifiable assumptions about the dropout mechanism. We consider a cohort study in Africa that uses an outreach programme to ascertain the vital status for dropout subjects. These data can be used to identify a number of relevant distributions. However, as only a subset of dropout subjects were followed, vital status ascertainment was incomplete. We use semi‐competing risk methods as our analysis framework to address this specific case where the terminal event is incompletely ascertained and consider various procedures for estimating the marginal distribution of dropout and the marginal and conditional distributions of survival. We also consider model selection and estimation efficiency in our setting. Performance of the proposed methods is demonstrated via simulations, asymptotic study and analysis of the study data.     

The Identifiability of Dependent Competing Risks Models Induced by Bivariate Frailty Models

In this paper, we propose to use a special class of bivariate frailty models to study dependent censored data. The proposed models are closely linked to Archimedean copula models. We give sufficient conditions for the identifiability of this type of competing risks models. The proposed conditions are derived based on a property shared by Archimedean copula models and satisfied by several well‐known bivariate frailty models. Compared with the models studied by Heckman and Honoré and Abbring and van den Berg, our models are more restrictive but can be identified with a discrete (even finite) covariate. Under our identifiability conditions, expectation–maximization (EM) algorithm provides us with consistent estimates of the unknown parameters. Simulation studies have shown that our estimation procedure works quite well. We fit a dependent censored leukaemia data set using the Clayton copula model and end our paper with some discussions. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics     

Competing Mechanisms in a Common Value Environment

Consider strategic risk‐neutral traders competing in schedules to supply liquidity to a risk‐averse agent who is privately informed about the value of the asset and his hedging needs. Imperfect competition in this common value environment is analyzed as a multi‐principal game in which liquidity suppliers offer trading mechanisms in a decentralized way. Each liquidity supplier behaves as a monopolist facing a residual demand curve resulting from the maximizing behavior of the informed agent and the trading mechanisms offered by his competitors. There exists a unique equilibrium in convex schedules. It is symmetric and differentiable and exhibits typical features of market‐power: Equilibrium trading volume is lower than ex ante efficiency would require. Liquidity suppliers charge positive mark‐ups and make positive expected profits, but these profits decrease with the number of competitors. In the limit, as this number goes to infinity, ask (resp. bid) prices converge towards the upper (resp. lower) tail expectations obtained in Glosten (1994) and expected profits are zero.