Survival Convergence and the Preceding Mortality Crossover for Two Population Subgroups

In this paper, we present and develop the argument that if the survival functions for two population subgroups converge in later life, a mortality crossover must precede the occurrence of this convergence. Specifically, two survival curves, S ₁(x) and S ₂(x), associated with two distinct population subgroups, G₁ and G₂, tend to converge before all members die out, as often observed and anticipated. This convergence leads to an increased mortality acceleration for the “advantaged” group, and eventually fosters the occurrence of a mortality crossover. We present a mathematical proof for this relationship and offer several explanations for the mechanisms involved in the process of survival convergence and the preceding mortality crossover. This new presentation demonstrates that mortality crossover is a highly observable demographic event given the trend of survival convergence in later life.     

H_2O_2浸种对提高陈年种子发芽率的研究

适当浓度的H_2O_2液浸种陈年番茄、萝卜种子,能显著提高发芽率。其中,番茄以0.25％H_2O_2浸种4天,萝卜以0.5％H_2O_2浸种3天的效果最佳。应用垂直平板聚丙烯酰胺凝胶电泳法,分析番茄种子和萝卜种子萌发过程中的过氧化物酶同工酶,结果表明,处理组的酶带数目与酶活性强弱跟发芽率的提高相一致。说明采用一定浓度的H_2O_2浸种陈年种子,可使某些同工酶提前出现,种子的生理生化代谢增强,并能破坏抑制物质的抑制作用,从而提高种子萌发率。     

如何提高单手投篮命中率

本文论述投篮准确性的关键在于投篮手法的正确和投篮时力量的运用适当，以及投篮要有自信心等观点，并对投篮训练提出合理化建议．     

Bivariate frailty model for the analysis of multivariate survival time

Because of limitations of the univariate frailty model in analysis of multivariate survival data, a bivariate frailty model is introduced for the analysis of bivariate survival data. This provides tremendous flexibility especially in allowing negative associations between subjects within the same cluster. The approach involves incorporating into the model two possibly correlated frailties for each cluster. The bivariate lognormal distribution is used as the frailty distribution. The model is then generalized to multivariate survival data with two distinguished groups and also to alternating process data. A modified EM algorithm is developed with no requirement of specification of the baseline hazards. The estimators are generalized maximum likelihood estimators with subject-specific interpretation. The model is applied to a mental health study on evaluation of health policy effects for inpatient psychiatric care.     

A Flexible Approach to Time-varying Coefficients in the Cox Regression Setting

Research on methods for studying time-to-event data (survival analysis) has been extensive in recent years. The basic model in use today represents the hazard function for an individual through a proportional hazards model (Cox, 1972). Typically, it is assumed that a covariate's effect on the hazard function is constant throughout the course of the study. In this paper we propose a method to allow for possible deviations from the standard Cox model, by allowing the effect of a covariate to vary over time. This method is based on a dynamic linear model. We present our method in terms of a Bayesian hierarchical model. We fit the model to the data using Markov chain Monte Carlo methods. Finally, we illustrate the approach with several examples. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

An analytic method for randomized trials with informative censoring: Part II

Consider a randomized trial in which time to the occurrence of a particular disease, say pneumocystic pneumonia in an AIDS trial or breast cancer in a mammographic screening trial, is the failure time of primary interest. Suppose that time to disease is subject to informative censoring by the minimum of time to death, loss to and end of follow-up. In such a trial, the potential censoring time is observed for all study subjects, including failures. In the presence of informative censoring, it is not possible to consistently estimate the effect of treatment on time to disease without imposing additional non-identifiable assumptions. Robins (1995) specified two non-identifiable assumptions that allow one to test for and estimate an effect of treatment on time to disease in the presence of informative censoring. The goal of this paper is to provide a class of consistent and reasonably efficient semiparametric tests and estimators for the treatment effect under these assumptions. The tests in our class, like standard weighted-log-rank tests, are asymptotically distribution-free -level tests under the null hypothesis of no causal effect of treatment on time to disease whenever the censoring and failure distributions are conditionally independent given treatment arm. However, our tests remain asymptotically distribution-free -level tests in the presence of informative censoring provided either of our assumptions are true. In contrast, a weighted log-rank test will be an -level test in the presence of informative censoring only if (1) one of our two non-identifiable assumptions hold, and (2) the distribution of time to censoring is the same in the two treatment arms. We also study the estimation, in the presence of informative censoring, of the effect of treatment on the evolution over time of the mean of repeated measures outcome such as CD4 count.     

A Remark on the Alternative Expectation Formula

Students in their first course in probability will often see the expectation formula for nonnegative continuous random variables in terms of the survival function. The traditional approach for deriving this formula (using double integrals) is well-received by students. Some students tend to approach this using integration by parts, but often get stuck. Most standard textbooks do not elaborate on this alternative approach. We present a rigorous derivation here. We hope that students and instructors of the first course in probability will find this short note helpful.     

Failure time regression with continuous covariates measured with error

We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed covariates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on-going epidemiologic study.     

Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data

Summary.  A common objective in longitudinal studies is the joint modelling of a longitudinal response with a time-to-event outcome. Random effects are typically used in the joint modelling framework to explain the interrelationships between these two processes. However, estimation in the presence of random effects involves intractable integrals requiring numerical integration. We propose a new computational approach for fitting such models that is based on the Laplace method for integrals that makes the consideration of high dimensional random-effects structures feasible. Contrary to the standard Laplace approximation, our method requires much fewer repeated measurements per individual to produce reliable results.