Free Knot Splines with RJMCMC in Survival Data Analysis

The B-spline representation is a common tool to improve the fitting of smooth nonlinear functions, it offers a fitting as a piecewise polynomial. The regions that define the pieces are separated by a sequence of knots. The main difficulty in this type of modeling is the choice of the number and the locations of these knots. The Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm provides a solution to simultaneously select these two parameters by considering the knots as free parameters. This algorithm belongs to the MCMC techniques that allow simulations from target distributions on spaces of varying dimension. The aim of the present investigation is to use this algorithm in the framework of the analysis of survival time, for the Cox model in particular. In fact, the relation between the hazard ratio function and the covariates being assumed to be log-linear, this assumption is too restrictive. Thus, we propose to use the RJMCMC algorithm to model the log hazard ratio function by a B-spline representation with an unknown number of knots at unknown locations. This method is illustrated with two real data sets: the Stanford heart transplant data and lung cancer survival data. Another application of the RJMCMC is selecting the significant covariates, and a simulation study is performed.     

LIKELIHOOD APPROXIMATIONS AND DISCRETE MODELS FOR TIED SURVIVAL DATA

ABSTRACT

Ties among event times are often recorded in survival studies. For example, in a two week laboratory study where event times are measured in days, ties are very likely to occur. The proportional hazards model might be used in this setting using an approximated partial likelihood function. This approximation works well when the number of ties is small. On the other hand, discrete regression models are suggested when the data are heavily tied. However, in many situations it is not clear which approach should be used in practice. In this work, empirical guidelines based on Monte Carlo simulations are provided. These recommendations are based on a measure of the amount of tied data present and the mean square error. An example illustrates the proposed criterion.     

Performance of standard imputation methods for missing quality of life data as covariate in survival analysis based on simulations from the International Breast Cancer Study Group Trials VI and VII*

Abstract

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.     

Joint modelling of longitudinal binary data and survival data

The medical costs in an ageing society substantially increase when the incidences of chronic diseases, disabilities and inability to live independently are high. Healthy lifestyles not only affect elderly individuals but also influence the entire community. When assessing treatment efficacy, survival and quality of life should be considered simultaneously. This paper proposes the joint likelihood approach for modelling survival and longitudinal binary covariates simultaneously. Because some unobservable information is present in the model, the Monte Carlo EM algorithm and Metropolis-Hastings algorithm are used to find the estimators. Monte Carlo simulations are performed to evaluate the performance of the proposed model based on the accuracy and precision of the estimates. Real data are used to demonstrate the feasibility of the proposed model.     

水下高围压射流模拟装置的工程设计及测试分析

设计了水下高围压射流模拟装置的主体部分和辅助部分。结合对模拟装置的理论模型分析。实验测试了水下高围压射流模拟装置伴随射流时内部的压力变化过程,并验证了理论模型。     

宇航精密仪表及零件用LY12铝合金的尺寸稳定性

综述了宇航精密仪表及零件用LY12铝合金的尺寸稳定性,分析了影响尺寸稳定性的因素,提出了改善尺寸稳定性的途径.     

戈德尔的市场自由道德理论评介

戴卫·戈德尔是继罗尔斯之后 ,对契约主义思想影响最大 ,同时也带来了最多争议的思想家之一。他从塑造理想市场的需要出发界说人的道德与理性 ,认为二者同市场的运行原则———有限制最大化是和谐一致的。道德与理性的一致性假设虽然能够有效解决市场分析中的市场失灵问题 ,但是 ,这一假设本身依赖于一个理想市场的优先存在。两个假设的相互依赖最终使得戈德尔的道德学说陷入了解释学的循环     

Monte carlo sampling approach to testing nonnested hypothesis: monte carlo results

Alternative ways of using Monte Carlo methods to implement a Cox-type test for separate families of hypotheses are considered. Monte Carlo experiments are designed to compare the finite sample performances of Pesaran and Pesaran's test, a RESET test, and two Monte Carlo hypothesis test procedures. One of the Monte Carlo tests is based on the distribution of the log-likelihood ratio and the other is based on an asymptotically pivotal statistic. The Monte Carlo results provide strong evidence that the size of the Pesaran and Pesaran test is generally incorrect, except for very large sample sizes. The RESET test has lower power than the other tests. The two Monte Carlo tests perform equally well for all sample sizes and are both clearly preferred to the Pesaran and Pesaran test, even in large samples. Since the Monte Carlo test based on the log-likelihood ratio is the simplest to calculate, we recommend using it.     

Choosing the Number of Instruments

Properties of instrumental variable estimators are sensitive to the choice of valid instruments, even in large cross‐section applications. In this paper we address this problem by deriving simple mean‐square error criteria that can be minimized to choose the instrument set. We develop these criteria for two‐stage least squares (2SLS), limited information maximum likelihood (LIML), and a bias adjusted version of 2SLS (B2SLS). We give a theoretical derivation of the mean‐square error and show optimality. In Monte Carlo experiments we find that the instrument choice generally yields an improvement in performance. Also, in the Angrist and Krueger (1991) returns to education application, when the instrument set is chosen in the way we consider, it turns out that both 2SLS and LIML give similar (large) returns to education.     

不公平有几何？——中国城市居民收入分配公平感的测量

文章首先通过批判性地介绍几种已有的公平感测量方法,选取其中最为合适的一种在CGSS2005数据基础上测量中国城市居民的反身性公平感和非反身性公平感。其次,分别以性别、年龄、教育和单位体制变量分组,从多方面呈现了两种公平感在中国的现状。最后,作者通过使用对总体样本进行随机性拆分得到的两个样本对此测量方法的信度进行了验证。