Goodness of Fit Tests for Proportional Hazards Regression Models

We present a test of goodness of fit for the proportional hazard regression model. The test is based on a score statistic for testing against local mixture alternatives. Contrary to the findings of several other authors, we detect a significant lack of fit in Freireich's leukemia data.     

Relating Cox's Proportional Hazard Model to the Exponential Model for Survival

An approximate representation is given for the partial likelihood estimate of the regression coefficient in Cox's proportional hazard model which indicates how it measures the association between survival time and covariate. The case of a single covariate is concentrated on. The representation is closely related to the first step of a Newton-Raphson iteration, i.e. to the score test. A similar representation for the Feigl-Zelen exponential model shows that a similar type of association is being measured, if observed lifetimes are interpreted as expected lifetimes of ordered exponentials. Necessary and sufficient conditions for the existence of Cox's estimate in the simple case are also written down.     

An Asymptotically Optimal Adaptive Selection Procedure in the Proportional Hazards Model with Conditionally Independent Censoring

Assume k independent populations are given which are distributed according to R, …,R (ϑ_i ∈ Θ ⊆ R ). Taking samples of size n the population with the smallest ϑ-value is to be selected. Using the framework of Le Cam's decision theory (Le Cam , 1986; Strasser , 1985) under mild regularity assumptions, an asymptotically optimal selection procedure is derived for the sequence of localized models. In the proportional hazards model with conditionally independent censoring, an asymptotically optimal adaptive selection procedure is constructed by substituting the unknown nuisance parameter by a kernel estimator.     

Bayesian Approach to Proportional Odds Models for Survival Analysis

In this paper Bayesian approach is adopted to develop inferences about parameters in proportional odds models. Bayesian posterior intervals for coefficients in proportional odds models are derived by using approximation given in Pregibon (1981). The results are illustrated by using the lung cancer survival data reported by Prentice (1973).     

Cox回归模型在肝癌病人生存分析中应用的研究

生存时间是癌症患者和临床医师共同关心的焦点,也是临床癌症诊治工作的重要指标之一．生存分析是研究多种因素与生存时间的关系以及关系程度的大小．Cox回归模型是生存分析中常用的方法之一．本文利用Cox回归模型对786名肝癌患者进行生存分析,确定影响肝癌患者预后的主要因素是癌栓、肝癌部位、治疗方式、肝脏储备功能、端粒酶活性、细胞增殖活性、γ-GT(γ-谷氮酰转肽酶)、术后复发等．为临床研究延长肝癌病人的生存期,提高其生存率提供了有力的依据．     

Analysis of Dichotomized Factorial Data Using Cox's Proportional Hazards Model and Related Tests

This paper describes how Cox's Proportional Hazards model may be used to analyze dichotomized factorial data obtained from a right-censored epidemiological study where time to response is of interest. Exact maximum likelihood estimates of the relative mortality rates are derived for any number of prognostic factors, but for the sake of simplicity, the mathematical details are presented for the case of two factors. This method is not based on the life table procedure. Kaplan-Meier estimates are obtained for the survival function of the internal control population, Which are in turn used to determine the expected number of deaths in the study population. The asymptotic (large sample) joint sampling distribution of the relative mortality rates is derived and some relevant simultaneous and conditional statistical tests are discussed. The relative mortality rates of several prognostic factors may be jointly considered as the multivariate extension of the familiar standard mortality ratio (SMR) of epidemiological studies. A numerical example is discussed to illustrate the method.     

Analysis of Survival Data with Two Dependent Competing Risks

Here we consider a competing risks model where the two risks of interest are not independent. The dependence is due to the additive effect of an independent contaminating risk on two initially independent risks. The problem is identifiable when the three risks fllow independent exponential distributions and also when the two initial risks follow proportional hazards model. Procedures are suggested for estimation and testing hypotheses regarding the parameters of the three exponentials in the first can and the constant of proportionality in the second case, when the information available consists of the times to death and the causes of death of the individuals.     

The Analysis of Life Table and Follow-up Data with Covariates Using Poisson Regression Model

The Poisson regression model for the analysis of life table and follow-up data with covariates is presented. An example is presented to show how this technique can be used to construct a parsimonious model which describes a set of survival data. All parameters in the model, the hazard and survival functions are estimated by maximum likelihood.     

Fitting Survival Data to a Piecewise Linear Hazard Rate in the Presence of Covariates

This paper extends the work of KODLIN (1967), who proposed a method for analyzing patient survival data wherein the hazard rate was linearly related to the survival time. The present paper extends Kodlin's model to permit maximum likelihood estimation of the parameters so that covariate effects are included and the slope and intercept parameters are allowed to change over fixed intervals of the time domain of study. An illustration of the method using multiple myeloma data is given and the results are compared with those of Kodlin's model, the Feigl-Zelen, Zippin-Armitage model, the exponential model, and Cox's proportional hazards model.     

基于主成分分析水稻植株CH4排放估算模型

估算稻田甲烷（CH4）排放量是开展稻田甲烷排放研究的重要内容之一．通过观测南方红黄壤稻田不同水稻品种甲烷排放通量,测定了16个早稻、20个晚稻品种的植株节间组织的数量特征．选取株高、茎秆长度、茎秆维管束面积／茎壁横切面积、茎壁横切面积／节间横切面积、叶鞘横切面积／节间横切面积、气腔面积／茎壁横切面积、维管束总面积／茎壁横切面积等相关因子进行了主成分分析,建立基于水稻植株的CHa排放估算模型,早、晚稻估算模型相关系数分别为0．827、0．853．同时构造了综合评价函数,得出了水稻品种CH4排放综合分值,与实测结果相比较,吻合度较高．利用估算模型进行模拟,比较模拟值与实测值,相对误差较小,证明模型具有有效性和可行性,为估算水稻CH4排放提供参考依据,为评价水稻品种CH4排放高低提供经验参考．     

Principal Components of Electroencephalographic Spectrum as Markers of Opponent Processes Underlying Ultradian Sleep Cycles

Sleep-wake regulation involves reciprocal interactions between sleep- and wake-promoting processes that inhibit one another. To uncover the signatures of the opponent processes underlying ultradian sleep cycles, principal component analysis was performed on the sets of 16 single-Hz log-transformed electroencephalographic (EEG) power densities (1–16?Hz frequency range). Data were collected during unrestricted night sleep followed by 9 20-min naps (14 women aged 17–55 yrs) and during 12 20-min naps after either restriction or deprivation of sleep (9 males and 9 males, respectively, aged 18–22 yrs). It was found that any subset of power spectra could be reduced to the invariant four–principal component structure. The time courses of scores on these four components might be interpreted as the spectral EEG markers of the kinetics of two pairs of opponent chronoregulatory processes. In a sequence of ultradian sleep cycles, the 1st and 2nd components represent the alternations between competing drives for sleep and wakefulness, respectively, whereas the 3rd and 4th components reflect the alternations between light and deep sleep, respectively. The results suggest that principal component structuring of EEG spectrum can be employed for derivation of the parameters of the quantitative models conceptualizing the three major aspects of sleep-wake regulation—homeostatic, circadian, and ultradian processes. (Author correspondence: putilov@ngs.ru)     

Efficient computation of subset selection probabilities with application to Cox regression

An efficient method is presented to compute the probabilityof selection of a specified subset from the set of all subsetsof a fixed size where the subsets are taken from a populationwhose units have varying individual probabilities of selection.The problem is motivated by the computation of the exact marginallikelihood for the Cox proportional hazards model.     

Small Sample Properties of the Likelihood Estimator in Proportional Hazard Regression Models with Omitted Variables

The paper deals with the effects of incorrectly omitted regressor variables in a parametric proportional hazard regression model. By studying conditions for equality between the estimators of correct and incorrect models it is demonstrated analytically that such cases are not to be expected in practise. A small sample Monte Carlo experiment indicates severe negative effects on the retained parameters both in terms of bias and mean square error.     

A modification of the redistribution to the right algorithm using disease markers

Disease markers are time-dependent covariates which describeprogression towards development of disease. Traditional methodsin survival analysis do not make use of available data on thesemarkers to recover additional information from censored individuals.Using a heuristic modification of the redistribution to theright algorithm (Efron, 1967), a new approach for recoveringinformation for censored individuals using disease markers isproposed. Additionally, the statistical properties of the proposedmethod are examined. There are two possible advantages to thismodification: (i) bias reduction when censoring is informative,and (ii) an increase in efficiency in the case of truly noninformativecensoring.     

A Flexible Alternative to the Cox Proportional Hazards Model for Assessing the Prognostic Accuracy of Hospice Patient Survival

Prognostic models are often used to estimate the length of patient survival. The Cox proportional hazards model has traditionally been applied to assess the accuracy of prognostic models. However, it may be suboptimal due to the inflexibility to model the baseline survival function and when the proportional hazards assumption is violated. The aim of this study was to use internal validation to compare the predictive power of a flexible Royston-Parmar family of survival functions with the Cox proportional hazards model. We applied the Palliative Performance Scale on a dataset of 590 hospice patients at the time of hospice admission. The retrospective data were obtained from the Lifepath Hospice and Palliative Care center in Hillsborough County, Florida, USA. The criteria used to evaluate and compare the models'' predictive performance were the explained variation statistic R², scaled Brier score, and the discrimination slope. The explained variation statistic demonstrated that overall the Royston-Parmar family of survival functions provided a better fit (R² = 0.298; 95% CI: 0.236–0.358) than the Cox model (R² = 0.156; 95% CI: 0.111–0.203). The scaled Brier scores and discrimination slopes were consistently higher under the Royston-Parmar model. Researchers involved in prognosticating patient survival are encouraged to consider the Royston-Parmar model as an alternative to Cox.     

Rank Covariance Methods for the Analysis of Survival Data

A procedure for comparing survival times between several groups of patients through rank analysis of covariance was introduced by WOOLSON and LACHENBRUCH (1983). It is a modification of Quade' rank analysis of covariance procedure (1967) and can be used for the analysis of right-censored data. In this paper, two additional modifications of Quade' original test statistic are proposed and compared to the original modification introduced by Woolson and Lachenbruch. These statistics are compared to one another and to the score test from Cox' proportional hazards model by way of a limited Monte Carlo study. One of the statistics, Q_R2, is recommended for general use for the rank analysis of covariance of right-censored survivorship data.