Reliability analysis of web server cluster systems based on proportional hazards model

An approach for web server cluster(WSC)reliability and degradation process analysis is proposed.The reliability process is modeled as a non-homogeneous Markov process(NHMH)composed of several non-homogeneous Poisson processes(NHPPs).The arrival rate of each NHPP corresponds to the system software failure rate which is expressed using Cox s proportional hazards model(PHM)in terms of the cumulative and instantaneous load of the software.The cumulative load refers to software cumulative execution time,and the instantaneous load denotes the rate that the users requests arrive at a server.The result of reliability analysis is a time-varying reliability and degradation process over the WSC lifetime.Finally,the evaluation experiment shows the effectiveness of the proposed approach.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

Penalized Empirical Likelihood Via Adaptive LASSO for Cox＇s Proportional Hazards Model

Penalized empirical likelihood inferential procedure is proposed for Cox＇s pro- portional hazards model with adaptive LASSO（ALASSO）. Under reasonable conditions, we show that the proposed method has oracle property and the limiting distribution of a penal- ized empirical likelihood ratio via ALASSO is a chi-square distributions. The advantage of penalized empirical likelihood is illustrated in testing hypothesis and constructing confidence sets by simulation studies and a real example.

The Additive-multiplicative Hazards Model for Multiple Type of Recurrent Gap Times

Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards functions, there exist two types of hazards models： the multiplicative hazards model and the additive hazards model. In the paper, we propose a more flexible additive-multiplicative hazards model for multiple type of recurrent gap times data, wherein some covariates are assumed to be additive while others are multiplicative. An estimating equation approach is presented to estimate the regression parameters. We establish asymptotic properties of the proposed estimators.

Exclusive Hypothesis Testing for Cox's Proportional Hazards Model

Exclusive hypothesis testing is a new and special class of hypothesis testing.This kind of testing can be applied in survival analysis to understand the association between genomics information and clinical information about the survival time.Besides,it is well known that Cox's proportional hazards model is the most commonly used model for regression analysis of failure time.In this paper,the authors consider doing the exclusive hypothesis testing for Cox's proportional hazards model with right-censored data.The authors propose the comprehensive test statistics to make decision,and show that the corresponding decision rule can control the asymptotic TypeⅠerrors and have good powers in theory.The numerical studies indicate that the proposed approach works well for practical situations and it is applied to a set of real data arising from Rotterdam Breast Cancer Data study that motivated this study.

Multivariate analysis by Cox Proportional Hazards Model on pro gnoses of patients with bile duct carcinoma after resection

OBJECTIVE: To evaluate the influence of various clinicopathologic factors on the survival of patients with bile duct carcinoma after curative resection. METHODS: A retrospective analysis was performed on 86 cases of bile duct carcinoma treated from January 1981 to September 1995. Fifteen clinicopathologic factors that could possibly influence survival were selected. A multivariate analysis of these individuals was performed using the Cox Proportional Hazards Model. RESULTS: The overall cumulative survival rate was 73% for 1 year, 32% for 3 years and 19% for 5 years. The results of univariate analysis showed that the major significant prognostic factors for influencing survival of these patients were type of histological lesion, lymph node metastasis, pancreatic invasion, duodenal invasion, perineural invasion, macroscopic vessel involvement, resected surgical margin and depth of cancer invasion (P

Multivariate analysis by Cox Proportional Hazards Model on prognoses of patients with bile duct carcinoma after resection

To evaluate the influence of various clinicopathologic factors on the survival of patients with bile duct carcinoma after curative resection Methods A retrospective analysis was performed on 86 cases of bile duct carcinoma treated from January 1981 to September 1995 Fifteen clinicopathologic factors that could possibly influence survival were selected A multivariate analysis of these individuals was performed using the Cox Proportional Hazards Model Results The overall cumulative survival rate was 73% for 1 year, 32% for 3 years and 19% for 5 years The results of univariate analysis showed that the major significant prognostic factors for influencing survival of these patients were type of histological lesion, lymph node metastasis, pancreatic invasion, duodenal invasion, perineural invasion, macroscopic vessel involvement, resected surgical margin and depth of cancer invasion ( P 【0 05) Pancreatic invasion, perineural invasion and lymph node metastases were the three most important prognostic factors determined by multivariate analysis using the Cox Proportional Hazards Model Conclusion Pancreatic invasion, perineural invasion and lymph node metastases are the most important prognostic factors for bile duct carcinoma after curative resection

SICA for Cox's Proportional Hazards Model with a Diverging Number of Parameters

The smooth integration of counting and absolute deviation （SICA） penalized variable selection procedure for high-dimensional linear regression models is proposed by Lv and Fan （2009）. In this article, we extend their idea to Cox＇s proportional hazards （PH） model by using a penalized log partial likelihood with the SICA penalty. The number of the regression coefficients is allowed to grow with the sample size. Based on an approximation to the inverse of the Hessian matrix, the proposed method can be easily carried out with the smoothing quasi-Newton （SQN） algorithm. Under appropriate sparsity conditions, we show that the resulting estimator of the regression coefficients possesses the oracle property. We perform an extensive simulation study to compare our approach with other methods and illustrate it on a well known PBC data for predicting survival from risk factors.

An Additive Hazards Model for Clustered Recurrent Gap Times

In this article, clustered recurrent gap time is investigated. A marginal additive haz- ards model is proposed without specifying the association of the individuals within the same cluster. The relationship among the gap times for the same individual is also left unspecified. An estimating equation-based inference procedure is developed for the model parameters, and the asymptotic proper- ties of the resulting estimators are established. In addition, a lack-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a clinic study on chronic granulomatous disease （CGD） is illustrated.

Additive-multiplicative Hazards Model for Case-Cohort Studies with Multiple Disease Outcomes

Case-cohort design is an efficient and economical design to study risk factors for diseases with expensive measurements, especially when the disease rate is low. When several diseases are of interest, multiple case-cohort design studies may be conducted using the same subcohort. To study the association between risk factors and each disease occurrence or death, we consider a general additive-multiplicative hazards model for case-cohort designs with multiple disease outcomes. We present an estimation procedure for the regression parameters of the additive-multiplicative hazards model, and show that the proposed estimator is consistent and asymptotically normal. Large sample approximation works well in finite sample studies in simulation. Finally, we apply the proposed method to a real data example for illustration.

Optimal Generalized Case-Cohort Analysis with Cox's Proportional Hazards Model

Generalized case-cohort design has been proved to be a cost-effective way to enhance the efficiency of large epidemiological cohort. In this article, we propose an inference procedure for estimating the unknown parameters in Cox＇s proportional hazards model in generalized case-cohort design and establish an optimal sample size allocation to achieve the maximum power at a given budget. The finite sample performance of the proposed method is evaluated through simulation studies. The proposed method is applied to a real data set from the National Wilm＇s Tumor Study Group.

Analyzing Right-Censored Length-Biased Data with Additive Hazards Model

Length-biased data are often encountered in observational studies, when the survival times are left-truncated and right-censored and the truncation times follow a uniform distribution. In this article, we propose to analyze such data with the additive hazards model, which specifies that the hazard function is the sum of an arbitrary baseline hazard function and a regression function of covariates. We develop estimating equation approaches to estimate the regression parameters. The resultant estimators are shown to be consistent and asymptotically normal. Some simulation studies and a real data example are used to evaluate the finite sample properties of the proposed estimators.

More Efficient Estimators for Marginal Additive Hazards Model in Case-cohort Studies with Multiple Outcomes

Case-cohort study designs are widely used to reduce the cost of large cohort studies. When several diseases are of interest, we can use the same subcohort. In this paper, we will study the casecohort design of marginal additive hazards model for multiple outcomes by a more efficient version. Instead of analyzing each disease separately, ignoring the additional exposure measurements collected on subjects with other diseases, we propose a new weighted estimating equation approach to improve the efficiency by utilizing as much information collected as possible. The consistency and asymptotic normality of the resulting estimator are established. Simulation studies are conducted to examine the finite sample performance of the proposed estimator, which confirm the efficiency gains.

The Proportional Hazards Model for Multiple Type Recurrent Gap Times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies,and often more than one type of recurrent events is of interest.In this paper,we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covaxiates on the censored event processes of interest.An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions.We examine asymptotic properties of the proposed estimators.Finite sample properties of these estimators are demonstrated by simulations.

Asymptotics on Semiparametric Analysis of Multivariate Failure Time Data Under the Additive Hazards Model

Many survival studies record the times to two or more distinct failures oneach subject. The failures may be events of different natures or may be repetitions of the same kindof event. In this article, we consider the regression analysis of such multivariate failure timedata under the additive hazards model. Simple weighted estimating functions for the regressionparameters are proposed, and asymptotic distribution theory of the resulting estimators are derived.In addition, a class of generalized Wald and generalized score statistics for hypothesis testingand model selection are presented, and the asymptotic properties of these statistics are examined.

Jackknifed random weighting for Cox proportional hazards model

The Cox proportional hazards model is the most used statistical model in the analysis of survival time data.Recently,a random weighting method was proposed to approximate the distribution of the maximum partial likelihood estimate for the regression coefficient in the Cox model.This method was shown not as sensitive to heavy censoring as the bootstrap method in simulation studies but it may not be second-order accurate as was shown for the bootstrap approximation.In this paper,we propose an alternative random weighting method based on one-step linear jackknife pseudo values and prove the second accuracy of the proposed method.Monte Carlo simulations are also performed to evaluate the proposed method for fixed sample sizes.

An Efficient Risk Estimator with External Information Under Additive Hazards Model

Rare event data is encountered when the events of interest occur with low frequency, and the estimators based on the cohort data only may be inefficient. However, when external information is available for the estimation, the estimators utilizing external information can be more efficient. In this paper, we propose a method to incorporate external information into the estimation of the baseline hazard function and improve efficiency for estimating the absolute risk under the additive hazards model. The resulting estimators are shown to be uniformly consistent and converge weakly to Gaussian processes. Simulation studies demonstrate that the proposed method is much more efficient. An application to a bone marrow transplant data set is provided.

A class of weighted estimating equations for additive hazards models with covariates missing at random

Missing covariate data arise frequently in biomedical studies.In this article,we propose a class of weighted estimating equations for the additive hazards regression model when some of the covariates are missing at random.Time-specific and subject-specific weights are incorporated into the formulation of weighted estimating equations.Unified results are established for estimating selection probabilities that cover both parametric and non-parametric modelling schemes.The resulting estimators have closed forms and are shown to be consistent and asymptotically normal.Simulation studies indicate that the proposed estimators perform well for practical settings.An application to a mouse leukemia study is illustrated.

Regression Analysis for the Additive Hazards Model with General Biased Survival Data

In survival analysis,data are frequently collected by some complex sampling schemes,e.g.,length biased sampling,case-cohort sampling and so on.In this paper,we consider the additive hazards model for the general biased survival data.A simple and unified estimating equation method is developed to estimate the regression parameters and baseline hazard function.The asymptotic properties of the resulting estimators are also derived.Furthermore,to check the adequacy of the fitted model with general biased survival data,we present a test statistic based on the cumulative sum of the martingale-type residuals.Simulation studies are conducted to evaluate the performance of proposed methods,and applications to the shrub and Welsh Nickel Refiners datasets are given to illustrate the methodology.

Hierarchically penalized additive hazards model with diverging number of parameters

In many applications,covariates can be naturally grouped.For example,for gene expression data analysis,genes belonging to the same pathway might be viewed as a group.This paper studies variable selection problem for censored survival data in the additive hazards model when covariates are grouped.A hierarchical regularization method is proposed to simultaneously estimate parameters and select important variables at both the group level and the within-group level.For the situations in which the number of parameters tends to∞as the sample size increases,we establish an oracle property and asymptotic normality property of the proposed estimators.Numerical results indicate that the hierarchically penalized method performs better than some existing methods such as lasso,smoothly clipped absolute deviation(SCAD)and adaptive lasso.