Analysis of survival data with nonproportional hazard functions

Stablein, Donald M.; Carter, Walter H.; Novak, Joel W.

doi:10.1016/0197-2456(81)90005-2

Cited by 111 publications

(65 citation statements)

References 14 publications

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“…Firstly, we estimate two values of the reliability function using a nonparametric procedures. [6,36] show that the Compound Rayleigh model is acceptable for these data. Now, we suppose that the forty six patients are randomly grouped into 23 sets, with two patients in each ( = 2 k ), and the survival times for all sets are observed and listed in ascending order in Table 1.…”

Section: Symmetric Bayes Estimationmentioning

confidence: 99%

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Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Abushal¹

2011

OJS

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This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators have been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.

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Section: Symmetric Bayes Estimationmentioning

confidence: 99%

“…The original data is a subset of data reported by [6,36], represent the survival times in years of a gro f patients g 1.099.…”

Section: Symmetric Bayes Estimationmentioning

confidence: 99%

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Abushal¹

2011

OJS

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“…An interesting variation of the Cox model that overcomes the proportional hazard assumption is the stratified Cox model [Stablein et al 1981], which is used to account for variables that do not satisfy the proportionality assumption. In this case, the variables that do not satisfy this assumption are used to split the data set into different "strata."…”

Section: Cox Proportional Hazards Regression Modelmentioning

confidence: 99%

Modeling and managing changes in text databases

Ipeirotis

Ntoulas

Cho

et al. 2007

ACM Trans. Database Syst.

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Large amounts of (often valuable) information are stored in web-accessible text databases. "Metasearchers" provide unified interfaces to query multiple such databases at once. For efficiency, metasearchers rely on succinct statistical summaries of the database contents to select the best databases for each query. So far, database selection research has largely assumed that databases are static, so the associated statistical summaries do not evolve over time. However, databases are rarely static and the statistical summaries that describe their contents need to be updated periodically to reflect content changes. In this article, we first report the results of a study showing how the content summaries of 152 real web databases evolved over a period of 52 weeks. Then, we show how to use "survival analysis" techniques in general, and Cox's proportional hazards regression in particular, to model database changes over time and predict when we should update each This material is based upon work supported by the National Science Foundation under Grants Nos. IIS-97-33880, IIS-98-17434, IIS-0643846, IIS-0534784, and IIS-0347993. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org. content summary. Finally, we exploit our change model to devise update schedules that keep the summaries up to date by contacting databases only when needed, and then we evaluate the quality of our schedules experimentally over real web databases.

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“…The Cox proportional hazard model [3] has been the most widely used procedure over many years to estimate hazard ratio as well as construct its confidence interval, but the crucial assumption behind this procedure, proportional hazard assumption, may not be satisfied by data from epidemiologic studies or clinical trials, see the example provided by [25]. [26] derived two types of undersmoothed kernel confidence intervals for hazard ratio at a given time point t: one based on directly the asymptotic normality of kernel hazard ratio estimate and the other on the Fieller's transformation of hazard ratio estimator.…”

Section: Introductionmentioning

confidence: 99%

Empirical likelihood confidence intervals for ratio of hazard rates under right censorship

Jiang

2010

Statistics and Its Interface

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Hazard ratio is an important measure for relative difference between treatment groups in clinical trials or other types of studies with time-to-event as an endpoint. Nonparametric confidence intervals for hazard ratio were derived in [26] based on asymptotic normality of the kernel estimate for hazard ratio. Simulation studies found that, however, the actual coverage probabilities of these confidence intervals were still below the nominal level. In this paper, empirical likelihood ratio method is used to construct confidence intervals for hazard ratio functions under right censorship. The asymptotic distribution of the empirical likelihood ratio is established and simulation studies show that empirical likelihood method improves the coverage probabilities of confidence intervals based on asymptotic normality.AMS 2000 subject classifications: 60K35, 60K35, 60K35.

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Analysis of survival data with nonproportional hazard functions

Cited by 111 publications

References 14 publications

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

Modeling and managing changes in text databases

Empirical likelihood confidence intervals for ratio of hazard rates under right censorship

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