Journal ArticleDOI
Nonparametric estimation of a multivariate distribution in the presence of censoring.
James A. Hanley,Milton N. Parnes +1 more
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It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function.Abstract:
This paper presents examples of situations in which one wishes to estimate a multivariate distribution from data that may be right-censored. A distinction is made between what we term 'homogeneous' and 'heterogeneous' censoring. It is shown how a multivariate empirical survivor function must be constructed in order to be considered a (nonparametric) maximum likelihood estimate of the underlying survivor function. A closed-form solution, similar to the product-limit estimate of Kaplan and Meier, is possible with homogeneous censoring, but an iterative method, such as the EM algorithm, is required with heterogeneous censoring. An example is given in which an anomaly is produced if censored multivariate data are analyzed as a series of univariate variables; this anomaly is shown to disappear if the methods of this paper are used.read more
Citations
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Journal ArticleDOI
Bivariate survival models induced by frailties
TL;DR: In this article, the authors consider the class of bivariate survival distributions that can arise in this way, and show that the observable bivariate distribution determines the unobserved frailty distribution up to a scale parameter.
Journal ArticleDOI
Kaplan-Meier Estimate on the Plane
TL;DR: In this article, the product integral representation of univariate survival functions is generalized to the bivariate case and used to determine identifiability of the survival function of the partially observed data.
Journal ArticleDOI
Covariance and survivor function estimation using censored multivariate failure time data
Ross L. Prentice,Jianwen Cai +1 more
TL;DR: In this article, the covariance between counting process martingales is used to characterize the dependence between two failure time variates, and a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function.
Journal ArticleDOI
Censoring distributions as a measure of follow-up in survival analysis.
TL;DR: Estimation procedures for both grouped-time (cohort) data and continuous data, and an application are given, suggesting that estimates of the censoring distribution provide a more useful measure of the follow-up.
References
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Book ChapterDOI
Nonparametric Estimation from Incomplete Observations
Edward L. Kaplan,Paul Meier +1 more
TL;DR: In this article, the product-limit (PL) estimator was proposed to estimate the proportion of items in the population whose lifetimes would exceed t (in the absence of such losses), without making any assumption about the form of the function P(t).
Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
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