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11
Efficient Estimation from RightCensored Data when Failure Indicators are Missing at Random
, 1999
"... The KaplanMeier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed. It has been an open problem, however, to find an efficient estimator when failure indicators are missing at random. Lo (1991) showed that nonparametric maximum ..."
Abstract

Cited by 5 (1 self)
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The KaplanMeier estimator of a survival function is well known to be asymptotically efficient when cause of failure is always observed. It has been an open problem, however, to find an efficient estimator when failure indicators are missing at random. Lo (1991) showed that nonparametric maximum likelihood estimators are inconsistent, and this has led to several proposals of ad hoc estimators, none of which are efficient. We now introduce a sievednonparametric maximum likelihood estimator, and show that it is efficient. Our approach is related to the estimation of a bivariate survival function from bivariate rightcensored data.
Inconsistency of the MLE for the joint distribution of interval censored survival times
, 2007
"... and continuous marks ..."
Statistical Methods for Incomplete Or Indirectly Observable Data
"... Introduction This lecture is meant for students in the fourth or fifth year of their mathematics studies and Ph.D. students in their first two years, with basic knowledge of statistical estimation theory. We hope to give those students a glimpse of a very interesting research direction. Of course, ..."
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Introduction This lecture is meant for students in the fourth or fifth year of their mathematics studies and Ph.D. students in their first two years, with basic knowledge of statistical estimation theory. We hope to give those students a glimpse of a very interesting research direction. Of course, we cannot discuss this research direction in great detail, but hope that the examples covered will motivate the students for further study. In section 2, we will briefly review the definition of a maximum likelihood estimator in specific models. As far as parametric models are concerned, this will all be standard and known. For a nonparametric model, where we observe a sample from a distribution of which we do not want to assume anything in advance (like having a specific form as the exponential or normal distribution), we will argue that the empirical distribution function is the maximum likelihood estimator. What is important in this section is that the data that are available can b
Statistics In Medicine
"... this paper we extend Wei and Tanner's multiple imputation approach for linear regression with univariate censored data to bivariate censored data. We formulate a class of censored bivariate linear regression methods by iterating between the following two steps: 1, the data is augmented by imputing s ..."
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this paper we extend Wei and Tanner's multiple imputation approach for linear regression with univariate censored data to bivariate censored data. We formulate a class of censored bivariate linear regression methods by iterating between the following two steps: 1, the data is augmented by imputing survival times for censored observations; 2, a linear model is "t to the imputed complete data. We consider three di!erent methods to implement these two steps. In particular, the marginal (independence) approach ignores the possible correlation between two survival times when estimating the regression coe$cient. To improve the e$ciency, we propose two methods that account for the correlation between the survival times. First, we improve the e$ciency by using generalized least squares regression in step 2. Second, instead of generating data from an estimate of the marginal distribution we generate data from a bivariate logspline density estimate in step 1. Through simulation studies we "nd that the performance of the two methods that take the dependence into account is close and that they are both more e$cient than the marginal approach. The methods are applied to a data set from an otitis media clinical trial. Copyright # 1999 John Wiley & Sons, Ltd
Nonparametric . . . competing risks data
, 2006
"... While nonparametric analyses of bivariate failure times under independent censoring have been widely studied, nonparametric analyses of bivariate competing risks data have not been investigated. Such analyses are important in familial association studies, where multiple interacting failure types m ..."
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While nonparametric analyses of bivariate failure times under independent censoring have been widely studied, nonparametric analyses of bivariate competing risks data have not been investigated. Such analyses are important in familial association studies, where multiple interacting failure types may violate the independent censoring assumption. We develop nonparametric estimators for the bivariate causespecific hazards function and the bivariate cumulative incidence function, which are natural analogs of their univariate counterparts and make no assumptions about the dependence of the risks. The estimators are shown to be uniformly consistent and to converge weakly to Gaussian processes. Timedependent association measures are proposed, with the associated inferences yielding tests of causespecific independence in clusters. The methodology performs well in simulations with realistic sample sizes. Its practical utility is illustrated in an analysis of dementia in the Cache County Study, where the nonparametric methods indicate that disease associations are strongly timevarying.
unknown title
, 2008
"... Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks ..."
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Inconsistency of the MLE for the joint distribution of interval censored survival times and continuous marks
unknown title
, 2012
"... A generalization of KaplanMeier estimator for analyzing bivariate mortality under rightcensoring and lefttruncation with applications to modelchecking for survival copula models ..."
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A generalization of KaplanMeier estimator for analyzing bivariate mortality under rightcensoring and lefttruncation with applications to modelchecking for survival copula models