For random censoring independence of t and c is

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Unformatted text preview: lifetimes. For random censoring, independence of T and C is sufficient for it to be non-informative Examples Informative censoring: Withdrawal of life insurance policies: those in better health are more likely to withdraw. Non-informative censoring: The end of the investigation period. 6/42 Actuarial Statistics – Module 2: Non-parametric methods Censoring and truncation Truncation 1 Introduction 2 Censoring and truncation Censoring Truncation Likelihood for censored and truncated data 3 Estimating the lifetime distribution: non-parametric approach Preliminaries Maximum Likelihood with censoring The likelihood as a function of the discrete hazard function Kaplan-Meier (product limit) estimator Nelson-Aalen estimator 4 Comparing survival functions Introductory example A hypothesis test Special cases 7/42 Actuarial Statistics – Module 2: Non-parametric methods Censoring and truncation Truncation Truncation occurs when only those individual whose event times lies within a certain observation period (YL , YR ) are observed. Otherwise no information about this at all often confused with censoring: in presence of censoring at least partial information is available examples: A survival study of residents of a retirement center: individuals who died before the retirement age will not enter the center and thus are not in the study and are left truncated. Right truncation arises in estimating the distribution of stars from the earth in that stars too far away are not visible and are right truncated. 7/42 Actuarial Statistics – Module 2: Non-parametric methods Censoring and truncation Likelihood for censored and truncated data 1 Introduction 2 Censoring and truncation Censoring Truncation Likelihood for censored and truncated data 3 Estimating the lifetime distribution: non-parametric approach Preliminaries Maximum Likelihood with censoring The likelihood as a function of the discrete hazard function Kaplan-Meier (product limit) estimator Nelson-Aalen estimator 4 Comparing survival functions Introductory example A hypothesis test Special cases 8/42 Actuarial Statistics – Module 2: Non-parametric methods Censoring and truncation Likelihood for censored and truncated data Likelihood for censored and truncated data Likelihood for censored and truncated data Assume that lifetimes and censoring times are independent The likehood for the observation t , if if if if if it’s it’s it’s it’s it’s exact lifetime, f (t ) a right-censored observation, S (CR ) a...
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This document was uploaded on 04/03/2014.

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