• Title, Summary, Keyword: Censored Data

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Estimation in the exponential distribution under progressive Type I interval censoring with semi-missing data

  • Shin, Hyejung;Lee, Kwangho
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.6
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    • pp.1271-1277
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    • 2012
  • In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

Estimation for the Power Function Distribution Based on Type- II Censored Samples

  • Kang, Suk-Bok;Jung, Won-Tae
    • Journal of the Korean Data and Information Science Society
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    • v.19 no.4
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    • pp.1335-1344
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    • 2008
  • The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.

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Nonpararmetric estimation for interval censored competing risk data

  • Kim, Yang-Jin;Kwon, Do young
    • Journal of the Korean Data and Information Science Society
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    • v.28 no.4
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    • pp.947-955
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    • 2017
  • A competing risk analysis has been applied when subjects experience more than one type of end points. Geskus (2011) showed three types of estimators of CIF are equivalent under left truncated and right censored data. We extend his approach to an interval censored competing risk data by using a modified risk set and evaluate their performance under several sample sizes. These estimators show very similar results. We also suggest a test statistic combining Sun's test for interval censored data and Gray's test for right censored data. The test sizes and powers are compared under several cases. As a real data application, the suggested method is applied a data where the feasibility of the vaccine to HIV was assessed in the injecting drug uses.

Normality of the MPLE of a Proportional Hazard Model for Informative Censored Data (정보적 중도절단을 고려한 최대 편우도 추정량의 정규성)

  • 정대현;원동유
    • Journal of Applied Reliability
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    • v.1 no.2
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    • pp.149-163
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    • 2001
  • We study the normality of the maximum partial likelihood estimators for the proportional hazard model with informative censored data. The proposed models cover the cases in which the times to a primary event may be informatively or randomly censored and the times to a secondary event may be randomly censored. To estimate the parameters and to check the normality of the parameters in the model, we adopt the partial likelihood and counting process to use the martingale central limit theorem. Simulation studies are performed to examine the normality of the MPLE's for the five cases in which they depend upon the proportions of randomly censored and informative censored data.

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Regression analysis of doubly censored failure time data with frailty time data with frailty

  • Kim Yang-Jin
    • Proceedings of the Korean Statistical Society Conference
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    • pp.243-248
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    • 2004
  • The timings of two successive events of interest may not be measurable, instead it may be right censored or interval censored; this data structure is called doubly censored data. In the study of HIV, two such events are the infection with HIV and the onset of AIDS. These data have been analyzed by authors under the assumption that infection time and induction time are independent. This paper investigates the regression problem when two events arc modeled to allow the presence of a possible relation between two events as well as a subject-specific effect. We derive the estimation procedure based on Goetghebeur and Ryan's (2000) piecewise exponential model and Gauss-Hermite integration is applied in the EM algorithm. Simulation studies are performed to investigate the small-sample properties and the method is applied to a set of doubly censored data from an AIDS cohort study.

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Regression analysis of interval censored competing risk data using a pseudo-value approach

  • Kim, Sooyeon;Kim, Yang-Jin
    • Communications for Statistical Applications and Methods
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    • v.23 no.6
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    • pp.555-562
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    • 2016
  • Interval censored data often occur in an observational study where the subject is followed periodically. Instead of observing an exact failure time, two inspection times that include it are available. There are several methods to analyze interval censored failure time data (Sun, 2006). However, in the presence of competing risks, few methods have been suggested to estimate covariate effect on interval censored competing risk data. A sub-distribution hazard model is a commonly used regression model because it has one-to-one correspondence with a cumulative incidence function. Alternatively, Klein and Andersen (2005) proposed a pseudo-value approach that directly uses the cumulative incidence function. In this paper, we consider an extension of the pseudo-value approach into the interval censored data to estimate regression coefficients. The pseudo-values generated from the estimated cumulative incidence function then become response variables in a generalized estimating equation. Simulation studies show that the suggested method performs well in several situations and an HIV-AIDS cohort study is analyzed as a real data example.

Comparing Imputation Methods for Doubly Censored Data

  • Yoo, Han-Na;Lee, Jae-Won
    • The Korean Journal of Applied Statistics
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    • v.22 no.3
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    • pp.607-616
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    • 2009
  • In many epidemiological studies, the occurrence times of the event of interest are right-censored or interval censored. In certain situations such as the AIDS data, however, the incubation period which is the time between HIV infection and the diagnosis of AIDS is usually doubly censored. In this paper, we impute the interval censored HIV infection time using three imputation methods. Mid imputation, conditional mean imputation and approximate Bayesian bootstrap are implemented to obtain right censored data, and then Gibbs sampler is used to estimate the coefficient factor of the incubation period. By using Bayesian approach, flexible modeling and the use of prior information is available. We applied both parametric and semi-parametric methods for estimating the effect of the covariate and compared the imputation results incorporating prior information for the covariate effects.

Goodness-of-Fit-Test from Censored Samples

  • Cho, Young-Suk
    • Journal of the Korean Data and Information Science Society
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    • v.17 no.1
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    • pp.41-52
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    • 2006
  • Because most common assumption is normality in statistical analysis, testing normality is very important. The Q-Q plot is a powerful tool to test normality with full samples in statistical package. But the plot can't test normality in type-II censored samples. This paper proposed the modified the Q-Q plot and the modified normalized sample Lorenz curve(NSLC) for normality test in the type-II censored samples. Using the two Hodgkin's disease data sets and the type-II censored samples, we picture the modified Q-Q plot and the modified normalized sample Lorenz curve.

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Reliability Estimation in Bivariate Pareto Model with Bivariate Type I Censored Data

  • Cho, Jang-Sik;Cho, Kil-Ho;Kang, Sang-Gil
    • Journal of the Korean Data and Information Science Society
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    • v.14 no.4
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    • pp.837-844
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    • 2003
  • In this paper, we obtain the estimator of system reliability for the bivariate Pareto model with bivariate type 1 censored data. We obtain the estimators and approximated confidence intervals of the reliability for the parallel system based on likelihood function and the relative frequency, respectively. Also we present a numerical example by giving a data set which is generated by computer.

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Reliability Estimation in Bivariate Pareto Model with Bivariate Type I Censored Data

  • Cho, Jang-Sik;Cho, Kil-Ho;Kang, Sang-Gil
    • 한국데이터정보과학회:학술대회논문집
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    • pp.31-38
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    • 2003
  • In this paper, we obtain the estimator of system reliability for the bivariate Pareto model with bivariate type 1 censored data. We obtain the estimators and approximated confidence intervals of the reliability for the parallel system based on likelihood function and the relative frequency, respectively. Also we present a numerical example by giving a data set which is generated by computer.

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