Study of an imputation algorithm for the analysis of interval-censored data

In this article, an iterative single-point imputation (SPI) algorithm, called quantile-filling algorithm for the analysis of interval-censored data, is studied. This approach combines the simplicity of the SPI and the iterative thoughts of multiple imputation. The virtual complete data are imputed by conditional quantiles on the intervals. The algorithm convergence is based on the convergence of the moment estimation from the virtual complete data. Simulation studies have been carried out and the results are shown for interval-censored data generated from the Weibull distribution. For the Weibull distribution, complete procedures of the algorithm are shown in closed forms. Furthermore, the algorithm is applicable to the parameter inference with other distributions. From simulation studies, it has been found that the algorithm is feasible and stable. The estimation accuracy is also satisfactory.

[1]  Debasis Kundu,et al.  Bayesian Inference and Life Testing Plan for the Weibull Distribution in Presence of Progressive Censoring , 2008, Technometrics.

[2]  Klaus Langohr,et al.  Tutorial on methods for interval-censored data and their implementation in R , 2009 .

[3]  G. C. Wei,et al.  Applications of multiple imputation to the analysis of censored regression data. , 1991, Biometrics.

[4]  Zehui Li,et al.  A New Algorithm for Maximum Likelihood Estimation with Progressive Type-I Interval Censored Data , 2010, Commun. Stat. Simul. Comput..

[5]  Yong Wang,et al.  Dimension-reduced nonparametric maximum likelihood computation for interval-censored data , 2008, Comput. Stat. Data Anal..

[6]  Hon Keung Tony Ng,et al.  Statistical estimation for the parameters of Weibull distribution based on progressively type-I interval censored sample , 2009 .

[7]  B. Turnbull.  The Empirical Distribution Function with Arbitrarily Grouped, Censored, and Truncated Data , 1976 .

[8]  Suk Joo Bae,et al.  Direct Prediction Methods on Lifetime Distribution of Organic Light-Emitting Diodes From Accelerated Degradation Tests , 2010, IEEE Transactions on Reliability.

[9]  D.,et al.  Regression Models and Life-Tables , 2022 .

[10]  Debasis Kundu,et al.  Parameter estimation of the hybrid censored log-normal distribution , 2011 .

[11]  Martin Abba Tanner,et al.  Tools for Statistical Inference: Observed Data and Data Augmentation Methods , 1993 .

[12]  Kathryn Chaloner,et al.  Imputation methods for doubly censored HIV data , 2009, Journal of statistical computation and simulation.

[13]  Jianguo Sun,et al.  The Statistical Analysis of Interval-censored Failure Time Data , 2006 .

[14]  Necip Doganaksoy,et al.  Weibull Models , 2004, Technometrics.

[15]  D. Rubin,et al.  Multiple Imputation for Interval Estimation from Simple Random Samples with Ignorable Nonresponse , 1986 .

[16]  R. Peto,et al.  Experimental Survival Curves for Interval‐Censored Data , 1973 .

[17]  Dragan Banjevic,et al.  Trend analysis of the power law process using Expectation-Maximization algorithm for data censored by inspection intervals , 2011, Reliab. Eng. Syst. Saf..

[18]  R. Anderson,et al.  An Estimation Problem in Life-Testing , 1971 .

[19]  Ling Chen,et al.  A multiple imputation approach to the analysis of interval-censored failure time data with the additive hazards model , 2010, Comput. Stat. Data Anal..

[20]  Deo Kumar Srivastava,et al.  The exponentiated Weibull family: a reanalysis of the bus-motor-failure data , 1995 .

[21]  Zhibin Tan,et al.  A new approach to MLE of Weibull distribution with interval data , 2009, Reliab. Eng. Syst. Saf..

[22]  Lixing Zhu,et al.  A k-sample test with interval censored data , 2006 .

[23]  Debasis Kundu,et al.  Inference Based on Type-II Hybrid Censored Data From a Weibull Distribution , 2008, IEEE Transactions on Reliability.

[24]  Samiran Ghosh.  An imputation-based approach for parameter estimation in the presence of ambiguous censoring with application in industrial supply chain , 2011 .

[25]  N. Balakrishnan,et al.  Progressive Censoring: Theory, Methods, and Applications , 2000 .

[26]  Richard J Cook,et al.  A Multistate Model for Bivariate Interval‐Censored Failure Time Data , 2008, Biometrics.

[27]  Martin A. Tanner,et al.  An application of imputation to an estimation problem in grouped lifetime analysis , 1987 .

[28]  Jian Huang,et al.  Efficient estimation for the proportional hazards model with interval censoring , 1996 .

[29]  K. Krishnamoorthy,et al.  CONFIDENCE LIMITS FOR STRESS STRENGTH RELIABILITY INVOLVING WEIBULL MODELS , 2010 .

[30]  Adriana Hornikova,et al.  Stochastic Ageing and Dependence for Reliability , 2007, Technometrics.

[31]  A multiple imputation approach for clustered interval‐censored survival data , 2010, Statistics in medicine.