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Confidence Intervals for Current Status Data

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  • MOULINATH BANERJEE
  • JON A. WELLNER

Abstract

. The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio‐based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio‐based intervals are preferable from several perspectives.

Suggested Citation

  • Moulinath Banerjee & Jon A. Wellner, 2005. "Confidence Intervals for Current Status Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(3), pages 405-424, September.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:3:p:405-424
    DOI: 10.1111/j.1467-9469.2005.00454.x
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    Cited by:

    1. Mei-Cheng Wang & Yuxin Zhu, 2022. "Bias correction via outcome reassignment for cross-sectional data with binary disease outcome," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 659-674, October.
    2. Sungwook Kim & Michael P. Fay & Michael A. Proschan, 2021. "Valid and approximately valid confidence intervals for current status data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 438-452, July.
    3. Choi, Byeong Yeob & Lee, Jae Won, 2019. "The isotonic regression approach for an instrumental variable estimation of the potential outcome distributions for compliers," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 134-144.
    4. Pramita Bagchi & Subhra Sankar Dhar, 2020. "A study on the least squares estimator of multivariate isotonic regression function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1192-1221, December.
    5. Azadbakhsh, Mahdis & Jankowski, Hanna & Gao, Xin, 2014. "Computing confidence intervals for log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 248-264.
    6. Somnath Datta & Rajeshwari Sundaram, 2006. "Nonparametric Estimation of Stage Occupation Probabilities in a Multistage Model with Current Status Data," Biometrics, The International Biometric Society, vol. 62(3), pages 829-837, September.

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