Abstract
We describe a simple method for nonparametric estimation of a distribution function based on current status data where observations of current status information are subject to misclassification. Nonparametric maximum likelihood techniques lead to use of a straightforward set of adjustments to the familiar pool-adjacent-violators estimator used when misclassification is assumed absent. The methods consider alternative misclassification models and are extended to regression models for the underlying survival time. The ideas are motivated by and applied to an example on human papilloma virus (HPV) infection status of a sample of women examined in San Francisco.
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Ayer M, Brunk HD, Ewing GM, Reid WT, Silverman E (1955) An empirical distribution function for sampling with incomplete information. Ann Math Stat 26: 641–647
Banerjee M, Wellner JA (2001) Likelihood ratio tests for monotone functions. Ann Stat 29: 1699–1731
Banerjee M, Wellner JA (2005) Confidence intervals for current status data. Scand J Stat 32: 405–424
Barlow RE, Bartholomew DJ, Bremner JM, Brunk HD (1972) Statistical inference under order restrictions. Wiley, New York
Becker NG (1989) Analysis of infectious disease data. Chapman and Hall, New York, NY
Diamond ID, McDonald JW, Shah IH (1986) Proportional hazards models for current status data: application to the study of differentials in age at weaning in Pakistan. Demography 23: 607–620
Groeneboom P, Wellner JA (1992) Nonparametric maximum likelihood estimators for interval censoring and denconvolution. Birkhäuser-Boston, Boston
Grummer-Straun LM (1993) Regression analysis of current status data: an application to breast-feeding. J Am Stat Assoc 88: 758–765
Hardin JW, Schmiediche H, Carroll RJ (2003) The Simulation Extrapolation method for fitting generalized linear models with additive measurement error. Stata J 3(4): 1–12
Jewell NP (2007) Correspondences between regression models for complex binary outcomes and those for structured multivariate survival analyses. In: Nair V (eds) Advances in statistical modeling and inference. World Scientific, Hackensack, New Jersey, pp 45–64
Jewell NP, van der Laan M (2004) Current status data: review, recent developments and open problems. In: Advances in survival analysis, handbook in statistics #23. Elsevier, Amsterdam, pp 625–642
Jewell NP, van der Laan M, Henneman T (2003) Nonparametric estimation from current status data with competing risks. Biometrika 90: 183–197
Keiding K (1991) Age-specific incidence and prevalence:a statistical perspective. J R Stat Soc A 154: 371–412
Küchenhoff H, Mwalili SM, Lesaffre E (2006) A general method for dealing with misclassification in regression: The misclassification SIMEX. Biometrics 62: 85–96
Moscicki AB, Shiboski S, Broering J, Powell K, Clayton L, Jay N, Darragh TM, Brescia R, Kanowitz S, Miller SB, Stone J, Hanson E, Palefsky J (1998) The natural history of human papillomavirus infection as measured by repeated DNA testing in adolescent and young women. J Pediatr 132: 277–284
Neuhaus JM (1999) Bias and efficiency loss due to misclassified responses in binary regression. Biometrika 86: 843–855
Politis DN, Romano JP, Wolf M (1999) Subsampling. Springer, New York
Sen B, Banerjee M, Woodroofe M (2010) Inconsistency of bootstrap: the Grenander estimator. Ann Stat, to appear
Shiboski SC (1998) Generalized additive models for current status data. Lifetime Data Anal 4: 29–50
Shiboski SC, Jewell NP (1992) Statistical analysis of the time dependence of HIV infectivity based on partner study data. J Am Stat Assoc 87: 360–372
Young JG, Jewell NP, Samuels SJ (2008) Regression analysis of a disease onset distribution using diagnosis data. Biometrics 64: 20–28
Acknowledgments
The authors wish to thank Dr. B. Moscicki for permission to use the HPV data, obtained with support from the National Institute of Health through grant #R37-CA51323. We also acknowledge support for this research from the National Institute of Allergy and Infectious Diseases through grant #R01-ES015493.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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McKeown, K., Jewell, N.P. Misclassification of current status data. Lifetime Data Anal 16, 215–230 (2010). https://doi.org/10.1007/s10985-010-9154-0
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DOI: https://doi.org/10.1007/s10985-010-9154-0