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Bivariate current status data with univariate monitoring times

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  • Nicholas P. Jewell
  • Mark van der Laan
  • Xiudong Lei

Abstract

For bivariate current status data with univariate monitoring times, the identifiable part of the joint distribution is three univariate cumulative distribution functions, namely the two marginal distributions and the bivariate cumulative distribution function evaluated on the diagonal. We show that smooth functionals of these univariate cumulative distribution functions can be efficiently estimated with easily computed nonparametric maximum likelihood estimators based on reduced data consisting of univariate current status observations. This theory is then applied to functionals that address independence of the two survival times and the goodness-of-fit of a copula model used by Wang & Ding (2000). Some brief simulations are provided along with an illustration based on data on HIV transmission. Extension of the ideas to incorporate covariates, possibly time-dependent, are discussed. Copyright 2005, Oxford University Press.

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  • Nicholas P. Jewell & Mark van der Laan & Xiudong Lei, 2005. "Bivariate current status data with univariate monitoring times," Biometrika, Biometrika Trust, vol. 92(4), pages 847-862, December.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:4:p:847-862
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    File URL: http://hdl.handle.net/10.1093/biomet/92.4.847
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    Cited by:

    1. Hao Liu & Jing Qin, 2018. "Semiparametric probit models with univariate and bivariate current†status data," Biometrics, The International Biometric Society, vol. 74(1), pages 68-76, March.
    2. Yujie Zhong & Richard J. Cook, 2018. "Second-Order Estimating Equations for Clustered Current Status Data from Family Studies Using Response-Dependent Sampling," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 160-183, April.
    3. Jessica G. Young & Nicholas P. Jewell & Steven J. Samuels, 2008. "Regression Analysis of a Disease Onset Distribution Using Diagnosis Data," Biometrics, The International Biometric Society, vol. 64(1), pages 20-28, March.

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