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Bivariate Current Status Data with Univariate Monitoring Times

Nicholas P. Jewell, Mark Van Der Laan and Xiudong Lei
Biometrika
Vol. 92, No. 4 (Dec., 2005), pp. 847-862
Published by: Oxford University Press on behalf of Biometrika Trust
Stable URL: http://www.jstor.org/stable/20441240
Page Count: 16
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Bivariate Current Status Data with Univariate Monitoring Times
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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.

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