Articles |
Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data
Department of Biostatistics, Harvard University, 44 Binney Street, Boston, Massachusetts 02115, U.S.A. yili{at}jimmy.harvard.edu
Fred Hutchinson Cancer Research Center, 1959 NE Pacific Street, Seattle, Washington 98195, U.S.A. rprentic{at}whi.org
Department of Biostatistics, Harvard School of Public Health, 655 Huntington Avenue, Boston, Massachusetts 02115, U.S.A. xlin{at}hsph.harvard.edu
Received for publication 1 July 2007. Revision received 1 March 2008.
We consider a class of semiparametric normal transformation models for right-censored bivariate failure times. Nonparametric hazard rate models are transformed to a standard normal model and a joint normal distribution is assumed for the bivariate vector of transformed variates. A semiparametric maximum likelihood estimation procedure is developed for estimating the marginal survival distribution and the pairwise correlation parameters. This produces an efficient estimator of the correlation parameter of the semiparametric normal transformation model, which characterizes the dependence of bivariate survival outcomes. In addition, a simple positive-mass-redistribution algorithm can be used to implement the estimation procedures. Since the likelihood function involves infinite-dimensional parameters, empirical process theory is utilized to study the asymptotic properties of the proposed estimators, which are shown to be consistent, asymptotically normal and semiparametric efficient. A simple estimator for the variance of the estimates is derived. Finite sample performance is evaluated via extensive simulations.
Key Words: Asymptotic normality • Bivariate failure time • Consistency • Semiparametric efficiency • Semiparametric maximum likelihood estimate • Semiparametric normal transformation
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