Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data

Yi Li, Ross L. Prentice and Xihong Lin

Biometrika, 2008, vol. 95, issue 4, 947-960

Abstract: 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. Copyright 2008, Oxford University Press.

Date: 2008
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