Li Yi, Prentice Ross L, Lin Xihong
Department of Biostatistics, Harvard School of Public Health and Dana-Farber Cancer Institute, 44 Binney Street, Boston, MA 02115, USA,
Biometrika. 2008 Dec;95(4):947-960. doi: 10.1093/biomet/asn049.
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 bivariate 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, the 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 also derived. The finite sample performance is evaluated via extensive simulations.
我们考虑一类用于右删失双变量失效时间的半参数正态变换模型。非参数风险率模型被变换为一个标准正态模型，并假定变换后的变量的双变量向量服从联合正态分布。开发了一种半参数极大似然估计程序，用于估计边际生存分布和成对相关参数。这产生了半参数正态变换模型相关参数的一个有效估计量，该参数刻画了双变量生存结果的双变量依赖性。此外，可以使用一种简单的正质量重新分布算法来实现估计程序。由于似然函数涉及无穷维参数，利用经验过程理论来研究所提出估计量的渐近性质，这些性质被证明是一致的、渐近正态的和半参数有效的。还推导了估计量方差的一个简单估计量。通过广泛的模拟评估了有限样本性能。
