Scharfstein D O, Tsiatis A A, Gilbert P B
Department of Biostatistics, Johns Hopkins School of Hygiene and Public Health, Baltimore, MD 21205, USA.
Lifetime Data Anal. 1998;4(4):355-91. doi: 10.1023/a:1009634103154.
The generalized odds-rate class of regression models for time to event data is indexed by a non-negative constant rho and assumes that [formula: see text] where g: rho(s) = log(rho-1(s-rho - 1)) for rho > 0, g0(s) = log(-logs), S(t[symbol: see text]Z) is the survival function of the time to event for an individual with q x 1 covariate vector Z, beta is a q x 1 vector of unknown regression parameters, and alpha(t) is some arbitrary increasing function of t. When rho = 0, this model is equivalent to the proportional hazards model and when rho = 1, this model reduces to the proportional odds model. In the presence of right censoring, we construct estimators for beta and exp(alpha(t)) and show that they are consistent and asymptotically normal. In addition, we show that the estimator for beta is semiparametric efficient in the sense that it attains the semiparametric variance bound.
用于事件发生时间数据的回归模型的广义优势比类别由一个非负常数rho索引，并假设[公式：见文本]，其中对于rho > 0，g: rho(s) = log(rho - 1(s - rho - 1))，g0(s) = log(-logs)，S(t[符号：见文本]Z)是具有q×1协变量向量Z的个体的事件发生时间的生存函数，beta是未知回归参数的q×1向量，alpha(t)是t的某个任意递增函数。当rho = 0时，该模型等同于比例风险模型；当rho = 1时，该模型简化为比例优势模型。在存在右删失的情况下，我们构造了beta和exp(alpha(t))的估计量，并证明它们是一致的且渐近正态。此外，我们表明beta的估计量在达到半参数方差界的意义上是半参数有效的。
