Lam K F, Leung T L
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong.
Lifetime Data Anal. 2001 Mar;7(1):39-54. doi: 10.1023/a:1009673026121.
One major aspect in medical research is to relate the survival times of patients with the relevant covariates or explanatory variables. The proportional hazards model has been used extensively in the past decades with the assumption that the covariate effects act multiplicatively on the hazard function, independent of time. If the patients become more homogeneous over time, say the treatment effects decrease with time or fade out eventually, then a proportional odds model may be more appropriate. In the proportional odds model, the odds ratio between patients can be expressed as a function of their corresponding covariate vectors, in which, the hazard ratio between individuals converges to unity in the long run. In this paper, we consider the estimation of the regression parameter for a semiparametric proportional odds model at which the baseline odds function is an arbitrary, non-decreasing function but is left unspecified. Instead of using the exact survival times, only the rank order information among patients is used. A Monte Carlo method is used to approximate the marginal likelihood function of the rank invariant transformation of the survival times which preserves the information about the regression parameter. The method can be applied to other transformation models with censored data such as the proportional hazards model, the generalized probit model or others. The proposed method is applied to the Veteran's Administration lung cancer trial data.
医学研究的一个主要方面是将患者的生存时间与相关协变量或解释变量联系起来。在过去几十年中，比例风险模型得到了广泛应用，其假设协变量效应以乘法方式作用于风险函数，且与时间无关。如果患者随时间变得更加同质化，比如说治疗效果随时间下降或最终消失，那么比例优势模型可能更合适。在比例优势模型中，患者之间的优势比可以表示为其相应协变量向量的函数，其中，个体之间的风险比最终会收敛到1。在本文中，我们考虑对一个半参数比例优势模型的回归参数进行估计，该模型的基线优势函数是任意的非递减函数，但未明确指定。我们不使用确切的生存时间，而是仅使用患者之间的秩次信息。我们使用蒙特卡罗方法来近似生存时间的秩不变变换的边际似然函数，该变换保留了有关回归参数的信息。该方法可应用于其他带有删失数据的变换模型，如比例风险模型、广义概率单位模型等。所提出的方法应用于退伍军人管理局肺癌试验数据。
