Rosenberg P S
National Cancer Institute, Epidemiologic Methods Section, Rockville, Maryland 20852, USA.
Biometrics. 1995 Sep;51(3):874-87.
A flexible parametric procedure is given to model the hazard function as a linear combination of cubic B-splines and to obtain maximum likelihood estimates from censored survival data. The approach yields smooth estimates of the hazard and survivorship functions that are intermediate in structure between strongly parametric and non-parametric models. A simple method is described for selecting the number and location of knots. Simulation results show favorable root mean square error compared to non-parametric estimates for both the hazard and survivorship functions. Three methods are given to calculate confidence intervals based on the delta method, profile likelihood, and bootstrap, respectively. The procedure is applied to estimate hazard rates for acquired immunodeficiency syndrome (AIDS) following infection with human immunodeficiency virus (HIV). Spline methods can accommodate complex censoring mechanisms such as those that arise in the AIDS setting. To illustrate, HIV infection incidence is estimated for a cohort of hemophiliacs in which the dates of HIV infection are interval-censored and some subjects were born after the onset of the HIV epidemic.
给出了一种灵活的参数化方法，将风险函数建模为三次B样条的线性组合，并从删失生存数据中获得最大似然估计。该方法产生了风险函数和生存函数的平滑估计，其结构介于强参数模型和非参数模型之间。描述了一种选择节点数量和位置的简单方法。模拟结果表明，与风险函数和生存函数的非参数估计相比，均方根误差较小。分别给出了基于德尔塔方法、轮廓似然法和自助法计算置信区间的三种方法。该程序用于估计感染人类免疫缺陷病毒（HIV）后获得性免疫缺陷综合征（AIDS）的风险率。样条方法可以适应复杂的删失机制，如AIDS病例中出现的那些机制。为了说明这一点，对一组血友病患者的HIV感染发病率进行了估计，其中HIV感染日期为区间删失，且一些受试者在HIV流行开始后出生。
