Yan Jun, Huang Jian
Department of Statistics, University of Connecticut, Unit 4120, Storrs, Connecticut 06269, USA.
Biometrics. 2009 Jun;65(2):431-40. doi: 10.1111/j.1541-0420.2008.01071.x. Epub 2008 May 10.
Marginal mean models of temporal processes in event time data analysis are gaining more attention for their milder assumptions than the traditional intensity models. Recent work on fully functional temporal process regression (TPR) offers great flexibility by allowing all the regression coefficients to be nonparametrically time varying. The existing estimation procedure, however, prevents successive goodness-of-fit test for covariate coefficients in comparing a sequence of nested models. This article proposes a partly functional TPR model in the line of marginal mean models. Some covariate effects are time independent while others are completely unspecified in time. This class of models is very rich, including the fully functional model and the semiparametric model as special cases. To estimate the parameters, we propose semiparametric profile estimating equations, which are solved via an iterative algorithm, starting at a consistent estimate from a fully functional model in the existing work. No smoothing is needed, in contrast to other varying-coefficient methods. The weak convergence of the resultant estimators are developed using the empirical process theory. Successive tests of time-varying effects and backward model selection procedure can then be carried out. The practical usefulness of the methodology is demonstrated through a simulation study and a real example of recurrent exacerbation among cystic fibrosis patients.
在事件时间数据分析中，时间过程的边际均值模型因其比传统强度模型假设条件更宽松而受到越来越多的关注。最近关于全函数时间过程回归（TPR）的研究通过允许所有回归系数非参数地随时间变化，提供了极大的灵活性。然而，现有的估计程序在比较一系列嵌套模型时，阻止了对协变量系数进行连续的拟合优度检验。本文提出了一种基于边际均值模型的部分函数TPR模型。一些协变量效应与时间无关，而其他协变量效应在时间上则完全未作规定。这类模型非常丰富，包括全函数模型和半参数模型作为特殊情况。为了估计参数，我们提出了半参数轮廓估计方程，通过迭代算法求解，从现有工作中全函数模型的一致估计开始。与其他变系数方法不同，不需要进行平滑处理。利用经验过程理论研究了所得估计量的弱收敛性。然后可以进行随时间变化效应的连续检验和向后模型选择程序。通过模拟研究和囊性纤维化患者反复加重的实际例子证明了该方法的实用性。
