Wynant Willy, Abrahamowicz Michal
Department of Epidemiology and Biostatistics, McGill University, Montreal, Quebec, H3A 1A2, Canada.
Division of Clinical Epidemiology, McGill University Health Centre, Montreal, Quebec, H3A 1A1, Canada.
Biom J. 2016 Nov;58(6):1445-1464. doi: 10.1002/bimj.201500035. Epub 2016 Aug 23.
Standard optimization algorithms for maximizing likelihood may not be applicable to the estimation of those flexible multivariable models that are nonlinear in their parameters. For applications where the model's structure permits separating estimation of mutually exclusive subsets of parameters into distinct steps, we propose the alternating conditional estimation (ACE) algorithm. We validate the algorithm, in simulations, for estimation of two flexible extensions of Cox's proportional hazards model where the standard maximum partial likelihood estimation does not apply, with simultaneous modeling of (1) nonlinear and time-dependent effects of continuous covariates on the hazard, and (2) nonlinear interaction and main effects of the same variable. We also apply the algorithm in real-life analyses to estimate nonlinear and time-dependent effects of prognostic factors for mortality in colon cancer. Analyses of both simulated and real-life data illustrate good statistical properties of the ACE algorithm and its ability to yield new potentially useful insights about the data structure.
用于最大化似然性的标准优化算法可能不适用于那些参数非线性的灵活多变量模型的估计。对于模型结构允许将相互排斥的参数子集的估计分离为不同步骤的应用，我们提出了交替条件估计（ACE）算法。我们在模拟中验证了该算法，用于估计Cox比例风险模型的两个灵活扩展，其中标准的最大偏似然估计不适用，同时对（1）连续协变量对风险的非线性和时间依赖性效应，以及（2）同一变量的非线性相互作用和主效应进行建模。我们还将该算法应用于实际分析，以估计结肠癌死亡率预后因素的非线性和时间依赖性效应。对模拟数据和实际数据的分析都说明了ACE算法良好的统计特性及其产生有关数据结构的新的潜在有用见解的能力。
