Department of Biostatistics, University of Nebraska Medical Center, Omaha, NE, 68198, U.S.A.
Stat Med. 2014 May 10;33(10):1713-22. doi: 10.1002/sim.6057. Epub 2013 Dec 9.
In statistical analysis, a regression model is needed if one is interested in finding the relationship between a response variable and covariates. When the response depends on the covariate, then it may also depend on the function of this covariate. If one has no knowledge of this functional form but expect for monotonic increasing or decreasing, then the isotonic regression model is preferable. Estimation of parameters for isotonic regression models is based on the pool-adjacent-violators algorithm (PAVA), where the monotonicity constraints are built in. With missing data, people often employ the augmented estimating method to improve estimation efficiency by incorporating auxiliary information through a working regression model. However, under the framework of the isotonic regression model, the PAVA does not work as the monotonicity constraints are violated. In this paper, we develop an empirical likelihood-based method for isotonic regression model to incorporate the auxiliary information. Because the monotonicity constraints still hold, the PAVA can be used for parameter estimation. Simulation studies demonstrate that the proposed method can yield more efficient estimates, and in some situations, the efficiency improvement is substantial. We apply this method to a dementia study.
在统计分析中，如果人们有兴趣发现因变量和协变量之间的关系，就需要一个回归模型。当因变量取决于协变量时，它也可能取决于这个协变量的函数。如果人们对这个函数形式一无所知，但预期单调增加或减少，那么等单调回归模型就是首选。等单调回归模型的参数估计是基于池相邻违反者算法（PAVA），其中单调约束是内置的。在存在缺失数据的情况下，人们通常通过使用工作回归模型来结合辅助信息，采用增广估计方法来提高估计效率。然而，在等单调回归模型的框架下，PAVA 不起作用，因为单调约束被违反了。在本文中，我们开发了一种基于经验似然的方法，用于将辅助信息纳入等单调回归模型。因为单调约束仍然成立，所以可以使用 PAVA 进行参数估计。模拟研究表明，所提出的方法可以产生更有效的估计值，在某些情况下，效率的提高是显著的。我们将该方法应用于痴呆症研究。
