Department of Biostatistics, University of Michigan, Ann Arbor, MI, 48109, U.S.A.
Stat Med. 2013 Sep 30;32(22):3944-54. doi: 10.1002/sim.5834. Epub 2013 May 6.
We consider the problem of variable selection for monotone single-index models. A single-index model assumes that the expectation of the outcome is an unknown function of a linear combination of covariates. Assuming monotonicity of the unknown function is often reasonable and allows for more straightforward inference. We present an adaptive LASSO penalized least squares approach to estimating the index parameter and the unknown function in these models for continuous outcome. Monotone function estimates are achieved using the pooled adjacent violators algorithm, followed by kernel regression. In the iterative estimation process, a linear approximation to the unknown function is used, therefore reducing the situation to that of linear regression and allowing for the use of standard LASSO algorithms, such as coordinate descent. Results of a simulation study indicate that the proposed methods perform well under a variety of circumstances and that an assumption of monotonicity, when appropriate, noticeably improves performance. The proposed methods are applied to data from a randomized clinical trial for the treatment of a critical illness in the intensive care unit.
我们考虑单调单指标模型的变量选择问题。单指标模型假设结果的期望是协变量线性组合的未知函数。假设未知函数的单调性通常是合理的，并且允许更直接的推断。我们提出了一种自适应 LASSO 惩罚最小二乘法来估计连续结果模型中的索引参数和未知函数。单调函数估计是使用合并相邻违反者算法和核回归来实现的。在迭代估计过程中，使用未知函数的线性近似，因此将情况简化为线性回归，并允许使用标准 LASSO 算法，如坐标下降。模拟研究的结果表明，所提出的方法在各种情况下表现良好，并且在适当的情况下，单调性的假设显著提高了性能。所提出的方法应用于来自 ICU 中治疗危重病的随机临床试验的数据。
