Targeted Minimum Loss Based Estimation of an Intervention Specific Mean Outcome
Targeted Minimum Loss Based Estimation of an Intervention Specific Mean Outcome
复制标题
基于目标最小损失的干预特定平均结果估计
DOI：
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Susan Gruber
中科院分区：
文献类型：
--
作者：
M. J. Laan;Susan Gruber
基于目标最小损失估计（TMLE）提供了一个模板，用于在半参数删失数据或因果推断模型中，基于来自该数据生成分布的独立同分布副本样本，构造数据生成分布的目标参数的半参数局部有效双稳健替代估计（货车der Laan和Rubin（2006）、货车der Laan（2008）、货车der Laan和Rose（2011））。TMLE要求1）将目标参数作为从单元数据结构的概率分布的典型无限维参数到参数空间中的特定映射写入，2）计算目标参数映射的路径导数的规范梯度/有效影响曲线，3）指定可能由未知“干扰”参数索引的该参数的损失函数，4）通过所选择的参数的初始/当前估计器的最不利参数子模型/路径，使得在零波动处的广义基于损失的分数的线性跨度包括有效影响曲线，以及5）更新算法，其涉及最不利参数子模型/路径的波动参数上的损失特定经验风险的迭代最小化。基于子模型和损失函数的评分条件4），由此得出无限维参数的所得估计量求解有效影响曲线（即，有效得分）方程，为通过在目标参数映射中插入无限维参数的更新估计量而获得的目标参数的相应替代估计量的双重稳健性和渐近有效性提供了基础。为了提高目标参数的TMLE的有限样本性能，尽可能低维地选择损失函数的参数和干扰参数是有意义的。受这一目标的启发，我们提出了一个特定的封闭形式TMLE的干预具体的平均结果的基础上，一般的纵向数据结构。我们还提出了这种类型的TMLE的其他因果参数的推广。该TMLE提供了货车der Laan和Gruber（2010）以及Stitelman和vanderLaan（2011）基于对数似然损失函数的封闭形式TMLE的替代方案。TMLE的理论性质也实际证明了一个小规模的模拟研究。拟议的TMLE建立在Bang和Robins（2005）之前提出的估计器的基础上，将其一些关键和创新的想法集成到TMLE框架中。
Targeted minimum loss based estimation (TMLE) provides a template for the construction of semiparametric locally efficient double robust substitution estimators of the target parameter of the data generating distribution in a semiparametric censored data or causal inference model based on a sample of independent and identically distributed copies from this data generating distribution (van der Laan and Rubin (2006), van der Laan (2008), van der Laan and Rose (2011)). TMLE requires 1) writing the target parameter as a particular mapping from a typically infinite dimensional parameter of the probability distribution of the unit data structure into the parameter space, 2) computing the canonical gradient/efficient influence curve of the pathwise derivative of the target parameter mapping, 3) specifying a loss function for this parameter that is possibly indexed by unknown “nuisance” parameters, 4) a least favorable parametric submodel/path through an initial/current estimator of the parameter chosen so that the linear span of the generalized loss-based score at zero fluctuation includes the efficient influence curve, and 5) an updating algorithm involving the iterative minimization of the lossspecific empirical risk over the fluctuation parameters of the least favorable parametric submodel/path. By the generalized loss-based score condition 4) on the submodel and loss function, it follows that the resulting estimator of the infinite dimensional parameter solves the efficient influence curve (i.e., efficient score) equation, providing the basis for the double robustness and asymptotic efficiency of the corresponding substitution estimator of the target parameter obtained by plugging in the updated estimator of the infinite dimensional parameter in the target parameter mapping. To enhance the finite sample performance of the TMLE of the target parameter, it is of interest to choose the parameter and the nuisance parameter of the loss function as low dimensional as possible. Inspired by this goal, we present a particular closed form TMLE of an intervention specific mean outcome based on general longitudinal data structures. %We also present its generalization of this type of TMLE to other causal parameters. This TMLE provides an alternative to the closed form TMLE presented in van der Laan and Gruber (2010) and Stitelman and vanderLaan (2011) based on the log-likelihood loss function. The theoretical properties of the TMLE are also practically demonstrated with a small scale simulation study. The proposed TMLE builds upon a previously proposed estimator by Bang and Robins (2005) by integrating some of its key and innovative ideas into the TMLE framework.
自然直接效应的目标最大似然估计。
DOI：
10.2202/1557-4679.1361
发表时间：
2012
期刊：
The international journal of biostatistics
影响因子：
--
作者：
Zheng,Wenjing;vanderLaan,MarkJ
通讯作者：
vanderLaan,MarkJ
影响因子：
0.8
作者：
Wang H;Rose S;van der Laan MJ
通讯作者：
van der Laan MJ
影响因子：
5.4
作者：
Hernán, MA;Brumback, B;Robins, JM
通讯作者：
Robins, JM