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添加74字节 、 2022年3月23日 (三) 21:05
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当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。
 
当研究人员不能进行控制实验,但有观测数据进行建模时,逆概率加权估计量可用于证明因果关系。因为假设治疗不是随机分配的,如果总体中的所有受试者被分配了任何一种治疗,则目标是估计反事实或潜在结果。
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Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d (independent and identically distributed)]] from unknown distribution P, where
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Suppose observed data are <math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math> drawn [[Independent and identically distributed random variables|i.i.d ()]] from unknown distribution P, where
 
* <math>X \in \mathbb{R}^{p}</math> covariates
 
* <math>X \in \mathbb{R}^{p}</math> covariates
 
* <math>A \in \{0, 1\}</math> are the two possible treatments.
 
* <math>A \in \{0, 1\}</math> are the two possible treatments.
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The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.
 
The goal is to estimate the potential outcome, Y^{*}\bigl(a\bigr), that would be observed if the subject were assigned treatment a. Then compare the mean outcome if all patients in the population were assigned either treatment: \mu_{a} = \mathbb{E}Y^{*}(a). We want to estimate \mu_a using observed data \{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}.
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假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布数据,其中
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假设观测数据是<math>\{\bigl(X_i,A_i,Y_i\bigr)\}^{n}_{i=1}</math>,这些数据是从未知的分布中抽取出来的独立同分布([[Independent and identically distributed random variables|independent and identically distributed, i.i.d]])数据,其中
 
* <math>X \in \mathbb{R}^{p}</math> 为协变量;  
 
* <math>X \in \mathbb{R}^{p}</math> 为协变量;  
 
* <math>A \in \{0, 1\}</math> 是两个可能的处理;
 
* <math>A \in \{0, 1\}</math> 是两个可能的处理;
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