观察性研究中的因果推断方法二分钟

1、会计学1观察性研究中的因果推断方法二分钟观察性研究中的因果推断方法二分钟第1页/共44页2Outline1234Causal Effect Identification-in the Perspective of Causal diagram Causal diagramDirected Acyclic Graphs (DAG)AcknowledgementIntroduction to strategies for causal inferences 第2页/共44页 Motivation in epidemiological resrarchs Motivation in epidemio

2、logical resrarchs BL De Stavola | Causal modellingIntroduction to strategies for causal inferences 第3页/共44页 因果推断的四种基本策略因果推断的四种基本策略l 因果图病因模型（因果图病因模型（casual diagramcasual diagram）：）： 优优点是利用点是利用“图图+ +概率概率”的方式直观清晰的表达变的方式直观清晰的表达变量之间的时序关系、相关关系或因果关系等多种量之间的时序关系、相关关系或因果关系等多种语义，特别清晰地表达交互效应、效应修饰、中语义，特别清晰地表达交互效

3、应、效应修饰、中介效应、混杂偏倚、选择偏倚和信息偏倚等多种介效应、混杂偏倚、选择偏倚和信息偏倚等多种因果推断关键问题。缺点是主要适于分类变量间因果推断关键问题。缺点是主要适于分类变量间的因果推断。的因果推断。l 反事实病因模型（反事实病因模型（potential-outcome potential-outcome counterfactual) modelscounterfactual) models）：）：我们只能得到个体我们只能得到个体u u受到干预的数据受到干预的数据YtYt，或者个体，或者个体u u没有受到干预的没有受到干预的数据数据YcYc，但不能同时得到这两个数据。因此，在，但不能

4、同时得到这两个数据。因此，在没有假设的前提下，不可能在个体层面上进行因没有假设的前提下，不可能在个体层面上进行因果推断。方法是假设两个个体是相同的，采用人果推断。方法是假设两个个体是相同的，采用人工随机化或自然随机化方式分组，观察暴露与结工随机化或自然随机化方式分组，观察暴露与结局的因果关系。优点是能定量分析因果关系。局的因果关系。优点是能定量分析因果关系。Greenland S, et al. Int J Epidemiol. 2002;31(5):1030-7.4Introduction to strategies for causal inferences 第4页/共44页 因果推断的四

5、种基本策略因果推断的四种基本策略l 充分充分/ /组合病因模型（组合病因模型（ sufficient-component sufficient-component cause models cause models ）：）：任何疾病涉及许多组合病因的任何疾病涉及许多组合病因的结合结合, , 而这些病因成分的联合作用而这些病因成分的联合作用, , 即充分病因即充分病因自身的群集效应。在解释一些复杂病因关系上自身的群集效应。在解释一些复杂病因关系上, , 具有很好的直观性和合理性具有很好的直观性和合理性, , 是病因网说的一大是病因网说的一大发展发展, , 并具有一定的疾病防治意义。并具有一定的疾

6、病防治意义。l 结构方程病因模型（结构方程病因模型（structural-equations structural-equations modelsmodels）：）：主要是为了验证假设的因果关系主要是为了验证假设的因果关系，融，融合了因素分析和路径分析的多元统计技术，整合合了因素分析和路径分析的多元统计技术，整合了由因子分析所代表的潜在变量研究模型与路径了由因子分析所代表的潜在变量研究模型与路径分析所代表的传统线性因果关系模型，特别适于分析所代表的传统线性因果关系模型，特别适于定量因果关系的验证。定量因果关系的验证。Greenland S, et al. Int J Epidemiol. 2

7、002;31(5):1030-7.5Introduction to strategies for causal inferences 第5页/共44页Introduction to strategies for causal inferences Denitions of causation in the statistical literature Denitions of causation in the statistical literature BL De Stavola | Causal modelling第6页/共44页Causal diagramCausal Directed

8、Acyclic Graphs (DAG) Denitions of causation in the statistical literature Denitions of causation in the statistical literature BL De Stavola | Causal modelling第7页/共44页Causal diagramCausal Directed Acyclic Graphs (DAG) Denitions of causation in the statistical literature Denitions of causation in the

9、 statistical literature BL De Stavola | Causal modellingn Causal graph models (Judea Pearls framework)directed acyclic graph第8页/共44页Mathematically formalized bynPearl (1988, 1995, 2000)nSprites, Glymour, and Scheines (1993, 2000)9University of California, Los Angeles(UCLA)Causal diagramCausal Direct

10、ed Acyclic Graphs (DAG)n Causal graph models (Judea Pearls framework)第9页/共44页10Causal diagramCausal Directed Acyclic Graphs (DAG)n Causal graph models (Judea Pearls framework)BL De Stavola | Causal modelling第10页/共44页11Causal diagramCausal Directed Acyclic Graphs (DAG) Why DAGs?E. Versio

11、n 5/2013 ngn DAGs graphically represent non-parametric structural equation models. They may look like the path models of yore, but they are far more general.Rigorous mathematical objects, support proofs Very general (nonparametric) For many purposes, DAGs are more accessible than potential outcomes

12、notation All pictures, no algebra Focus attention on causal assumptions (language of applied scientists) Great for deriving (nonparametric) identification results Great for deriving the testable implications of a causal model Intuition for understanding many problems in causal inference. Particularl

13、y helpful for complex causal models Limitations Dont display the parametric assumptions that are oftennecessary for estimation in practice. Generality can obscure important distinctions betweenestimands.第11页/共44页 Causal diagramCausal Directed Acyclic Graphs (DAG) R1D1S1D2R2D1dxD2dxS2I1I2?An Example:

14、 An Example: a causal diagram for a causal diagram for gastroesophageal reflux(gastroesophageal reflux(胃胃食管反流食管反流) and esophageal ) and esophageal diseasedisease（食管疾病）（食管疾病）. .R=reflux (反流)S=symptoms（症状）T=treatment（治疗）I=imaging（影像表型）D=esophagus status （食管病变）Ddx=diagnosed esophagus status （诊断）TCausal

15、 diagramCausal Directed Acyclic Graphs (DAG)第12页/共44页因果图的基本概念（causal diagrams）（空气污染水平）（性别）（支气管反应）（抗哮喘治疗）（哮喘发作）l 因果图是根据变量之间的因果假定关系而因果图是根据变量之间的因果假定关系而抽象出来的一种图模型。图抽象出来的一种图模型。图1是一个假定的是一个假定的因果图，借此说明因果图的基本术语：因果图，借此说明因果图的基本术语： 边（边（edge）: 是连接两个变量之间的线或是连接两个变量之间的线或箭头。如果两个变量（如箭头。如果两个变量（如AC）直接被边）直接被边相连，则称其为相连，则

16、称其为邻接（邻接（adjacent），），否则称否则称为不邻接（如为不邻接（如A与与D）。直接连接两个变量）。直接连接两个变量的单项箭头表示变量之间的的单项箭头表示变量之间的直接因果关系直接因果关系（例如（例如AC ）。）。 顶点（note）: 是因果图中的变量（例如，图1中的A、B、C、E、D）。 路（path）: 是由正向箭头（）、反向箭头（）或连线（）不间断地连接若干“点”而形成的路线。如，E C D、 A C D、B C E D。路中的点称为截断（intercept），例如，路 A C D被C截断。引自：Greenland S. Epidemiology.1999;10(1):37-4

17、813Causal diagramCausal Directed Acyclic Graphs (DAG)第13页/共44页因果图的基本概念（因果图的基本概念（causal diagrams）（空气污染水平）（性别）（支气管反应）（抗哮喘治疗）（哮喘发作） 因果路（因果路（causal path）:是由一系列同向单是由一系列同向单向箭头相继连接若干点而成的路。例如，向箭头相继连接若干点而成的路。例如， A C D是因果路，而是因果路，而E C D则不是因则不是因果路。果路。 祖先节点（祖先节点（ ancestor node ）和和后代节点后代节点（descendant node）: 在从变量在

18、从变量X . 变变量量Y的因果路中，变量的因果路中，变量X叫做变量叫做变量Y的祖先节的祖先节点，而变量点，而变量Y叫做变量叫做变量X的后代节点。例如，的后代节点。例如，A、B、C均是均是E、D的祖先节点，而的祖先节点，而E、D则则均是均是A、B、C的后代节点。的后代节点。引自：Greenland S. Epidemiology.1999;10(1):37-48 父母节点（父母节点（parent node）和和子女节点子女节点(child node)：连接变量：连接变量X与变量与变量Y的直的直接因果路接因果路X Y中的变量中的变量X叫做变量叫做变量Y父母节点，而变量父母节点，而变量Y叫做变量叫做

19、变量X的子女节的子女节点。例如，点。例如，A、C是是E的父母节点，而的父母节点，而C、E是是A的子女节点。的子女节点。14Causal diagramCausal Directed Acyclic Graphs (DAG)第14页/共44页因果图的基本概念（因果图的基本概念（causal diagrams）（空气污染水平）（A和B共享的共同祖先节点集）（支气管反应）（抗哮喘治疗）（哮喘发作） 共享祖先节点（共享祖先节点（sharing ancestors）: 在因果图中连接两个变量在因果图中连接两个变量X、Y之间的之间的双向箭头（双向箭头（X Y）通常用于表示这）通常用于表示这两个变量共享一个

20、或多个祖先节点两个变量共享一个或多个祖先节点（共同原因），但这些祖先节点以及（共同原因），但这些祖先节点以及它们之间的内在关系在因果图中未表它们之间的内在关系在因果图中未表示出来（未观察或测量）。通常，在示出来（未观察或测量）。通常，在因果图中用因果图中用带有虚线箭头的字母带有虚线箭头的字母U表示表示这些未加定义的共享祖先，这些未加定义的共享祖先，U可能是多可能是多个变量。个变量。引自：Greenland S. Epidemiology.1999;10(1):37-48（性别）例如，例如，在空气污染水平高的时期内，儿童在家避免户外活动，既可以减少污染物在空气污染水平高的时期内，儿童在家避免户外

21、活动，既可以减少污染物暴露水平，有可以独立地减少过敏原接触机会而降低哮喘发作风险。暴露水平，有可以独立地减少过敏原接触机会而降低哮喘发作风险。15Causal diagramCausal Directed Acyclic Graphs (DAG)第15页/共44页因果图的基本概念（因果图的基本概念（causal diagrams）（空气污染水平）（性别）（抗哮喘治疗）（哮喘发作） 关联（关联（association ）: 两个变量间不带箭两个变量间不带箭头的连接（头的连接（XY）表示因某种原因具有相）表示因某种原因具有相关性而非共享祖先节点或一个影响到另一关性而非共享祖先节点或一个影响到另一个

22、变量。通常，用不带箭头的虚线表示在个变量。通常，用不带箭头的虚线表示在因果图中为关联原因未定义（或未测量）。因果图中为关联原因未定义（或未测量）。图图3中定义了中定义了A和和B之间的关联性，但其原之间的关联性，但其原因未观察或测量。因未观察或测量。引自：Greenland S. Epidemiology.1999;10(1):37-48 有向无环图（有向无环图（directed acyclic graphy, DAG）: 所有边均带箭头的图叫所有边均带箭头的图叫有向图有向图，即有向图中不含无方向的边；而，如果一个有向图无法从某个顶点出发经过若干即有向图中不含无方向的边；而，如果一个有向图无法从

23、某个顶点出发经过若干条边回到该点，则这个图是一个有向无环图（条边回到该点，则这个图是一个有向无环图（DAG）。例如，）。例如，图图1和和图图2均为有均为有向无环图。向无环图。 DAGs是因果推断的基本模型。是因果推断的基本模型。16Causal diagramCausal Directed Acyclic Graphs (DAG)第16页/共44页17 Directed Acyclic Graphs（DAGs）and Causal DAGs n DAGs are “directed” in that each arrow is single headed, expressing a singl

24、e causal statement, e.g. T directly causes C. (Well meet bi-headed arrows later.)n DAGs are “acyclic” in that they contain no directed(“The future cannot directly or indirectly cause the past.”). n Causal DAGs include all common causes of any pair of variables already included in the DAG. . E.g., th

25、ere is no variable U3 with direct effects into U2 and T.n Causal DAGs encode the qualitative causal assumptions of the data-enerating model (“model-of-how-the-world-works”) against which all inferences must be judged. n Specifically, the DAG must capture the causal structure of 1). How the variables

26、 take their values in “nature”; 2). What variables and values are ollectedCausal diagramCausal Directed Acyclic Graphs (DAG)第17页/共44页因果图的基本概念（因果图的基本概念（causal diagrams） 后门路（后门路（backdoor path）: 因果图因果图1，从，从E到到D的所的所有路中，有箭头指向有路中，有箭头指向E的所有非因果路，叫后门路。的所有非因果路，叫后门路。包括：包括：EACD、ECD、ECBD、EACBD。 前门路（前门路（frontdoor

27、 path）: 因果图因果图1中，从中，从A到到D的所有路中，从的所有路中，从A发出的所有非直接因果路，叫前发出的所有非直接因果路，叫前门路。包括：门路。包括：ACD、AC ED、AED、ACBD。 碰撞节点（碰撞节点（collides）: 在后门路在后门路EACBD中，有中，有2个箭头同时指向个箭头同时指向C，则，则C称为碰撞节点。称为碰撞节点。引自：Greenland S. Epidemiology.1999;10(1):37-48（空气污染水平）（支气管反应）（抗哮喘治疗）（哮喘发作）（性别） 阻塞路（阻塞路（blocked path）和未阻塞路（）和未阻塞路（unblocked pat

28、h）: 如果某通路中含有一如果某通路中含有一个或多个碰撞节点，则该路为个或多个碰撞节点，则该路为阻塞路阻塞路，否则为，否则为未阻塞路未阻塞路。例如，图。例如，图1中的后门路中的后门路EACBD在在C处被阻塞，而路处被阻塞，而路E A C D为未阻塞路，因为该路中为未阻塞路，因为该路中不含任何碰撞节点。不含任何碰撞节点。18Causal diagramCausal Directed Acyclic Graphs (DAG)第18页/共44页 Causal diagram (DAG)-Paths and its Colliders n n Target path: X Y Causal diagr

29、amCausal Directed Acyclic Graphs (DAG)第19页/共44页n Back-door path: A path that connects X to Y is a back-door path from X to Y if it has an arrowhead pointing to X. e.g. X U1Y; X U2Y. n Front-door path: A path that connects X to Y is a front-door path from X to Y if it has an non-direct causal path ar

30、rowhead emanating from X. e.g. X T C Y. n Blocked path & Unblocked path: A path is blocked if it has one or more colliders; otherwise it is unblocked. e.g. U1 X U2. n Conditioning: Examining the distribution of one variable within levels of another by regression adjustment, stratification, restr

31、iction(Subgroup analysis), or caused by Sample selection, Attrition, censoring, nonresponse. 20 Causal diagram (DAG)- backdoor path & frontdoor pathTarget path: X Y n Causal path: A directed path from X node to Y is one that can be traced through a sequence of single headed arrows, always enteri

32、ng an arrow through the tail and leaving through the head; X T C Y. .XYCausal diagramCausal Directed Acyclic Graphs (DAG)第20页/共44页 Causal diagram - causal paths, confounding paths and colliding causal paths, confounding paths and colliding pathspaths.n All DAGs can be constructed from just three ele

33、mentscausal paths, confounding paths and colliding pathsthe very elements that give rise to all associations via causation, confounding and collider variable. causal pathconfounding path colliding paths Sources of Association Between Two Variables A & BCausal diagramCausal Directed Acyclic Graph

34、s (DAG)第21页/共44页 Causal diagram - causal paths, confounding paths and colliding causal paths, confounding paths and colliding pathspaths.causal pathconfounding path colliding paths Sources of Bias in Estimating the Causal Effect of A on B0|,ACE B A CAC01BACBPLogitACP01BABPLogitAPCausal diagramCausal

35、 Directed Acyclic Graphs (DAG)0+1BACBPLogitACP第22页/共44页XGXGZXG Pearls do-calculus Causal Effect Identification-in the Perspective of Causal diagramRule 1 Rule 1 Insertion/deletion of observations:Insertion/deletion of observations:w)do(x),|P(yw)z,do(x),|P(yXGW)X,|Z(Y ifXYWZXYWZGXGRule 2Rule 2 Action

36、/observation exchange:Action/observation exchange:w)z,do(x),|P(yw)do(z),do(x),|P(yZXGW)X,|Z(Y ifZYWXZYWXGXZGRule 3 Rule 3 Insertion/deletion of actions:Insertion/deletion of actions:w)do(x),|P(yw)do(z),do(x),|P(yXZ(W)G(YZ|X,W)ifwhere Z(W) is the set of Z-nodes that are not ancestors of any W-node XY

37、WZ1Z2XYWZ1Z2GXZ(W)G第23页/共44页24n The quantity Pt(s) is identifiable if, given the Causal diagram G, the quantity Pt(s) can be determined from the distribution of the observed variables P(n) alone. The possibility of separating causal from noncausal associations with ideal data .n Three strategies： Gr

38、aphical Identification CriteriaXYXXXYYYCausal Effect Identification-in the Perspective of Causal diagram第24页/共44页 如果连接两个变量（或变量集合）的所有路均被关闭，则如果连接两个变量（或变量集合）的所有路均被关闭，则称为两个变量（两个变量集合）被有向分隔，否则被有向称为两个变量（两个变量集合）被有向分隔，否则被有向连接。有向分隔包括右图的三种情形：连接。有向分隔包括右图的三种情形： 1）路中含碰撞节点（路中含碰撞节点（E M1 D）; 2）对因果路的中介变量施加条件（对因果路的中介变

39、量施加条件（ E M2 D ）; 3）对混杂路上的混杂因子施加条件（对混杂路上的混杂因子施加条件（ E M3 D ）。）。有向分隔后，有向分隔后，E与与D条件独立，即符合马尔科夫准则。在因条件独立，即符合马尔科夫准则。在因果推断中，有向分隔准则是识别和创建变量独立性的有力果推断中，有向分隔准则是识别和创建变量独立性的有力工具。工具。 如果对如果对SC1，C2施加条件，则施加条件，则E与与D被有向分隔。被有向分隔。l 有向分隔准则（有向分隔准则（ D-separation/ ）和有向连接准则（）和有向连接准则（ D-connectedness ） M2EDM1M32502()2DEMLogit

40、PEM03()3DEMLogit PEM Graphical Identification Criteria- d-Separation CriterionCausal Effect Identification-in the Perspective of Causal diagram第25页/共44页 Graphical Identification Criteria- d-Separation Criterion26n d-Separation : A path P is said to be “d-separated” (or “blocked”) by a conditioning s

41、et of nodes Z iff 1) P contains a chain XZ2 Y or a confounding paths XZ3 Y such that the middle node M is in Z, or 2) P contains a colliding path XZ1 Y such that neither the middle node Z, nor any descendant of Z, is in Z. Z2XYZ1Z302()2DXZLogit PXZ03()3DXZLogit PXZn d-connected: A path P is said to

42、be “d-connected” (or “unblocked” or “open”) by a conditioning set of nodes Z iff it is not dseparated.n Note: Z may be the empty set . (See Pearl 2009)n Theorem: If two sets of variables X and Y aredseparated by Z along all paths in a DAG, then X s statistically independent of Y conditional on Z in

43、every distribution compatible with the DAG. Conversely, if X and Y are not d-separated by Z alongall paths in the DAG, then X and Y are dependent conditional on Z in at least one distribution compatible with the DAG.Causal Effect Identification-in the Perspective of Causal diagram第26页/共44页 Graphical

44、 Identification Criteria- d-Separation Criterion27n One important use of DAGs is that they support the derivation of all testable (structural) implications of a model. n Using the d-separation/blocking criterion, we can read all implied marginal and conditional dependences and independences off the

45、DAG.Causal Effect Identification-in the Perspective of Causal diagram第27页/共44页 Graphical Identification Criteria- Adjustment Criterion28n A set of variables Z (which may be empty) fulfills the adjustment criterion relative to the total causal effectof T on Y iff 1). Z blocks all noncausal paths from

46、 T to Y, and 2). No element of Z is on a causal path from T to Y or descends from a variable on a causal path from T to Y. n The adjustment criterion is “complete,” meaning that it detects all, and only those, sets of variables Z that identify the effect of T on Y by simply conditioning on Z. (Shpit

47、ser et al. 2010)U is unobservedn One way to interpret this with DAGs, is to note that the total causal effect of T on Y is identifiable if one can condition on (“adjust for”) a set of variables Z that1) blocks all non-causal paths between T and Y, 2) without blocking any causal paths between T and Y

48、.n Equivalently: d-separate T and Y along all noncausal paths while leaving all causal paths d-connected.0|,XTE Y X TXTTYCausal Effect Identification-in the Perspective of Causal diagram第28页/共44页 设设S是后门路上的节点的集合，若是后门路上的节点的集合，若S满足满足如下如下2准则：准则：1）S不包含不包含E的后代节点的后代节点 ；2）对对S施加条件后，没有开放的后门路，即可施加条件后，没有开放的后门路，

49、即可将所有后门路关闭。此时，称将所有后门路关闭。此时，称S满足后门准满足后门准则。关闭所有后门路后，才能推断暴露则。关闭所有后门路后，才能推断暴露（E）对结局（）对结局（D）的因果作用。）的因果作用。 在在S中，找到充分小的子集，并对其进行中，找到充分小的子集，并对其进行调整，是关闭所有门路的关键。例如，右调整，是关闭所有门路的关键。例如，右图中，图中，SC,U1,U，但仅对，但仅对C和和U两个已观两个已观测变量施加条件（调整），即能关闭所有测变量施加条件（调整），即能关闭所有后门路。后门路。29 Graphical Identification Criteria- Backdoor Crit

50、erionCausal Effect Identification-in the Perspective of Causal diagram第29页/共44页 Graphical Identification Criteria- Backdoor Criterion30n A set of variables Z =X satisfies thebackdoor criterion relative to an ordered pair of variables (T,Y) in a DAG if: 1) no node in Z is a descendant of T, and 2) Z

51、blocks (d-separates) every path between T and Y that contain an arrow into T. If Z satisfies the back-door criterion relative to (T, Y), then the causal effect of T on Y is identifiableTY(y|()(y|do(), )P( |do()(y| , )P( )xxPdo TtPTt xxTtPt xxSmokingLung CancerTar Depositsn We compute in two steps:)|

52、(xyP( |( )( | )P z do xP z x1)2)( |( )( | , ) ( | )xP y do zP y x z P x z( |( )( | )( |, ) ( )zxP y do xP z xP y x z P xPutting things together:Backdoor criterion-based check identification:1) List all backdoor paths connecting T and Y.2) Check whether all backdoor paths are naturally (unconditional

53、ly) blocked. Yes: identified. No: move on.3) Check whether the unblocked paths can be blocked by conditioning on non-descendants of T. Yes: move on. No:not identified.4) Check whether Step 3 unblocked any non-causal paths and then check if those can be blocked. Yes: move on.No: not identified.5) Che

54、ck whether any of the variables that must be conditioning on to block backdoor paths are on the causal pathway from T to Y or are descendants of a variable on the causal pathway. Yes: Not identified. No: identified.Causal Effect Identification-in the Perspective of Causal diagramRule 2 and Rule 3 of

55、 do-calculusule3:P( |do()P( )RxTtxule2: (y|do(), )(y| , )RPTt xPt x第30页/共44页 设设S是前门路上的节点的集合，若是前门路上的节点的集合，若S满足如下满足如下3准则：准则：1）S阻断了所有从暴露（阻断了所有从暴露（E）到结局（）到结局（D）因果路；）因果路；2）从从暴露（暴露（E）到）到S不存在后门路；不存在后门路；3）从从S到结局（到结局（D）的所）的所有后门路均被暴露（有后门路均被暴露（E）关闭。此时，称）关闭。此时，称S满足前门准则。满足前门准则。开放所有前门路后，才能推断开放所有前门路后，才能推断E D的因果作用。

56、的因果作用。 右图中，右图中，M 满足前门准则，且前门路满足前门准则，且前门路E M D开开放。若推断放。若推断E对对D的因果作用，可利用前门准则。先估的因果作用，可利用前门准则。先估计计E M，此时需关闭，此时需关闭E U D M （因（因D是碰撞是碰撞节点，故自然关闭），节点，故自然关闭）， 故故E M为为1；再估计再估计M D，此时需通过调整此时需通过调整E关闭关闭M E U D得到得到2。所以。所以E对对D的因果作用为的因果作用为1 *2。 当存在未观测到的混杂因子时，前门准则更有优势。当存在未观测到的混杂因子时，前门准则更有优势。吸烟肺癌肺部尼古丁沉积未观察混杂1231 Graphi

57、cal Identification Criteria- Front-door CriterionCausal Effect Identification-in the Perspective of Causal diagram第31页/共44页 Graphical Identification Criteria- Front-door Criterion32TYn A set of variables Z =C is said to satisfy the front-door criterion relative to an ordered pair of variables (T, Y)

58、 if 1) Z intercepts all directed paths from T to Y; 2) there is no back-door path from T to Z; 3) all back-door paths from Z to Y are closed by T.n If Z satisfies the front-door criterion relative to (T,Y) and if P(t,z) 0, then the causal effect of T on Y is identifiable and is given by formula:n Th

59、e front-door criterion may be obtained by a double application of the back-door criterion, as shown in the tar deposits examplen In the smoking-lung cancer model with genotype and tar, we may use the front-door criterion and get:) (), |()|()(xzxxPzxyPxzPyPSmokingLung CancerTar Deposits(y|()(|)(y|,)P

60、()TPdo TtP Cc TtP YTt CcTtCausal Effect Identification-in the Perspective of Causal diagramRule 2 and Rule 3ule2: (|()(|)RPT t doC cPC c T tule2,3:(y|()=(y|,)P()TRP Ydo CcP YTt CcTt第32页/共44页 在推断暴露（在推断暴露（E）对结局（）对结局（D）的因果作用时，）的因果作用时，如果存在一个变量（如果存在一个变量（G），满足：），满足： 1）G对对E有因果作用；有因果作用； 2) G与混杂（与混杂（U）独立；）独立； 3）给定）给定E和