1、Causal Diagrams for Epidemiological Research,Eyal Shahar, MD, MPH Professor Division of Epidemiology & Biostatistics Mel and Enid Zuckerman College of Public Health The University of Arizona,What is it and why does it matter?,A tool (method) that: clarifies our wordy or vague causal thoughts about t
2、he research topichelps us to decide which covariates should enter the statistical modeland which should notunifies our understanding of confounding bias, selection bias, and information bias,What is the key question in a non-randomized study?,When estimating the effect of E (“exposure”) on D (“disea
3、se”), what should we adjust for?orConfounder selection strategy,The “change-in-estimate” method List “potential confounders” Adjust for (condition on) potential confounders Compare adjusted estimate to crude estimate (or “fully adjusted” to “partially adjusted”) Decide whether “potential confounders
4、” were “real confounders” Decide how much confounding existedPremise: The data informs us about confounding.,Adjusting for Confounders Common Practice,Are we asking too much from the data?,Adjusting for Confounders Common Practice,What is “a potential confounder”? Typically, “a cause of the disease
5、that is associated with the exposure”,E,D,Confounder,What is the effect of a confounder? Contributes to the crude (observed, marginal) association between E and D,Adjusting for Confounders Common Practice,Extension to multiple confounders,E,D,C1,E,D,C4,E,D,C2,E,D,C3,E,D,C5,E,D,C6,Adjusting for Confo
6、unders Common Practice Problems,A sequence of isolated, independent, causal diagrams but C1, C2, C3, C4, C5, might be connected causallyUnidirectional arrow = a causal direction but what is the meaning of the bidirectional arrow?Even with a single confounder, the “change-in-estimate” method could fa
7、il,Adjusting for Confounders Problems,An example where the “change-in-estimate” method fails,E,D,C,U1,U2,The crude estimate may be closer to the truth than the C-adjusted estimate To be explained,Alternative A Causal Diagram,A method for selecting covariates Extension of the confounder triangle Prem
8、ises displayed in the diagram New terms: Path Collider on a path Confounding path,Selected references,Pearl J. Causality: models, reasoning, and inference. 2000. Cambridge University PressGreenland S et al. Causal diagrams for epidemiologic research. Epidemiology 1999;10:37-48Robins JM. Data, design
9、, and background knowledge in etiologic inference. Epidemiology 2001;11:313-320Hernan MA et al. A structural approach to selection bias. Epidemiology 2004;15:615-625Shahar E. Causal diagrams for encoding and evaluation of information bias. J Eval Clin Pract (forthcoming),A Causal Diagram Notation an
10、d Terms,An arrow=causal direction between two variables,E,D,An arrow could abbreviate both direct and indirect effects,E,D,could summarize,E,D,U2,U3,U1,A Causal Diagram Notation and Terms,A path between E and D: any sequence of causal arrows that connects E to D,E,D,E,U1,U2,D,E,U1,U2,D,E,U1,U2,D,A C
11、ausal Diagram Notation and Terms,Circularity (self-causation) does not exist: Directed Acyclic Graph,E,U1,U2,D,E,U1,U2,D,E and U2 collide at U1,A collider on the path between E and D,A Causal Diagram Notation and Terms,A confounding path for the effect of E on D: Any path between E and D that meets
12、the following criteria: The arrow next to E points to E There are no colliders on the path,E,D,C,U1,U2,U3,V1,V2,In short: a path showing a common cause of E and D,The paths below are NOT confounding paths for the effect of E on D,E,D,C,U1,U2,U3,V1,V2,E,D,C,U1,U3,V1,V2,U2,V1,E,D,C,U1,U2,U3,V2,What ca
13、n affect the association between E and D? (Why do we observe an association between two variables?),Causal path: E causes DCausal path: D causes EConfounding pathsAdjustment for colliders on a path from E to D,E,D,D,E,E,D,C,Later,Why does a confounding path affect the crude (marginal) association be
14、tween E and D?,Intuitively: Association= being able to “guess” the value of one variable (D) from the value of another (E) ED allows us to guess D from E (and E from D) A confounding path allows for sequential guesses along the path,E,D,U1,U2,U3,V1,V2,C,How can we block a confounding path between E
15、and D?,Condition on a variable on the path (on any variable) Methods for conditioning Restriction Stratification Regression,E,D,U1,U2,U3,V1,V2,C,A point to remember,We dont need to adjust for confounders (the top of the triangle.) Adjustment for any U or V below will do. U and V are surrogates for t
16、he confounder C,E,D,U1,U2,U3,V1,V2,C,Example,If the diagram below corresponds to reality, then we have several options for conditioning For example: On C and U2 Only on U2 Only on U3,E,D,U1,U2,U3,V1,V2,C,What can affect the association between E and D?,Causal path: E causes DCausal path: D causes EC
17、onfounding pathsAdjustment for colliders on a path from E to D,E,D,D,E,E,D,C,NOW!,Conditioning on a Collider A Trap,A collider may be viewed as the opposite of a confounder Collider and confounder are symmetrical entities, like matter and anti-matter,E,D,U1,U2,U3,V1,V2,C,Conditioning on a Collider A
18、 Trap,A path from E to D that contains a collider is NOT a confounding path. There is no transfer of “guesses” across a collider.A path from E to D that contains a collider does NOT generate an association between E and DConditioning on the collider, however, will turn that path into a confounding p
19、ath.,Why?,Conditioning on a Collider A Trap,The horizontal line indicates an association (the possibility of “guesses”) that was induced by conditioning on a collider,E,D,U1,U2,U3,V1,V2,C,Properties of a Collider Intuitive Explanation,Brake condition(good, bad),Street condition(good, bad),Accident (
20、yes, no),A dataset contains three variables for N cars: Brake condition (good/bad) Street condition in the owners town (good/bad) Involved in an accident in the owners town? (yes/no),Accident is a collider. Brake condition and street condition are not associated in the dataset. We cannot use the dat
21、a to guess one from the other.,Properties of a Collider Intuitive Explanation,Why cant we make a guess from the data? Lets try. Suppose we are told: Car A has good brakes and car B has bad brakes. This information tells us nothing about the street condition in each owners town.,Intuition: a common e
22、ffect (collider) does not induce an association between its causes (colliding variables),Properties of a Collider Intuitive Explanation,If, however, we condition (stratify) on the collider “accident”, we can make some guesses about the street condition from the brake condition.,Stratum #1 Accident =
23、 yes,Properties of a Collider Intuitive Explanation,Similarly, in the other stratum,Stratum #2 Accident = no,Properties of a Collider,In summary: Conditioning on a collider creates an association between the colliding variables and, therefore, may open a confounding path,E,D,C,U1,U2,Before condition
24、ing on C,After conditioning on C,E,D,C,U1,U2,Derivations,The “change-in-estimate” method could fail if we condition on colliders, and thereby open confounding pathsTo (rationally) select covariates for adjustment, we must commit to a causal diagram (premises)(But we often say that we dont know and c
25、ant commit, and hope that the change-in-estimate method will work.),Causal inference, like all scientific inference, is conditional on premises (which may be false)not on ignorance,Derivations,Do not condition on colliders, if possible If you condition on a collider, Connect the colliding variables
26、by a line Check if you opened a new confounding path Condition on another variable to block that new path,E,D,C,U1,U2,E,D,C,U1,U2,Conditioning on C alone,Conditioning on C and (U1 or U2),Practical advice,Study one exposure at a timeA model that may be good for exposure A might not be good for exposu
27、re B (even if B is in the model)Never adjust for an effect of the exposureNever adjust for an effect of the diseaseNever select covariates by stepwise regressionNever look at p-values to decide on confounding (actually, never look at p-values),Extension to other problems of causal inquiry,Causation
28、always remains uncertain, even if we deal with a single confounder,E,D,C,We draw,And naively condition on C,E,D,C,U1,U2,Unbeknown to us the reality happens to be,And our adjustment may fail,Extension to other problems of causal inquiry,Estimating the “direct” effect by conditioning on an intermediar
29、y variable, I,E,I,D,We should remember that variable I may be a collider,E,I,Extension to other problems of causal inquiry,Causal diagrams explain the mechanism of selection bias Example:What happens if we estimate the effect of marital status on dementia in a sample of nursing home residents?Assume
30、: no effectboth variables affect “place of residence” (home, or nursing home),Extension to other problems of causal inquiry,Marital status,Dementia,Place of residence (home, nursing home),By studying a sample of nursing home residents, we are conditioning on a collider (on a “sampling collider”) and
31、 might create an association between marital status and dementia in that stratum,Extension to other problems of causal inquiry,Marital status,Dementia,Place of residence (home, nursing home),Nursing home,“Stratification”,Home,Extensions: control selection bias (Source: Hernan et al, Epidemiology 200
32、4),Extensions: control selection bias (Source: Hernan et al, Epidemiology 2004),E,D,S (0,1),Estrogen,MI,F,S=1 (our case-control sample),S=0 (remainder of the source cohort),E,D,HRT,MI,Association of E and D was created,Extensions: information bias (LAST EXAMPLE),Summary Points,The “change-in-estimat
33、e” method could fail if we condition on colliders, and thereby open confounding pathsThe theory of causal diagrams extends the idea of a confounder to the multi-confounder case Unification of confounding bias, selection bias, and information bias under a single theoretical framework,“Back-door algor
34、ithm” Sufficient set for adjustment Minimally sufficient set Differential losses to follow-up Time-dependent confounders Interpretation of hazard ratios Conditioning on a common effect always induced an association between its causes, but this association could be restricted to some levels of the co
35、mmon effect,Smoking status,FEV1,Sex,?,Age (young, old),Smoking drive(low, high),Physical activity(low, high),Asthma (yes, no),Smoking status,FEV1,Sex,?,Age (young, old),Smoking drive(low, high),Physical activity(low, high),Asthma (yes, no),Smoking status,FEV1,Sex,?,Age (young, old),Smoking drive(low
36、, high),Physical activity(low, high),Asthma (yes, no),Hospitalization Statushospitalizednot hospitalized,Pneumonia,Ulcer,Coughing,Abdominal Pain,Pneumonia,Ulcer,Coughing,Abdominal Pain,Stratification,hospitalized patients,other patients,?,?,Example: Do men have higher systolic blood pressure than wo
37、men? (In other words: estimate the gender effect on systolic blood pressure)The following table summarizes the answer to this question from two regression models,So, which is the true estimate and which is biased?,Gender,SBP,WHR,BMI,Z1,Z2,. .,Gender,SBP,WHR,BMI,Z1,Z2,. .,U,Gender,SBP,WHR,BMI,Z1,Z2,. .,U,
