causal diagrams: directed acyclic graphs to understand, identify, and control for confounding maya...

Causal Diagrams: Directed Acyclic Graphs

to Understand, Identify, and Control for Confounding

Maya PetersenMaya Petersen

PH 250B: 11/03/04PH 250B: 11/03/04

What is causation? Ex: We Ex: We observeobserve a high degree of association a high degree of association

between carrying matches and lung cancer between carrying matches and lung cancer Can we infer that carrying matches Can we infer that carrying matches causescauses lung lung

cancer? cancer?

The counterfactual definition of causation: The counterfactual definition of causation: Carrying matches is a cause of lung cancer if Carrying matches is a cause of lung cancer if

the risk of lung cancer is higher in people who the risk of lung cancer is higher in people who carry matches than it would be if these exact carry matches than it would be if these exact same people did not carry matchessame people did not carry matches

Causal diagrams Intuitive approach to representing our Intuitive approach to representing our

assumptions about causal relationshipsassumptions about causal relationships Provide relatively straightforward tool for Provide relatively straightforward tool for

relating relating observed statistical associationsobserved statistical associations and and causal effectscausal effects

What do we need to know (or assume) before we What do we need to know (or assume) before we can infer that an exposure causes a disease, and can infer that an exposure causes a disease, and get an unbiased estimate of this effect?get an unbiased estimate of this effect?

Causal diagrams Today will focus on Today will focus on

1.1. How to draw a causal diagramHow to draw a causal diagram2.2. Use of causal diagrams to decide:Use of causal diagrams to decide:

Is confounding present?Is confounding present? What should we adjust for to get an What should we adjust for to get an

unbiased estimate of effect?unbiased estimate of effect?3.3. Causal diagrams to illustrate a situation where Causal diagrams to illustrate a situation where

the traditional approach to controlling the traditional approach to controlling confounding (i.e. multivariable adjustment) confounding (i.e. multivariable adjustment) failsfails

Ex . Constructing a Causal Diagram We are interested in the effect of We are interested in the effect of maternal multivitamin usematernal multivitamin use

on on birth defectsbirth defects, and make the following causal assumptions:, and make the following causal assumptions:1.1. Prenatal care (PNC) leads to an increase in vitamin use (as a Prenatal care (PNC) leads to an increase in vitamin use (as a

result of intervention and education.)result of intervention and education.)2.2. Prenatal care protects against birth defects in ways other than Prenatal care protects against birth defects in ways other than

by increasing vitamin use . by increasing vitamin use . 3.3. Difficulty conceiving may cause a woman to seek out PNC Difficulty conceiving may cause a woman to seek out PNC

once she becomes pregnantonce she becomes pregnant4.4. Maternal genetics that lead to difficulty conceiving can also Maternal genetics that lead to difficulty conceiving can also

lead to birth defects.lead to birth defects.5.5. Socio-economic characteristics directly affect both access to Socio-economic characteristics directly affect both access to

PNC and use of vitaminsPNC and use of vitamins

Ex: Constructing a Causal Diagram

Vitamins Birth Defects

Pre-Natal Care

Difficulty conceivingSES

Maternal genetics

Directed Acyclic Graph (DAG) construction: Basics Direct causal relationships between variables are Direct causal relationships between variables are

represented by arrowsrepresented by arrows All causal relationships have a direction, All causal relationships have a direction,

because any given variable cannot be because any given variable cannot be simultaneously a cause and an effectsimultaneously a cause and an effect ( (DirectedDirected))

There are no feedback loops There are no feedback loops ( ( AcyclicAcyclic)) There can be no feedback loops because causes There can be no feedback loops because causes

always precede their effectsalways precede their effects To avoid feedback loops, extend graph over timeTo avoid feedback loops, extend graph over time

Malnutrition

Infection Infect. (t=0) Infect. (t=1)

Malnut. (t=0) Malnut. (t=1)

Directed Acyclic Graph (DAG) construction: Terminology Parent & Child: Parent & Child:

Directly connected by an arrow (No intermediates)Directly connected by an arrow (No intermediates) Pre-Natal care is a “parent” of birth defectsPre-Natal care is a “parent” of birth defects Birth defects is a “child” of Pre-natal careBirth defects is a “child” of Pre-natal care

Ancestor & Descendant: Ancestor & Descendant: Connected by a directed path of a series of arrowsConnected by a directed path of a series of arrows

SES is an “ancestor” of Birth DefectsSES is an “ancestor” of Birth Defects Birth Defects is a “descendant” of SESBirth Defects is a “descendant” of SES


Pre-Natal Care


Maternal genetics

Directed Acyclic Graph (DAG) construction: Assumptions Not all intermediate steps between two variables Not all intermediate steps between two variables

need to be represented (depends on level of detail need to be represented (depends on level of detail of the model)of the model) Ex: can represent the effect of smoking on lung Ex: can represent the effect of smoking on lung

cancer as:cancer as:Smoking -> Cancer Smoking -> Cancer oror Smoking -> tar -> mutations -> CancerSmoking -> tar -> mutations -> Cancer

Absence of a directed path from X to Y implies Absence of a directed path from X to Y implies that X has no effect on Ythat X has no effect on Y

Directed Acyclic Graph (DAG) construction: Assumptions DAGs assume that all common causes of exposure DAGs assume that all common causes of exposure

and disease of interest are included in causal and disease of interest are included in causal diagramdiagram If common causes are unknown, or cannot be observed, If common causes are unknown, or cannot be observed,

they must still be included they must still be included Ex:Ex:

Unmeasured characteristics (religious beliefs, culture, lifestyle, etc.)

Alcohol Use

Smoking

Heart Disease

Ex: What assumptions does the DAG we constructed make? SES has no effect on difficulty conceivingSES has no effect on difficulty conceiving Difficulty conceiving has no effect on maternal vitamin Difficulty conceiving has no effect on maternal vitamin

use, other than through its effect on seeking prenatal careuse, other than through its effect on seeking prenatal care SES has no effect on birth defects other than via its effects SES has no effect on birth defects other than via its effects

on access to prenatal care and on vitamin useon access to prenatal care and on vitamin use There are no additional common causes of vitamin use and There are no additional common causes of vitamin use and

birth defectsbirth defects Etc…Etc…


Pre-Natal Care


Maternal genetics

Back to our basic problem:Back to our basic problem:

What can we say about causal What can we say about causal effects, based on the associations effects, based on the associations

we observe in our data?we observe in our data?

Associations between exposure and Associations between exposure and disease in our crude data can arise in disease in our crude data can arise in several waysseveral ways

A crude association between smoking and cancer could be due A crude association between smoking and cancer could be due toto

Smoking -> CancerSmoking -> Cancer Smoking -> tar -> mutations -> CancerSmoking -> tar -> mutations -> Cancer

Adjusting for an intermediate in the causal pathway between Adjusting for an intermediate in the causal pathway between exposure and disease removes any association that results exposure and disease removes any association that results from that pathwayfrom that pathway

In the DAG above, if we control for tar levels, we will block the In the DAG above, if we control for tar levels, we will block the association between smoking and cancerassociation between smoking and cancer

Smoking tar mutations CancerSmoking tar mutations Cancer

By adjusting for the effects of the exposure, we will no longer be able By adjusting for the effects of the exposure, we will no longer be able to study themto study them

Crude (unadjusted) associations in our observational data: 1) Exposure causes disease

Crude (unadjusted) associations in our observational data: 2) Exposure and disease share a common cause

A crude association between matches and cancer could A crude association between matches and cancer could be due tobe due to

Matches have no causal effect on cancer, but the two are Matches have no causal effect on cancer, but the two are associated because they have a common cause (smoking)associated because they have a common cause (smoking)

This is a classic example of confoundingThis is a classic example of confounding By adjusting for the common cause, association is By adjusting for the common cause, association is

eliminated eliminated Matches are no longer associated with cancer after we stratify Matches are no longer associated with cancer after we stratify

on smokingon smoking This is what we do when we adjust for a confounderThis is what we do when we adjust for a confounder

Smoking

Matches Cancer

Yet again- What is confounding? If the crude association between exposure and disease is If the crude association between exposure and disease is

unconfounded, thenunconfounded, then All of the association we see between exposure and All of the association we see between exposure and

disease is due to the disease is due to the effecteffect of exposure on disease of exposure on disease None of the association between exposure and None of the association between exposure and

disease is due to common causes that they share. disease is due to common causes that they share. (confounding)(confounding)

In other words: If exposure has no In other words: If exposure has no effecteffect on disease, on disease, would we still expect to observe an would we still expect to observe an associationassociation in our in our data?data? If yes -> confounding is presentIf yes -> confounding is present

How can we use a DAG to check for presence of confounding?1.1. Remove all direct effects of the exposure Remove all direct effects of the exposure

These are the effects we are interested in. We want to see These are the effects we are interested in. We want to see if, in their absence, an association is still present.if, in their absence, an association is still present.

2.2. Check whether disease and exposure share a common Check whether disease and exposure share a common cause (ancestor)cause (ancestor)

Does any variable connect E and D by following only Does any variable connect E and D by following only forward pointing arrows?forward pointing arrows?

If E and D have a common cause -> confounding is If E and D have a common cause -> confounding is presentpresent

Any common cause they share will lead to an Any common cause they share will lead to an association between E and D that is not due to the association between E and D that is not due to the effect of E on Deffect of E on D

Vitamins and Birth Defects Is confounding present?1.1. Remove all direct effects of vitamin useRemove all direct effects of vitamin use

2.2. Do exposure and disease share a common Do exposure and disease share a common cause (ancestor)?cause (ancestor)?


Pre-Natal Care


Maternal genetics

How can we use a DAG to decide what variables to control for in our analysis? We want to choose a set of variables that, We want to choose a set of variables that,

when adjusted for, will give us an when adjusted for, will give us an unconfounded estimate of the effect of unconfounded estimate of the effect of exposure on diseaseexposure on disease

In other words, if the exposure had In other words, if the exposure had nono effect on disease, after adjusting for effect on disease, after adjusting for these variables, exposure and disease these variables, exposure and disease will no longer be associatedwill no longer be associated

How can two variables become associated? Review: A crude (unadjusted) association between exposure Review: A crude (unadjusted) association between exposure

(E) and disease (D) can be due to (E) and disease (D) can be due to 1.1. Causal pathway from E to D (or vice versa)Causal pathway from E to D (or vice versa)

EE -> -> DD oror EE -> x -> y -> -> x -> y -> DD2.2. Common cause of E and DCommon cause of E and D

3.3. By adjusting (or stratifying) on a third variable, it is possible By adjusting (or stratifying) on a third variable, it is possible to introduce to introduce a new source of non-causal associationa new source of non-causal association (confounding) between E & D(confounding) between E & D

As we begin to adjust for variables in attempt to control As we begin to adjust for variables in attempt to control for confounding, we must take this potential source of for confounding, we must take this potential source of association into account association into account

C

DE

Adjusting for a common effect of two variables will induce a new association between them (Even if they were unassociated before adjusting)

Ex: Ex:

Being on a diet does not cause cancer (or vice versa), and dieting and Being on a diet does not cause cancer (or vice versa), and dieting and cancer share no common causes: In our crude data, diet and cancer will not cancer share no common causes: In our crude data, diet and cancer will not be associatedbe associated Whether or not an individual was on a diet does not tell us anything about whether or Whether or not an individual was on a diet does not tell us anything about whether or

not he/she has cancer.not he/she has cancer. If we stratify on weight loss, we can create If we stratify on weight loss, we can create a new associationa new association between between

dieting and cancer dieting and cancer Within the strata of people who lost weight, if we know an individual was on a diet, it Within the strata of people who lost weight, if we know an individual was on a diet, it

tells us that he/she is less likely to have cancer (dieting provides an alternate tells us that he/she is less likely to have cancer (dieting provides an alternate explanation for weight loss). explanation for weight loss).

Weight-loss diet Cancer

Weight Loss

Using a DAG to decide what variable to adjust for in analysis

Ex 1: Is adjusting for prenatal care Ex 1: Is adjusting for prenatal care sufficient to control for confounding sufficient to control for confounding of the effect of vitamin use on birth of the effect of vitamin use on birth

defects? defects?

Using a DAG to decide what to adjust for in analysis

Step 1: Is prenatal care caused by vitamin Step 1: Is prenatal care caused by vitamin use? If yes, we should not adjust for it. use? If yes, we should not adjust for it. Do not adjust for an effect of the exposure of interestDo not adjust for an effect of the exposure of interest


Pre-Natal Care


Maternal genetics

Step 2: Delete all non-ancestors of vitamin Step 2: Delete all non-ancestors of vitamin use, birth defects, and pre-natal careuse, birth defects, and pre-natal care If a variable is not an ancestor of vitamin use or birth If a variable is not an ancestor of vitamin use or birth

defects, it cannot be a common cause, and so cannot be defects, it cannot be a common cause, and so cannot be a source of crude association between thema source of crude association between them

If a variable is not an ancestor of prenatal care, new If a variable is not an ancestor of prenatal care, new associations with that variable can not be created by associations with that variable can not be created by adjusting for prenatal careadjusting for prenatal care



Pre-Natal Care


Maternal genetics

Step 3: Delete all direct effects of VitaminsStep 3: Delete all direct effects of Vitamins These are the effects we are interested in. We want to These are the effects we are interested in. We want to

see if, in their absence, an association is still present. If see if, in their absence, an association is still present. If it is, we still have confounding.it is, we still have confounding.



Pre-Natal Care


Maternal genetics

Step 4: Connect any two causes sharing a Step 4: Connect any two causes sharing a common effectcommon effect Adjustment for the effect will result in association of Adjustment for the effect will result in association of

its common causesits common causes



Pre-Natal Care


Maternal genetics

Step 5 : Strip arrow heads from all edgesStep 5 : Strip arrow heads from all edges We are moving from a graph that represents causal We are moving from a graph that represents causal

effects, to a graph that represents the associations we effects, to a graph that represents the associations we expect to expect to observeobserve (as a result of both causal effects and (as a result of both causal effects and the adjustment process)the adjustment process)



Pre-Natal Care


Maternal genetics

Step 6 : Delete prenatal careStep 6 : Delete prenatal care This is equivalent to adjusting for prenatal care, now This is equivalent to adjusting for prenatal care, now

that we have added to the graph the new associations that we have added to the graph the new associations that will be created by adjusting that will be created by adjusting




Maternal genetics

Test: Are Vitamins and Birth Defects still Test: Are Vitamins and Birth Defects still connected? connected?

YesYes: : Adjusting for Prenatal Care is Adjusting for Prenatal Care is notnot sufficient for sufficient for control of confounding control of confounding

After adjusting for prenatal care, vitamin use and After adjusting for prenatal care, vitamin use and birth defects will birth defects will still be associatedstill be associated in our data, even in our data, even if vitamin use has if vitamin use has no causal effectno causal effect on birth defects on birth defects




Maternal genetics


Adjustment for which variables Adjustment for which variables wouldwould result in control of confounding?result in control of confounding?

Our DAG shows that adjusting for any one or more Our DAG shows that adjusting for any one or more of the three remaining variables, in addition to of the three remaining variables, in addition to prenatal care, would be sufficient for control of prenatal care, would be sufficient for control of confoundingconfounding (e.g.(e.g. SES and prenatal care)SES and prenatal care)


Difficulty conceiving

Maternal genetics

Vitamins and Birth Defects: Lessons learned It may not be immediately intuitive what variables It may not be immediately intuitive what variables

we need to control for in our analysiswe need to control for in our analysis The process of adjustment/stratifiction can introduce new sources of The process of adjustment/stratifiction can introduce new sources of

association in our data that must be accounted for in any attempt to association in our data that must be accounted for in any attempt to control confoundingcontrol confounding

Step by step analysis of a DAG provides a rigorous check whether Step by step analysis of a DAG provides a rigorous check whether we have adequately controlled for confoundingwe have adequately controlled for confounding

Adjustment for several different sets of confounders Adjustment for several different sets of confounders may each be sufficient to control confounding of may each be sufficient to control confounding of the same exposure disease relationship.the same exposure disease relationship. Can inform study designCan inform study design

DAGs for control of confounding: Summary of Steps

Problem:Problem: Is adjustment for/stratification on a set of Is adjustment for/stratification on a set of confounders “C” sufficient to control for confounding of confounders “C” sufficient to control for confounding of the relationship between E and D?the relationship between E and D?

1)1) No variables in C should be descendants of ENo variables in C should be descendants of E2)2) Delete all non-ancestors of {E, D, C}Delete all non-ancestors of {E, D, C}3)3) Delete all arrows emanating from EDelete all arrows emanating from E4)4) Connect any two parents with a common childConnect any two parents with a common child5)5) Strip arrowheads from all edgesStrip arrowheads from all edges6)6) Delete CDelete CTest:Test: If E is disconnected from D in the remaining graph, then If E is disconnected from D in the remaining graph, then

adjustment for C is sufficient to remove confoundingadjustment for C is sufficient to remove confounding

Pearl, J. Causality. Cambridge University Press, Cambridge UK. 2001. pp. 355-57.

Stratification has its limits…

Up till now, you have heard about one way to Up till now, you have heard about one way to remove confounding: adjustment or stratification remove confounding: adjustment or stratification on certain variableson certain variables

But… in some situations, there are no variables But… in some situations, there are no variables you can stratify on and sucessfully remove you can stratify on and sucessfully remove confoundingconfounding We will illustrate this using a DAGWe will illustrate this using a DAG In a future lecture, you will hear about a In a future lecture, you will hear about a

method you can use in these circumstances method you can use in these circumstances (Marginal Structural Models)(Marginal Structural Models)

A DAG-based illustration of time-dependent confounding:

A situation in which traditional methods to control for confounding (i.e. adjustment/stratification) break

downEx: What variables should we control for Ex: What variables should we control for

to estimate the effect of antiretroviral to estimate the effect of antiretroviral therapy on CD4 count?therapy on CD4 count?

Ex.: Antiretroviral therapy and CD4 count Question of interest: What is the effect of Question of interest: What is the effect of

antiretroviral therapy on CD4 count?antiretroviral therapy on CD4 count? Study Population: A cohort of HIV-infected Study Population: A cohort of HIV-infected

individualsindividuals Outcome: CD4 count at the end of the studyOutcome: CD4 count at the end of the study Exposure: Antiretroviral therapy (ART) Exposure: Antiretroviral therapy (ART)

(treated or not for the entire study period)(treated or not for the entire study period)

Ex. : Antiretroviral therapy and CD4 count Sicker individuals (those with lower Sicker individuals (those with lower

baseline CD4 counts at the beginning of the baseline CD4 counts at the beginning of the study) are more likely to be treated with study) are more likely to be treated with ARTART Low baseline CD4 count causes Low baseline CD4 count causes

physicians to treat their patientsphysicians to treat their patients CD4 count at baseline also affects CD4 CD4 count at baseline also affects CD4

count at the end of the studycount at the end of the study

Representing these relations in a DAG

Exposure: Antiretroviral Treatment

CD4 Count at beginning of study

Outcome: CD4 countat the end of a study

Causal effect of interest

Simple confounding

CD4 count at baseline is a confounderCD4 count at baseline is a confounder If we don’t adjust for baseline CD4 count, we will If we don’t adjust for baseline CD4 count, we will

underestimate the effect of ART on preserving final underestimate the effect of ART on preserving final CD4 count CD4 count

Sicker people/ those with lower initial counts will be Sicker people/ those with lower initial counts will be overrepresented among those who get treatedoverrepresented among those who get treated

We can see this in the DAG- we must adjust for We can see this in the DAG- we must adjust for baseline CD4 or ART and final CD4 will still be baseline CD4 or ART and final CD4 will still be connected once we delete our causal effect of connected once we delete our causal effect of interest interest CD4 and ART share a common causeCD4 and ART share a common cause

Representing these relations in a DAG

Exposure: Antiretroviral Treatment

CD4 Count at beginning of study

Outcome: CD4 countat the end of a study

Confounder

Antiretroviral therapy and CD4 count: A more realistic example Same study population and outcomeSame study population and outcome

Cohort of HIV-infectedCohort of HIV-infected Outcome is final CD4 countOutcome is final CD4 count

Now, an individual can change treatment status Now, an individual can change treatment status during the course of follow-upduring the course of follow-up E.g. an individual who is not treated at the E.g. an individual who is not treated at the

beginning of the study (t=0) may go on beginning of the study (t=0) may go on treatment partway through the study (e.g. t=1)treatment partway through the study (e.g. t=1)

CD4 also measured during course of follow-upCD4 also measured during course of follow-up

DAG- Expanded to incorporate changing treatment over time

Antiretroviral Treatment at t=0

AntiretroviralTreatment at t=1

CD4 Count partway through study (t=1)

CD4 Count at beginning of study (t=0)

Y: Final CD4 count


Baseline confounder

Something is missing….

Our effect of interest is how antiretroviral Our effect of interest is how antiretroviral treatment throughout the study (eg t=0 and t=1) treatment throughout the study (eg t=0 and t=1) affects final CD4 countaffects final CD4 count We have left out an important causal We have left out an important causal

relationship in the previous DAG!relationship in the previous DAG! Antiretroviral treatment at baseline affects Antiretroviral treatment at baseline affects

intermediate CD4 counts (e.g. CD4 measured at intermediate CD4 counts (e.g. CD4 measured at t=1) , which in turn affect final CD4 countst=1) , which in turn affect final CD4 counts

This is part of our causal effect of interest!This is part of our causal effect of interest!

Filling in the DAG





Y: Final CD4 count


Baseline confounder

Something is still missing…

CD4 count at t=1 will also affect CD4 count at t=1 will also affect subsequent treatment (ART at t=1)subsequent treatment (ART at t=1) Note: we take the convention that CD4(t) is measured Note: we take the convention that CD4(t) is measured

before ART(t)before ART(t) Patients with lower CD4 counts at t=1 are Patients with lower CD4 counts at t=1 are

more likely to start ART partway through more likely to start ART partway through the studythe studyA patient getting sicker causes his/her A patient getting sicker causes his/her

physician to start them on treatmentphysician to start them on treatment

Filling in the DAG





Y: Final CD4 count


Baseline confounder

What does this DAG tell us about what we need to adjust for to control

confounding?

Using the DAG to decide what we need to control for1.1. We can’t adjust for anything that is a descendant of We can’t adjust for anything that is a descendant of

(caused by) ART(caused by) ART Rules out CD4 at t=1Rules out CD4 at t=1

2.2. Delete all non-ancestors of exposure, disease, and things Delete all non-ancestors of exposure, disease, and things we are considering adjusting forwe are considering adjusting for

NA: Everything in current graph is an ancestor of NA: Everything in current graph is an ancestor of outcome or exposureoutcome or exposure





Y: Final CD4 count


Using the DAG to decide what we need to control for3.3. Delete any arrows from ARTDelete any arrows from ART

4.4. Connect parents sharing a common childConnect parents sharing a common child NA: Already connectedNA: Already connected





Y: Final CD4 count

Using the DAG to decide what we need to control for5.5. Strip arrowheadsStrip arrowheads

6.6. What can we delete that will leave ART and What can we delete that will leave ART and final CD4 unconnected?final CD4 unconnected?

Remember: CD4 at t=1 is not an option since Remember: CD4 at t=1 is not an option since ART at t=0 affects itART at t=0 affects it





Y: Final CD4 count

A Dilemma

From our analysis of the DAG it is clear that if we don’t From our analysis of the DAG it is clear that if we don’t adjust for CD4 at t=1, we fail to control for confoundingadjust for CD4 at t=1, we fail to control for confounding

But we know we cannot adjust for a variable affected by But we know we cannot adjust for a variable affected by our exposure of interestour exposure of interest Adjusting for CD4 at t=1 would be equivalent to Adjusting for CD4 at t=1 would be equivalent to

adjusting for part of our causal effect of interestadjusting for part of our causal effect of interest We would again fail to correctly estimate the total We would again fail to correctly estimate the total

effect of ART on final CD4 because we would lose that effect of ART on final CD4 because we would lose that component of the effect mediated by early changes in component of the effect mediated by early changes in CD4CD4

Adjusting for a variable on the causal pathway of interest



CD4 Count partway through study t=1

CD4 Count at beginning of study t=0

Y: Final CD4 count


Baseline confounder- could include it in traditional multivariable model

Time-dependent confounder

Time-dependent confounding

Time-dependent confounder: A covariate that is predictive of subsequent exposure, is an independent risk factor for the outcome, and is itself affected by prior exposure If we don’t adjust for the covariate we get bias due to If we don’t adjust for the covariate we get bias due to

confoundingconfounding If we do adjust, we fail to estimate the causal effect we If we do adjust, we fail to estimate the causal effect we

are interested in because we are adjusting for part of are interested in because we are adjusting for part of our effect of interest our effect of interest

You will see more of this problem, and hear about some You will see more of this problem, and hear about some ways to address it (i.e. Marginal Structural Models)ways to address it (i.e. Marginal Structural Models)

Conclusions Today we have outlined the steps to Today we have outlined the steps to

1.1. Construct a DAG, based on Construct a DAG, based on knowledge/assumptionsknowledge/assumptions

2.2. Use a DAG to decide if confounding is Use a DAG to decide if confounding is presentpresent

3.3. Use a DAG to decide what variables to Use a DAG to decide what variables to control for in analysis control for in analysis

We have also used a DAG to illustrate a We have also used a DAG to illustrate a situation where traditional methods for situation where traditional methods for controlling confounding are not adequate (time-controlling confounding are not adequate (time-dependent confounding)dependent confounding)

References

1.1. Pearl J. Pearl J. Causality: Models reasoning and Inference. Causality: Models reasoning and Inference. Cambridge University Press, Cambridge UK. 2001.Cambridge University Press, Cambridge UK. 2001.

2.2. Jewell NP. Statistics for Epidemiology. Chapman & Jewell NP. Statistics for Epidemiology. Chapman & Hall/CRC, USA. 2004:102-112Hall/CRC, USA. 2004:102-112

3.3. Greenland S. Causal Diagrams for Epidemiologic Greenland S. Causal Diagrams for Epidemiologic ResearchResearch. Epidemiology, 1999 Jan, 10(3): 37-48.. Epidemiology, 1999 Jan, 10(3): 37-48.

4.4. Robins JM. Data, design, and background Robins JM. Data, design, and background knowledge in etiologic inference. knowledge in etiologic inference. Epidemiology, Epidemiology, 2002;11:313-320. 2002;11:313-320.

5.5. Hernan M, et al. Causal knowledge as a prerequisite Hernan M, et al. Causal knowledge as a prerequisite for confounding evaluation: an application to birth for confounding evaluation: an application to birth defects epidemiology. defects epidemiology. Am J Epidemiol, 2002 Am J Epidemiol, 2002 155(2):176-184.155(2):176-184.

Example DAG from Maya’s research

Viral load (outcome)

Observed Mutations

Treatment History

Disease stage

Peak VL/ nadir CD4

VL/CD4 at therapy init

Latent mutations

U

Figure 1:Among patients on each drug

Duration before outcome is assessed

Example from Maya’s research

Effect of interest: Effect of observed viral Effect of interest: Effect of observed viral mutation profile (presence of specific mutation profile (presence of specific mutations) on viral load (i.e. response to mutations) on viral load (i.e. response to treatmenttreatment

DAG reveals that adjustment for treatment DAG reveals that adjustment for treatment history is sufficienthistory is sufficient

causal diagrams: directed acyclic graphs to understand, identify, and control for confounding maya...

Documents

causal effects

use of causal diagrams

following causal assumptions

lung cancer ex

cause of lung cancer

unbiased estimate of

risk of lung cancer

prenatal care pnc