1. Causal Diagrams: Directed Acyclic Graphs to Understand, Identify, and Control for Confounding Maya Petersen PH 250B: 11/03/04
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6. Ex: Constructing a Causal Diagram Vitamins Birth Defects Pre-Natal Care Difficulty conceiving SES Maternal genetics
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21. Using a DAG to decide what variable to adjust for in analysis Ex 1: Is adjusting for prenatal care sufficient to control for confounding of the effect of vitamin use on birth defects?
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33. A DAG-based illustration of time-dependent confounding: A situation in which traditional methods to control for confounding (i.e. adjustment/stratification) break down Ex: What variables should we control for to estimate the effect of antiretroviral therapy on CD4 count?
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36. Representing these relations in a DAG Exposure: Antiretroviral Treatment CD4 Count at beginning of study Outcome: CD4 count at the end of a study Causal effect of interest
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38. Representing these relations in a DAG Exposure: Antiretroviral Treatment CD4 Count at beginning of study Outcome: CD4 count at the end of a study Confounder
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40. DAG- Expanded to incorporate changing treatment over time Antiretroviral Treatment at t=0 Antiretroviral Treatment at t=1 CD4 Count partway through study (t=1) CD4 Count at beginning of study (t=0) Y: Final CD4 count Causal effect of interest Baseline confounder
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42. Filling in the DAG Antiretroviral Treatment at t=0 Antiretroviral Treatment at t=1 CD4 Count partway through study (t=1) CD4 Count at beginning of study (t=0) Y: Final CD4 count Causal effect of interest Baseline confounder
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44. Filling in the DAG Antiretroviral Treatment at t=0 Antiretroviral Treatment at t=1 CD4 Count partway through study (t=1) CD4 Count at beginning of study (t=0) Y: Final CD4 count Causal effect of interest Baseline confounder
45. What does this DAG tell us about what we need to adjust for to control confounding?
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50. Adjusting for a variable on the causal pathway of interest Antiretroviral Treatment at t=0 Antiretroviral Treatment at t=1 CD4 Count partway through study t=1 CD4 Count at beginning of study t=0 Y: Final CD4 count Causal effect of interest Baseline confounder- could include it in traditional multivariable model Time-dependent confounder
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54. 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
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Editor's Notes
Of course not. But why not? We have the familiar adage “correlation does not imply causation”. Why not? In this case, it is clear to us that both carrying matches and cancer could be due to some common cause, such as smoking. How can we turn this intuitive understanding into a formal definition of causation This will be the focus of today’s lecture.
For the sake of simplicity, we will assume we are dealing with an entire population, so there is no selection bias or error due to sampling, and that all variables are perfectly measured. Causal diagrams can also be extended to deal with issues of misclassification, selection bias, study design, etc.
For the sake of simplicity, we will assume we are dealing with an entire population, so there is no selection bias or error due to sampling, and that all variables are perfectly measured. Causal diagrams can also be extended to deal with issues of misclassification, selection bias, study design, etc.
Based on this information, draw a diagram to represent these causal relationships.
One of the appeals of drawing causal diagrams is that they are relatively intuitive to construct. Some points to clarify
One of the appeals of drawing causal diagrams is that they are relatively intuitive to construct. Some points to clarify
Can always add an additional level of detail
Further assumptions: so sampling, (no selection bias); all variables perfectly measured (no misclassification)
Again, For the sake of simplicity, we will assume we are dealing with an entire population, so there is no selection bias or error due to sampling, and that all variables are perfectly measured.
Basically, if smoking only causes cancer as a result of tar accumulation, in subjects with no tar accumulation, smoking will not be associated with cancer. More rigorously: We fix the value of tar by stratifying on it. Within each strata, the level of tar is the same, and so cannot vary as a result of the effect of smoking. So within each strata of tar, smoking has no effect on tar, and hence no effect on cancer.
This is equivalent to the first example of confounding Jack gave.
Is confounding present in the vitamins/birth defects example?
Yes, they share several common ancestors So confounding is present. How do we decide what to control for? Or… What confounders should we adjust fro to get an unbiased estimate of effect? Think about it for a minute, and write down what you would adjust for.
To answer this question, we need to understand the ways in which two variables can become associated. Let’s recap what we know about the relationship between causal pathways and observed associations in our data.
How can adjustment introduce a new source of association? Undiagnosed cancer! Otherwise, probably would be associated in crude
Now have all the tools we need to use our DAG to decide what to adjust for
Prenatal care is not caused by vitamin use -> move forward to step 2.
All variables in the DAG are ancestors of either vitamin use, birth defects, or prenatal care. Move forward to step 3
Now have all the tools we need to use our DAG to decide what to adjust for
By adjusting for a variable, we black all effects that pass through it
Result- control of prenatal care not sufficient. Even if no effect of vitamins on birth defects, we will still see an association between them after we control for prenatal care.
DAG shows us that adjusting for prenatal care will not be sufficient. It also shows us what else we need to adjust for.
Is this the answer you came to earlier?
Even if you did realize without use of the DAG that adjustment for both prenatal care and some additional variable was required, choosing which variables should be controlled for can become much more complicated as you begin to deal with more complex webs of causation. These same steps can be applied to much more complex DAGs, and give a rigorous answer about whether a certain set of variables is adequate to control confounding.
Simplified DAG- CD4 count as only confounder Easy- don’t need to do any analysis- just adjust for CD4
Simplified DAG- CD4 count as only confounder Easy- don’t need to do any analysis- just adjust for CD4
Simplified DAG- CD4 count as only confounder As we showed before, we need to adjust for L(1). But if we adjust for it in a traditional way, we lose our ability to estimate part of the causal effect of interest. In the presence of time-dependent confounding, traditional multivariable methods (ie- adjusted causal effects) give biased results
Simplified DAG- CD4 count as only confounder As we showed before, we need to adjust for L(1). But if we adjust for it in a traditional way, we lose our ability to estimate part of the causal effect of interest. In the presence of time-dependent confounding, traditional multivariable methods (ie- adjusted causal effects) give biased results
Simplified DAG- CD4 count as only confounder As we showed before, we need to adjust for L(1). But if we adjust for it in a traditional way, we lose our ability to estimate part of the causal effect of interest. In the presence of time-dependent confounding, traditional multivariable methods (ie- adjusted causal effects) give biased results
Simplified DAG- CD4 count as only confounder As we showed before, we need to adjust for L(1). But if we adjust for it in a traditional way, we lose our ability to estimate part of the causal effect of interest. In the presence of time-dependent confounding, traditional multivariable methods (ie- adjusted causal effects) give biased results
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