-
@@ -85,7 +89,7 @@
Common Structures of Bias
Malcolm Barrett
-2018-08-23
+2019-09-11
Source:vignettes/bias-structures.Rmd
bias-structures.Rmd2018-08-23
A quick note on terminology: I use the terms confounding and selection bias below, the terms of choice in epidemiology. The terms, however, depend on the field. In some fields, confounding is referred to as omitted variable bias or selection bias. Selection bias also sometimes refers to variable selection bias, a related issue that refers to misspecified models.
- +Introduction
@@ -107,23 +111,23 @@
Confounders and confounding
Classical confounding is simple. A confounder is associated with both the exposure and the outcome. Let’s consider a classic example: coffee, smoking, and cancer. Smoking is a risk factor for a number of cancers, and people who drink coffee are more likely to smoke. Coffee doesn’t actually cause lung cancer, but they are d-connected through smoking, so they will appear to be associated:
-confounder_triangle(x = "Coffee", y = "Lung Cancer", z = "Smoking") %>%
- ggdag_dconnected(text = FALSE, use_labels = "label")confounder_triangle(x = "Coffee", y = "Lung Cancer", z = "Smoking") %>%
+ ggdag_dconnected(text = FALSE, use_labels = "label")
But if you think about it, this DAG is incorrect. Smoking doesn’t cause coffee drinking; something else, say a predilection towards addictive substances, causes a person to both smoke and drink coffee. Let’s say that we had a psychometric tool that accurately measures addictive behavior, so we can control for it. Now our DAG looks like this:
-coffee_dag <- dagify(cancer ~ smoking,
- smoking ~ addictive,
- coffee ~ addictive,
- exposure = "coffee",
- outcome = "cancer",
- labels = c("coffee" = "Coffee", "cancer" = "Lung Cancer",
- "smoking" = "Smoking", "addictive" = "Addictive \nBehavior")) %>%
- tidy_dagitty(layout = "tree")
-
-ggdag(coffee_dag, text = FALSE, use_labels = "label")coffee_dag <- dagify(cancer ~ smoking,
+ smoking ~ addictive,
+ coffee ~ addictive,
+ exposure = "coffee",
+ outcome = "cancer",
+ labels = c("coffee" = "Coffee", "cancer" = "Lung Cancer",
+ "smoking" = "Smoking", "addictive" = "Addictive \nBehavior")) %>%
+ tidy_dagitty(layout = "tree")
+
+ggdag(coffee_dag, text = FALSE, use_labels = "label")
Which one is the confounder, addictive behavior or smoking? Only one or the other needs to be controlled for to block the path:
- +ggdag_adjustment_set(coffee_dag, text = FALSE, use_labels = "label", shadow = TRUE)
Focusing on individual confounders, rather than confounding pathways, is a common error in thinking about adjusting our estimates. We should be more concerned blocking all confounding pathways than with including any particular variable along those pathways. (It’s worth noting, though, that when I say you only need one variable to block a path, that assumes you are measuring and modeling the variable correctly. If, for example, there is measurement error, controlling for that variable may still leave residual confounding, necessitating a more subtle level of control with other variables on the pathway; see the section on measurement error below. Moreover, it’s important to know that you expect to block the path on average; normal sampling issues, e.g. sample size, still come into play.)
Colliders, M-bias, and butterfly bias
Stratifying on a collider is a major culprit in systematic bias. Controlling for a collider–a node where two or more arrow heads meet–induces an association between its parents, through which confounding can flow:
- +collider_triangle() %>%
+ ggdag_dseparated(controlling_for = "m")
Here, the example is fairly simple and easy to deal with: m is a child of x and y and just shouldn’t be adjusted for. It can get more complicated, though, when m is something that seems like it is a confounder or when it represents a variable that contributes to whether or not a person enters the study. Often this takes the form of M-shaped bias, or M-bias. Let’s consider an example from Modern Epidemiology: the association between education and diabetes. Let’s assume that lack of education isn’t a direct cause of diabetes. When we are putting together our analysis, we ask: should we adjust for the participant’s mother’s history of diabetes? It’s linked to education via income and to participant’s diabetes status via genetic risk, so it looks like this:
-m_bias(x = "Education", y = "Diabetes", a = "Income during Childhood",
- b = "Genetic Risk \nfor Diabetes", m = "Mother's Diabetes") %>%
- ggdag(use_labels = "label")m_bias(x = "Education", y = "Diabetes", a = "Income during Childhood",
+ b = "Genetic Risk \nfor Diabetes", m = "Mother's Diabetes") %>%
+ ggdag(use_labels = "label")
From a classical confounding perspective, it seems like the mother’s diabetes status might be a confounder: it’s associated with both the exposure and outcome, and it’s not a descendant of either. However, the association with the outcome and exposure is not direct for either; it’s due to confounding by genetic risk and childhood income, respectively. Drawing it as a DAG makes it clear that the mother’s diabetes status is a collider, and adjusting for it will induce an association between genetic risk and childhood income, thus opening a back-door path from education to diabetes status:
-m_bias(x = "Education", y = "Diabetes", a = "Income during \nChildhood",
- b = "Genetic Risk \nfor Diabetes", m = "Mother's Diabetes") %>%
- ggdag_dseparated(controlling_for = "m", use_labels = "label")m_bias(x = "Education", y = "Diabetes", a = "Income during \nChildhood",
+ b = "Genetic Risk \nfor Diabetes", m = "Mother's Diabetes") %>%
+ ggdag_dseparated(controlling_for = "m", use_labels = "label")
Again, this is relatively easy–just don’t control for the collider. But what about when your study design already stratifies on m? Let’s consider an example where m represents having surgery. Let’s say we are conducting a study involving participants who had surgery due to back pain. We suspect that people who are ready to commit to physical therapy and changes in their daily life will have a greater decrease in pain after a year than those who aren’t. We’ve developed a psychometric tool that measures readiness for surgery, and we are going to look at the association between readiness and change in pain. The readiness scale depends on an underlying latent variable that is true readiness, which we are measuring with some error. Change in pain depends on baseline pain. Both underlying readiness and baseline pain are also predictive of whether or not someone has surgery. By definition, we are selecting on surgical status: we feel it’s unethical to withhold it and irresponsible to force all participants to have surgery. So, we can’t know how people who didn’t have surgery would react. Surgical status is inherently stratified for, because we’re only looking at people who have had it (note that from here on out, I’m not going to show the paths opened by adjusting for a collider, the default in ggdag, for clarity):
coords <- dagitty::coordinates(m_bias()) %>%
- coords2df()
-coords$name <- c("readiness", "pain", "surgery", "ready_tool", "pain_change")
-
-surgical_dag <- dagify(ready_tool ~ readiness,
- surgery ~ readiness + pain,
- pain_change ~ ready_tool + pain,
- exposure = "ready_tool",
- outcome = "pain_change",
- latent = "readiness",
- labels = c(ready_tool = "Measured \nReadiness",
- pain_change = "Change \nin Pain",
- readiness = "Underlying \nReadiness",
- pain = "Baseline \nPain",
- surgery = "Surgical \nStatus"),
- coords = coords2list(coords)) %>%
- control_for("surgery")
-
-ggdag_adjust(surgical_dag, text = FALSE, use_labels = "label", collider_lines = FALSE)coords <- dagitty::coordinates(m_bias()) %>%
+ coords2df()
+coords$name <- c("readiness", "pain", "surgery", "ready_tool", "pain_change")
+
+surgical_dag <- dagify(ready_tool ~ readiness,
+ surgery ~ readiness + pain,
+ pain_change ~ ready_tool + pain,
+ exposure = "ready_tool",
+ outcome = "pain_change",
+ latent = "readiness",
+ labels = c(ready_tool = "Measured \nReadiness",
+ pain_change = "Change \nin Pain",
+ readiness = "Underlying \nReadiness",
+ pain = "Baseline \nPain",
+ surgery = "Surgical \nStatus"),
+ coords = coords2list(coords)) %>%
+ control_for("surgery")
+
+ggdag_adjust(surgical_dag, text = FALSE, use_labels = "label", collider_lines = FALSE)
We can’t unstratify by surgical status, so our best bet is to block the back-door path opened by stratifying on it. We can’t adjust for the latent variable (and, if we’re measuring it really well, the latent variable and the tool are one in the same), so all we can do is control for baseline pain. Note that, technically, surgical status is part of the adjustment set:
- +ggdag_adjustment_set(surgical_dag, text = FALSE, use_labels = "label", shadow = TRUE)
What about if a variable is both a collider and a cause of the exposure and outcome (a classical confounder)? This is an extension of M-bias sometimes called butterfly bias or bow-tie bias. The variable is a part of two paths: one that it’s blocking as a collider and a back-door path that is confounding the relationship between x and y. What to do?
- +ggdag_butterfly_bias(edge_type = "diagonal")
The strategy is basically the same as above; we need to control for m to block the back-door path, but that opens up a relationship between a and b, so we need to block that path, too.
- +ggdag_adjustment_set(butterfly_bias(), shadow = TRUE)
Adjusting for either set, {a, m} or {b, m}, will give allow us to estimate the causal effect of x on y.
Measurement error
Measurement error is the degree to which we mismeasure a variable, which can lead to bias in a number of ways. If the error is dependent on the exposure or the outcome, (e.g. we measure the exposure with less accuracy for a group without a disease than with it), it is called differential measurement error. If the error has nothing to do with the exposure or outcome, it’s called non-differential measurement error. Under most conditions, non-differential error will bias the estimate of effect towards the null. In this way, it’s at least predictable, but for small effects or inadequately powered studies, it can make a true effect disappear. If there is error in both the exposure and outcome, the errors themselves can also be associated, opening a back-door path between the exposure and outcome.
Let’s consider an example with non-differential error for the outcome and differential error for the exposure. One common situation where this can occur is recall bias. Let’s say we want to know if taking multivitamins in childhood helps protect against bladder cancer later in life.
-# set coordinates
-coords <- tibble::tribble(
- ~name, ~x, ~y,
- "bladder_cancer", 1, 0,
- "vitamins", 0, 0,
- "diagnosed_bc", 1, 1,
- "recalled_vits", 0, 1,
- "bc_error", 1, 2,
- "vits_error", 0, 2,
-)
-
-bladder_dag <- dagify(diagnosed_bc ~ bc_error + bladder_cancer,
- recalled_vits ~ vitamins + vits_error,
- vits_error ~ bladder_cancer,
- labels = c(bladder_cancer = "Bladder Cancer",
- vitamins = "Childhood Vitamin \nIntake",
- diagnosed_bc = "Diagnosed \nBladder Cancer",
- recalled_vits = "Memory of \nTaking Vitamins",
- bc_error = "Measurement Error, \nDiagnosis",
- vits_error = "Measurement Error, \nVitamins"),
- coords = coords)
-ggdag(bladder_dag, text = FALSE, use_labels = "label")# set coordinates
+coords <- tibble::tribble(
+ ~name, ~x, ~y,
+ "bladder_cancer", 1, 0,
+ "vitamins", 0, 0,
+ "diagnosed_bc", 1, 1,
+ "recalled_vits", 0, 1,
+ "bc_error", 1, 2,
+ "vits_error", 0, 2,
+)
+
+bladder_dag <- dagify(diagnosed_bc ~ bc_error + bladder_cancer,
+ recalled_vits ~ vitamins + vits_error,
+ vits_error ~ bladder_cancer,
+ labels = c(bladder_cancer = "Bladder Cancer",
+ vitamins = "Childhood Vitamin \nIntake",
+ diagnosed_bc = "Diagnosed \nBladder Cancer",
+ recalled_vits = "Memory of \nTaking Vitamins",
+ bc_error = "Measurement Error, \nDiagnosis",
+ vits_error = "Measurement Error, \nVitamins"),
+ coords = coords)
+ggdag(bladder_dag, text = FALSE, use_labels = "label")
For the outcome, the bias only depends on how well diagnosis of bladder cancer represents actually having bladder cancer. For the exposure, however, it also depends on if you have cancer or not: people who are sick tend to spend more time reflecting on what could have caused the illness. Thus, they will remember the vitamins they took as children, on average, a little better than controls. If there is no effect of vitamins on bladder cancer, this dependency will make it seem as if vitamins are a risk for bladder cancer. If it is, in fact, protective, recall bias can reduce or even reverse the association.
Measurement error can also cause bias in longitudinal settings. Let’s consider another example from Modern Epidemiology, which uses the Centers for Epidemiologic Studies–Depression (CES-D) scale, a common tool to assess depression that is known to have measurement error. In this example, the question is if graduating from college with an honors degree affects how depression changes after graduation. Assuming it doesn’t, adjusting for baseline CES-D score–a common practice–can induce bias via measurement error:
-# set coordinates
-coords <- tibble::tribble(
- ~name, ~x, ~y,
- "honors", 1, 3,
- "depression", 2, 3,
- "cesd", 2, 2,
- "baseline_error", 2, 1,
- "depression_change", 3, 3,
- "cesd_change", 3, 2,
- "followup_error", 3, 1
-)
-
-cesd_dag <- dagify(depression ~ honors,
- cesd ~ depression + baseline_error,
- cesd_change ~ depression_change + followup_error + baseline_error,
- labels = c(honors = "Honors Degree",
- depression = "Depression",
- cesd = "CES-D",
- cesd_change = "Change \nin CES-D",
- depression_change = "Change in \nDepression",
- baseline_error = "Measurement Error, \nBaseline",
- followup_error = "Measurement Error, \nFollow-up"),
- coords = coords)
-
-cesd_dag %>%
- ggdag_dconnected(from = "honors", to = "cesd_change", controlling_for = "cesd",
- text = FALSE, use_labels = "label", collider_lines = FALSE)# set coordinates
+coords <- tibble::tribble(
+ ~name, ~x, ~y,
+ "honors", 1, 3,
+ "depression", 2, 3,
+ "cesd", 2, 2,
+ "baseline_error", 2, 1,
+ "depression_change", 3, 3,
+ "cesd_change", 3, 2,
+ "followup_error", 3, 1
+)
+
+cesd_dag <- dagify(depression ~ honors,
+ cesd ~ depression + baseline_error,
+ cesd_change ~ depression_change + followup_error + baseline_error,
+ labels = c(honors = "Honors Degree",
+ depression = "Depression",
+ cesd = "CES-D",
+ cesd_change = "Change \nin CES-D",
+ depression_change = "Change in \nDepression",
+ baseline_error = "Measurement Error, \nBaseline",
+ followup_error = "Measurement Error, \nFollow-up"),
+ coords = coords)
+
+cesd_dag %>%
+ ggdag_dconnected(from = "honors", to = "cesd_change", controlling_for = "cesd",
+ text = FALSE, use_labels = "label", collider_lines = FALSE)
Because both the baseline score and the change are due, in part, to measurement error at baseline, controlling for baseline CES-D score (a collider) causes change in CES-D and receiving an honors degree to be d-connected.
Selection bias
We have already seen a few examples of selection bias, but let’s consider a couple more that are potential pitfalls in common design types. Let’s say we’re doing a case-control study and want to assess the effect of smoking on glioma, a type of brain cancer. We have a group of glioma patients at a hospital and want to compare them to a group of controls, so we pick people in the hospital with a broken bone, since that seems to have nothing to do with brain cancer. However, perhaps there is some unknown confounding between smoking and being in the hospital with a broken bone, like being prone to reckless behavior. In the normal population, there is no causal effect of smoking on glioma, but in our case, we’re selecting on people who have been hospitalized, which opens up a back-door path:
-coords <- tibble::tribble(
- ~name, ~x, ~y,
- "glioma", 1, 2,
- "hospitalized", 2, 3,
- "broken_bone", 3, 2,
- "reckless", 4, 1,
- "smoking", 5, 2
-)
-
-dagify(hospitalized ~ broken_bone + glioma,
- broken_bone ~ reckless,
- smoking ~ reckless,
- labels = c(hospitalized = "Hospitalization",
- broken_bone = "Broken Bone",
- glioma = "Glioma",
- reckless = "Reckless \nBehavior",
- smoking = "Smoking"),
- coords = coords) %>%
- ggdag_dconnected("glioma", "smoking", controlling_for = "hospitalized",
- text = FALSE, use_labels = "label", collider_lines = FALSE)coords <- tibble::tribble(
+ ~name, ~x, ~y,
+ "glioma", 1, 2,
+ "hospitalized", 2, 3,
+ "broken_bone", 3, 2,
+ "reckless", 4, 1,
+ "smoking", 5, 2
+)
+
+dagify(hospitalized ~ broken_bone + glioma,
+ broken_bone ~ reckless,
+ smoking ~ reckless,
+ labels = c(hospitalized = "Hospitalization",
+ broken_bone = "Broken Bone",
+ glioma = "Glioma",
+ reckless = "Reckless \nBehavior",
+ smoking = "Smoking"),
+ coords = coords) %>%
+ ggdag_dconnected("glioma", "smoking", controlling_for = "hospitalized",
+ text = FALSE, use_labels = "label", collider_lines = FALSE)
Even though smoking doesn’t actually cause glioma, it will appear as if there is an association. Actually, in this case, it may make smoking appear to be protective against glioma, since controls are more likely to be smokers.
Let’s also consider how bias arises in loss-to-follow-up. In a randomized clinical trial or cohort study, the main threat of selection bias is not through who enters the study (although that may affect generalizability) but who leaves it. If loss-to-follow-up is associated with the exposure or outcome, the relationship between the two may be biased. Let’s consider a trial where we are testing a new HIV drug and its effect on CD4 white blood cell count. If the treatment causes symptoms, participants may leave the trial. Similarly, there may be those whose HIV is getting worse and thus more symptomatic, which also may cause people to leave the trial. If we only have information on people who stay in the study, we are stratifying by follow-up status:
-dagify(follow_up ~ symptoms,
- symptoms ~ new_rx + dx_severity,
- cd4 ~ dx_severity,
- labels = c(
- follow_up = "Follow-Up",
- symptoms = "Symptoms",
- new_rx = "New HIV Drug",
- dx_severity = "Underyling \nHIV Severity",
- cd4 = "CD4 Count"
- )) %>%
- ggdag_adjust("follow_up", layout = "mds", text = FALSE,
- use_labels = "label", collider_lines = FALSE)dagify(follow_up ~ symptoms,
+ symptoms ~ new_rx + dx_severity,
+ cd4 ~ dx_severity,
+ labels = c(
+ follow_up = "Follow-Up",
+ symptoms = "Symptoms",
+ new_rx = "New HIV Drug",
+ dx_severity = "Underyling \nHIV Severity",
+ cd4 = "CD4 Count"
+ )) %>%
+ ggdag_adjust("follow_up", layout = "mds", text = FALSE,
+ use_labels = "label", collider_lines = FALSE)
But follow-up is downstream from a collider, symptoms. Controlling for a downstream collider induces bias and, because we only have information on people who remain in the study, we are inadvertently stratifying on follow-up status (see the vignette introducing DAGs for more on downstream colliders). Thus, the effect estimate between the HIV drug and CD4 count will be biased.
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Articles • ggdag
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An Introduction to Directed Acyclic Graphs • ggdag
-
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@@ -61,6 +62,9 @@
Common Structures of Bias
+
+
+ News
@@ -85,7 +89,7 @@
An Introduction to Directed Acyclic Graphs
Malcolm Barrett
- 2018-08-23
+ 2019-09-11
Source: vignettes/intro-to-dags.Rmd
intro-to-dags.Rmd
@@ -95,30 +99,30 @@ 2018-08-23
A quick note on terminology: I use the terms confounding and selection bias below, the terms of choice in epidemiology. The terms, however, depend on the field. In some fields, confounding is referred to as omitted variable bias or selection bias. Selection bias also sometimes refers to variable selection bias, a related issue that refers to misspecified models.
-
+
Directed Acyclic Graphs
A DAG displays assumptions about the relationship between variables (often called nodes in the context of graphs). The assumptions we make take the form of lines (or edges) going from one node to another. These edges are directed, which means to say that they have a single arrowhead indicating their effect. Here’s a simple DAG where we assume that x affects y:
-
+
You also sometimes see edges that look bi-directed, like this:
-
+
But this is actually shorthand for an unmeasured cause of the two variables (in other words, unmeasured confounding):
-# canonicalize the DAG: Add the latent variable in to the graph
-dagify(y ~~ x) %>%
- ggdag_canonical()
+# canonicalize the DAG: Add the latent variable in to the graph
+dagify(y ~~ x) %>%
+ ggdag_canonical()
A DAG is also acyclic, which means that there are no feedback loops; a variable can’t be its own descendant. The above are all DAGs because they are acyclic, but this is not:
-
+
@@ -130,20 +134,20 @@
Relationships between variables
Let’s say we’re looking at the relationship between smoking and cardiac arrest. We might assume that smoking causes changes in cholesterol, which causes cardiac arrest:
-smoking_ca_dag <- dagify(cardiacarrest ~ cholesterol,
- cholesterol ~ smoking + weight,
- smoking ~ unhealthy,
- weight ~ unhealthy,
- labels = c("cardiacarrest" = "Cardiac\n Arrest",
- "smoking" = "Smoking",
- "cholesterol" = "Cholesterol",
- "unhealthy" = "Unhealthy\n Lifestyle",
- "weight" = "Weight"),
- latent = "unhealthy",
- exposure = "smoking",
- outcome = "cardiacarrest")
-
-ggdag(smoking_ca_dag, text = FALSE, use_labels = "label")
+smoking_ca_dag <- dagify(cardiacarrest ~ cholesterol,
+ cholesterol ~ smoking + weight,
+ smoking ~ unhealthy,
+ weight ~ unhealthy,
+ labels = c("cardiacarrest" = "Cardiac\n Arrest",
+ "smoking" = "Smoking",
+ "cholesterol" = "Cholesterol",
+ "unhealthy" = "Unhealthy\n Lifestyle",
+ "weight" = "Weight"),
+ latent = "unhealthy",
+ exposure = "smoking",
+ outcome = "cardiacarrest")
+
+ggdag(smoking_ca_dag, text = FALSE, use_labels = "label")
The path from smoking to cardiac arrest is directed: smoking causes cholesterol to rise, which then increases risk for cardiac arrest. Cholesterol is an intermediate variable between smoking and cardiac arrest. Directed paths are also chains, because each is causal on the next. Let’s say we also assume that weight causes cholesterol to rise and thus increases risk of cardiac arrest. Now there’s another chain in the DAG: from weight to cardiac arrest. However, this chain is indirect, at least as far as the relationship between smoking and cardiac arrest goes.
We also assume that a person who smokes is more likely to be someone who engages in other unhealthy behaviors, such as overeating. On the DAG, this is portrayed as a latent (unmeasured) node, called unhealthy lifestyle. Having a predilection towards unhealthy behaviors leads to both smoking and increased weight. Here, the relationship between smoking and weight is through a forked path (weight <- unhealthy lifestyle -> smoking) rather than a chain; because they have a mutual parent, smoking and weight are associated (in real life, there’s probably a more direct relationship between the two, but we’ll ignore that for simplicity).
@@ -157,11 +161,11 @@
There are also common ways of describing the relationships between nodes: parents, children, ancestors, descendants, and neighbors (there are a few others, as well, but they refer to less common relationships). Parents and children refer to direct relationships; descendants and ancestors can be anywhere along the path to or from a node, respectively. Here, smoking and weight are both parents of cholesterol, while smoking and weight are both children of an unhealthy lifestyle. Cardiac arrest is a descendant of an unhealthy lifestyle, which is in turn an ancestor of all nodes in the graph.
So, in studying the causal effect of smoking on cardiac arrest, where does this DAG leave us? We only want to know the directed path from smoking to cardiac arrest, but there also exists an indirect, or back-door, path. This is confounding. Judea Pearl, who developed much of the theory of causal graphs, said that confounding is like water in a pipe: it flows freely in open pathways, and we need to block it somewhere along the way. We don’t necessarily need to block the water at multiple points along the same back-door path, although we may have to block more than one path. We often talk about confounders, but really we should talk about confounding, because it is about the pathway more than any particular node along the path.
Chains and forks are open pathways, so in a DAG where nothing is conditioned upon, any back-door paths must be one of the two. In addition to the directed pathway to cardiac arrest, there’s also an open back-door path through the forked path at unhealthy lifestyle and on from there through the chain to cardiac arrest:
-
+ggdag_paths(smoking_ca_dag, text = FALSE, use_labels = "label", shadow = TRUE)
We need to account for this back-door path in our analysis. There are many ways to go about that–stratification, including the variable in a regression model, matching, inverse probability weighting–all with pros and cons. But each strategy must include a decision about which variables to account for. Many analysts take the strategy of putting in all possible confounders. This can be bad news, because adjusting for colliders and mediators can introduce bias, as we’ll discuss shortly. Instead, we’ll look at minimally sufficient adjustment sets: sets of covariates that, when adjusted for, block all back-door paths, but include no more or no less than necessary. That means there can be many minimally sufficient sets, and if you remove even one variable from a given set, a back-door path will open. Some DAGs, like the first one in this vignette (x -> y), have no back-door paths to close, so the minimally sufficient adjustment set is empty (sometimes written as “{}”). Others, like the cyclic DAG above, or DAGs with important variables that are unmeasured, can not produce any sets sufficient to close back-door paths.
For the smoking-cardiac arrest question, there is a single set with a single variable: {weight}. Accounting for weight will give us an unbiased estimate of the relationship between smoking and cardiac arrest, assuming our DAG is correct. We do not need to (or want to) control for cholesterol, however, because it’s an intermediate variable between smoking and cardiac arrest; controlling for it blocks the path between the two, which will then bias our estimate (see below for more on mediation).
-
+ggdag_adjustment_set(smoking_ca_dag, text = FALSE, use_labels = "label", shadow = TRUE)
More complicated DAGs will produce more complicated adjustment sets; assuming your DAG is correct, any given set will theoretically close the back-door path between the outcome and exposure. Still, one set may be better to use than the other, depending on your data. For instance, one set may contain a variable known to have a lot of measurement error or with a lot of missing observations. It may, then, be better to use a set that you think is going to be a better representation of the variables you need to include. Including a variable that doesn’t actually represent the node well will lead to residual confounding.
What about controlling for multiple variables along the back-door path, or a variable that isn’t along any back-door path? Even if those variables are not colliders or mediators, it can still cause a problem, depending on your model. Some estimates, like risk ratios, work fine when non-confounders are included. This is because they are collapsible: risk ratios are constant across the strata of non-confounders. Some common estimates, though, like the odds ratio and hazard ratio, are non-collapsible: they are not necessarily constant across strata of non-confounders and thus can be biased by their inclusion. There are situations, like when the outcome is rare in the population (the so-called rare disease assumption), or when using sophisticated sampling techniques, like incident-density sampling, when they approximate the risk ratio. Otherwise, including extra variables may be problematic.
@@ -171,29 +175,29 @@
Colliders and collider-stratification bias
In a path that is an inverted fork (x -> m <- y), the node where two or more arrowheads meet is called a collider (because the paths collide there). An inverted fork is not an open path; it is blocked at the collider. That is to say, we don’t need to account for m to assess for the causal effect of x on y; the back-door path is already blocked by m.
Let’s consider an example. Influenza and chicken pox are independent; their causes (influenza viruses and the varicella-zoster virus, respectively) have nothing to do with each other. In real life, there may be some confounders that associate them, like having a depressed immune system, but for this example we’ll assume that they are unconfounded. However, both the flu and chicken pox cause fevers. The DAG looks like this:
-fever_dag <- collider_triangle(x = "Influenza",
- y = "Chicken Pox",
- m = "Fever")
-
-ggdag(fever_dag, text = FALSE, use_labels = "label")
+fever_dag <- collider_triangle(x = "Influenza",
+ y = "Chicken Pox",
+ m = "Fever")
+
+ggdag(fever_dag, text = FALSE, use_labels = "label")
If we want to assess the causal effect of influenza on chicken pox, we do not need to account for anything. In the terminology used by Pearl, they are already d-separated (direction separated), because there is no effect on one by the other, nor are there any back-door paths:
-
+ggdag_dseparated(fever_dag, text = FALSE, use_labels = "label")
However, if we control for fever, they become associated within strata of the collider, fever. We open a biasing pathway between the two, and they become d-connected:
-
+ggdag_dseparated(fever_dag, controlling_for = "m",
+ text = FALSE, use_labels = "label")
This can be counter-intuitive at first. Why does controlling for a confounder reduce bias but adjusting for a collider increase it? It’s because whether or not you have a fever tells me something about your disease. If you have a fever, but you don’t have the flu, I now have more evidence that you have chicken pox. Pearl presents it like algebra: I can’t solve y = 10 + m. But when I know that m = 1, I can solve for y.
Unfortunately, there’s a second, less obvious form of collider-stratification bias: adjusting on the descendant of a collider. That means that a variable downstream from the collider can also cause this form of bias. For example, with our flu-chicken pox-fever example, it may be that having a fever leads to people taking a fever reducer, like acetaminophen. Because fever reducers are downstream from fever, controlling for it induces downstream collider-stratification bias:
-dagify(fever ~ flu + pox,
- acetaminophen ~ fever,
- labels = c("flu" = "Influenza",
- "pox" = "Chicken Pox",
- "fever" = "Fever",
- "acetaminophen" = "Acetaminophen")) %>%
-ggdag_dseparated(from = "flu", to = "pox", controlling_for = "acetaminophen",
- text = FALSE, use_labels = "label")
+dagify(fever ~ flu + pox,
+ acetaminophen ~ fever,
+ labels = c("flu" = "Influenza",
+ "pox" = "Chicken Pox",
+ "fever" = "Fever",
+ "acetaminophen" = "Acetaminophen")) %>%
+ggdag_dseparated(from = "flu", to = "pox", controlling_for = "acetaminophen",
+ text = FALSE, use_labels = "label")
Collider-stratification bias is responsible for many cases of bias, and it is often not dealt with appropriately. Selection bias, missing data, and publication bias can all be thought of as collider-stratification bias. It becomes trickier in more complicated DAGs; sometimes colliders are also confounders, and we need to either come up with a strategy to adjust for the resulting bias from adjusting the collider, or we need to pick the strategy that’s likely to result in the least amount of bias. See the vignette on common structures of bias for more.
@@ -201,8 +205,8 @@
Mediation
Controlling for intermediate variables may also induce bias, because it decomposes the total effect of x on y into its parts. Depending on the research question, that may be exactly what you want, in which case you should use mediation analysis, e.g. via SEM, which can estimate direct, indirect, and total effects. Let’s return to the smoking example. Here, we only care about how smoking affects cardiac arrest, not the pathways through cholesterol it may take. Moreover, since cholesterol (at least in our DAG) intercepts the only directed pathway from smoking to cardiac arrest, controlling for it will block that relationship; smoking and cardiac arrest will appear unassociated (note that I’m not including the paths opened by controlling for a collider in this plot for clarity):
-ggdag_dseparated(smoking_ca_dag, controlling_for = c("weight", "cholesterol"),
- text = FALSE, use_labels = "label", collider_lines = FALSE)
+ggdag_dseparated(smoking_ca_dag, controlling_for = c("weight", "cholesterol"),
+ text = FALSE, use_labels = "label", collider_lines = FALSE)
Now smoking and cardiac arrest are d-separated. Since our question is about the total effect of smoking on cardiac arrest, our result is now going to be biased.
@@ -210,7 +214,7 @@
Resources
-- Judea Pearl also has a number of texts on the subject of varying technical difficulty. A friendly start is his recently released Book of Why, as well as his article summarizing the book: The Seven Tools of Causal Inference with Reflections on Machine Learning. A more technical introduction is Causal Inference in Statistics: A Primer. See also his article with Sander Greenland and James Robins on collapsibility: Confounding and Collapsibility in Causal Inference.
+- Judea Pearl also has a number of texts on the subject of varying technical difficulty. A friendly start is his recently released Book of Why, as well as his article summarizing the book: The Seven Tools of Causal Inference with Reflections on Machine Learning. A more technical introduction is Causal Inference in Statistics: A Primer. See also his article with Sander Greenland and James Robins on collapsibility: Confounding and Collapsibility in Causal Inference.
- Miguel Hernán, who has written extensively on the subject of causal inference and DAGs, has an accessible course on edx that teaches the use of DAGs for causal inference: Causal Diagrams: Draw Your Assumptions Before Your Conclusions. Also see his article The Hazard of Hazard Ratios for more on issues with hazard ratios in causal inference.
- Julia Rohrer has a very readable paper introducing DAGs, mostly from the perspective of psychology: Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data
@@ -242,9 +246,8 @@
-
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index bec76843..2aa841cc 100644
--- a/docs/articles/intro-to-ggdag.html
+++ b/docs/articles/intro-to-ggdag.html
@@ -1,18 +1,18 @@
-
+
An Introduction to ggdag • ggdag
-
-
-
+
+
+
-
@@ -22,14 +22,15 @@
@@ -61,6 +62,9 @@
Common Structures of Bias
+
+
+ News
@@ -85,7 +89,7 @@
An Introduction to ggdag
Malcolm Barrett
- 2018-08-23
+ 2019-09-11
Source: vignettes/intro-to-ggdag.Rmd
intro-to-ggdag.Rmd
@@ -103,138 +107,138 @@
Creating Directed Acyclic Graphs
If you already use dagitty, ggdag can tidy your DAG directly.
-library(dagitty)
-library(ggdag)
-
-dag <- dagitty("dag{y <- z -> x}")
-tidy_dagitty(dag)
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # A tibble: 4 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 z 28.5 23.3 -> x 28.5 24.4 FALSE
-#> 2 z 28.5 23.3 -> y 28.5 22.1 FALSE
-#> 3 x 28.5 24.4 <NA> <NA> NA NA FALSE
-#> 4 y 28.5 22.1 <NA> <NA> NA NA FALSE
+library(dagitty)
+library(ggdag)
+
+dag <- dagitty("dag{y <- z -> x}")
+tidy_dagitty(dag)
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # A tibble: 4 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 z 28.5 23.3 -> x 28.5 24.4 FALSE
+#> 2 z 28.5 23.3 -> y 28.5 22.1 FALSE
+#> 3 x 28.5 24.4 <NA> <NA> NA NA FALSE
+#> 4 y 28.5 22.1 <NA> <NA> NA NA FALSE
Note that, while dagitty supports a number of graph types, ggdag currently only supports DAGs.
dagitty uses a syntax similar to the dot language of graphviz. This syntax has the advantage of being compact, but ggdag also provides the ability to create a dagitty object using a more R-like formula syntax through the dagify() function. dagify() accepts any number of formulas to create a DAG. It also has options for declaring which variables are exposures, outcomes, or latent, as well as coordinates and labels for each node.
-dagified <- dagify(x ~ z,
- y ~ z,
- exposure = "x",
- outcome = "y")
-tidy_dagitty(dagified)
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 4 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 z 23.6 20.4 -> x 23.6 21.5 FALSE
-#> 2 z 23.6 20.4 -> y 23.6 19.2 FALSE
-#> 3 x 23.6 21.5 <NA> <NA> NA NA FALSE
-#> 4 y 23.6 19.2 <NA> <NA> NA NA FALSE
+dagified <- dagify(x ~ z,
+ y ~ z,
+ exposure = "x",
+ outcome = "y")
+tidy_dagitty(dagified)
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 4 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 z 23.6 20.4 -> x 23.6 21.5 FALSE
+#> 2 z 23.6 20.4 -> y 23.6 19.2 FALSE
+#> 3 x 23.6 21.5 <NA> <NA> NA NA FALSE
+#> 4 y 23.6 19.2 <NA> <NA> NA NA FALSE
Currently, ggdag supports directed (x ~ y) and bi-directed (a ~~ b) relationships
tidy_dagitty() uses layout functions from ggraph and igraph for coordinates if none are provided, which can be specified with the layout argument. Objects of class tidy_dagitty or dagitty can be plotted quickly with ggdag(). If the DAG is not yet tidied, ggdag() and most other quick plotting functions in ggdag do so internally.
-
+ggdag(dag, layout = "circle")
A tidy_dagitty object is just a list with a tbl_df, called data, and the dagitty object, called dag:
-tidy_dag <- tidy_dagitty(dagified)
-str(tidy_dag)
-#> List of 2
-#> $ data:Classes 'tbl_df', 'tbl' and 'data.frame': 4 obs. of 8 variables:
-#> ..$ name : chr [1:4] "z" "z" "x" "y"
-#> ..$ x : num [1:4] 23.3 23.3 22.9 23.7
-#> ..$ y : num [1:4] 25.5 25.5 26.6 24.4
-#> ..$ direction: Factor w/ 3 levels "<-","->","<->": 2 2 NA NA
-#> ..$ to : chr [1:4] "x" "y" NA NA
-#> ..$ xend : num [1:4] 22.9 23.7 NA NA
-#> ..$ yend : num [1:4] 26.6 24.4 NA NA
-#> ..$ circular : logi [1:4] FALSE FALSE FALSE FALSE
-#> $ dag : 'dagitty' Named chr "dag {\nx [exposure]\ny [outcome]\nz\nz -> x\nz -> y\n}\n"
-#> - attr(*, "class")= chr "tidy_dagitty"
+tidy_dag <- tidy_dagitty(dagified)
+str(tidy_dag)
+#> List of 2
+#> $ data:Classes 'tbl_df', 'tbl' and 'data.frame': 4 obs. of 8 variables:
+#> ..$ name : chr [1:4] "z" "z" "x" "y"
+#> ..$ x : num [1:4] 23.3 23.3 22.9 23.7
+#> ..$ y : num [1:4] 25.5 25.5 26.6 24.4
+#> ..$ direction: Factor w/ 3 levels "<-","->","<->": 2 2 NA NA
+#> ..$ to : chr [1:4] "x" "y" NA NA
+#> ..$ xend : num [1:4] 22.9 23.7 NA NA
+#> ..$ yend : num [1:4] 26.6 24.4 NA NA
+#> ..$ circular : logi [1:4] FALSE FALSE FALSE FALSE
+#> $ dag : 'dagitty' Named chr "dag {\nx [exposure]\ny [outcome]\nz\nz -> x\nz -> y\n}\n"
+#> - attr(*, "class")= chr "tidy_dagitty"
Working with DAGs
Most of the analytic functions in dagitty have extensions in ggdag and are named dag_*() or node_*(), depending on if they are working with specific nodes or the entire DAG. A simple example is node_parents(), which adds a column to the to the tidy_dagitty object about the parents of a given variable:
-node_parents(tidy_dag, "x")
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 4 x 9
-#> name x y direction to xend yend circular parent
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <fct>
-#> 1 z 23.3 25.5 -> x 22.9 26.6 FALSE parent
-#> 2 z 23.3 25.5 -> y 23.7 24.4 FALSE parent
-#> 3 x 22.9 26.6 <NA> <NA> NA NA FALSE child
-#> 4 y 23.7 24.4 <NA> <NA> NA NA FALSE <NA>
+node_parents(tidy_dag, "x")
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 4 x 9
+#> name x y direction to xend yend circular parent
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <fct>
+#> 1 z 23.3 25.5 -> x 22.9 26.6 FALSE parent
+#> 2 z 23.3 25.5 -> y 23.7 24.4 FALSE parent
+#> 3 x 22.9 26.6 <NA> <NA> NA NA FALSE child
+#> 4 y 23.7 24.4 <NA> <NA> NA NA FALSE <NA>
Or working with the entire DAG to produce a tidy_dagitty that has all pathways between two variables:
-bigger_dag <- dagify(y ~ x + a + b,
- x ~ a + b,
- exposure = "x",
- outcome = "y")
-# automatically searches the paths between the variables labelled exposure and
-# outcome
-dag_paths(bigger_dag)
-#> # A DAG with 4 nodes and 15 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 20 x 11
-#> set name x y direction to xend yend circular path type
-#> <chr> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <ch> <lgl>
-#> 1 1 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 2 1 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 3 1 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 4 1 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 5 1 x 16.8 18.2 -> y 17.7 18.2 FALSE ope… NA
-#> 6 1 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 7 2 a 17.3 19.2 -> x 16.8 18.2 FALSE ope… NA
-#> 8 2 a 17.3 19.2 -> y 17.7 18.2 FALSE ope… NA
-#> 9 2 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 10 2 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 11 2 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 12 2 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 13 2 x 16.8 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 14 3 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 15 3 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 16 3 b 17.3 17.2 -> x 16.8 18.2 FALSE ope… NA
-#> 17 3 b 17.3 17.2 -> y 17.7 18.2 FALSE ope… NA
-#> 18 3 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 19 3 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 20 3 x 16.8 18.2 <NA> <NA> NA NA FALSE ope… NA
+bigger_dag <- dagify(y ~ x + a + b,
+ x ~ a + b,
+ exposure = "x",
+ outcome = "y")
+# automatically searches the paths between the variables labelled exposure and
+# outcome
+dag_paths(bigger_dag)
+#> # A DAG with 4 nodes and 15 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 20 x 11
+#> set name x y direction to xend yend circular path type
+#> <chr> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <chr> <lgl>
+#> 1 1 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 2 1 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 3 1 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 4 1 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 5 1 x 16.8 18.2 -> y 17.7 18.2 FALSE open… NA
+#> 6 1 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 7 2 a 17.3 19.2 -> x 16.8 18.2 FALSE open… NA
+#> 8 2 a 17.3 19.2 -> y 17.7 18.2 FALSE open… NA
+#> 9 2 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 10 2 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 11 2 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 12 2 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 13 2 x 16.8 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 14 3 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 15 3 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 16 3 b 17.3 17.2 -> x 16.8 18.2 FALSE open… NA
+#> 17 3 b 17.3 17.2 -> y 17.7 18.2 FALSE open… NA
+#> 18 3 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 19 3 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 20 3 x 16.8 18.2 <NA> <NA> NA NA FALSE open… NA
ggdag also supports piping of functions and includes the pipe internally (so you don’t need to load dplyr or magrittr). Basic dplyr verbs are also supported (and anything more complex can be done directly on the data object).
-library(dplyr)
-# find how many variables are in between x and y in each path
-bigger_dag %>%
- dag_paths() %>%
- group_by(set) %>%
- filter(!is.na(path) & !is.na(name)) %>%
- summarize(n_vars_between = n() - 1L)
-#> # A tibble: 3 x 2
-#> set n_vars_between
-#> <chr> <int>
-#> 1 1 1
-#> 2 2 3
-#> 3 3 3
+library(dplyr)
+# find how many variables are in between x and y in each path
+bigger_dag %>%
+ dag_paths() %>%
+ group_by(set) %>%
+ filter(!is.na(path) & !is.na(name)) %>%
+ summarize(n_vars_between = n() - 1L)
+#> # A tibble: 3 x 2
+#> set n_vars_between
+#> <chr> <int>
+#> 1 1 1
+#> 2 2 3
+#> 3 3 3
Plotting DAGs
Most dag_*() and node_*() functions have corresponding ggdag_*() for quickly plotting the results. They call the corresponding dag_*() or node_*() function internally and plot the results in ggplot2.
-
+ggdag_paths(bigger_dag)
-
+ggdag_parents(bigger_dag, "x")
-# quickly get the miniminally sufficient adjustment sets to adjust for when
-# analyzing the effect of x on y
-ggdag_adjustment_set(bigger_dag)
+# quickly get the miniminally sufficient adjustment sets to adjust for when
+# analyzing the effect of x on y
+ggdag_adjustment_set(bigger_dag)
@@ -242,35 +246,35 @@
Plotting directly in ggplot2
ggdag() and friends are, by and large, fairly thin wrappers around included ggplot2 geoms for plotting nodes, text, and edges to and from variables. For example, ggdag_parents() can be made directly in ggplot2 like this:
-bigger_dag %>%
- node_parents("x") %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend, color = parent)) +
- geom_dag_point() +
- geom_dag_edges() +
- geom_dag_text(col = "white") +
- theme_dag() +
- scale_color_hue(breaks = c("parent", "child")) # ignores NA in legend
+bigger_dag %>%
+ node_parents("x") %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend, color = parent)) +
+ geom_dag_point() +
+ geom_dag_edges() +
+ geom_dag_text(col = "white") +
+ theme_dag() +
+ scale_color_hue(breaks = c("parent", "child")) # ignores NA in legend
The heavy lifters in ggdag are geom_dag_node()/geom_dag_point(), geom_dag_edges(), geom_dag_text(), theme_dag(), and scale_adjusted(). geom_dag_node() and geom_dag_text() plot the nodes and text, respectively, and are only modifications of geom_point() and geom_text(). geom_dag_node() is slightly stylized (it has an internal white circle), while geom_dag_point() looks more like geom_point() with a larger size. theme_dag() removes all axes and ticks, since those have little meaning in a causal model, and also makes a few other changes. expand_plot() is a convenience function that makes modifications to the scale of the plot to make them more amenable to nodes with large points and text scale_adjusted() provides defaults that are common in analyses of DAGs, e.g. setting the shape of adjusted variables to a square.
geom_dag_edges() is also a convenience function that plots directed and bi-directed edges with different geoms and arrows. Directed edges are straight lines with a single arrow head, while bi-directed lines, which are a shorthand for a latent parent variable between the two bi-directed variables (e.g. a <- L -> b), are plotted as an arc with arrow heads on either side.
You can also call edge functions directly, particularly if you only have directed edges. Much of ggdag’s edge functionality comes from ggraph, with defaults (e.g. arrow heads, truncated lines) set with DAGs in mind. Currently, ggdag has four type of edge geoms: geom_dag_edges_link(), which plots straight lines, geom_dag_edges_arc(), geom_dag_edges_diagonal(), and geom_dag_edges_fan().
-dagify(y ~ x,
- m ~ x + y) %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
- geom_dag_point() +
- geom_dag_edges_arc() +
- geom_dag_text() +
- theme_dag()
+dagify(y ~ x,
+ m ~ x + y) %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
+ geom_dag_point() +
+ geom_dag_edges_arc() +
+ geom_dag_text() +
+ theme_dag()
If you have bi-directed edges but would like to plot them as directed, node_canonical() will automatically insert the latent variable for you.
-dagify(y ~ x + z,
- x ~~ z) %>%
- node_canonical() %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
- geom_dag_point() +
- geom_dag_edges_diagonal() +
- geom_dag_text() +
- theme_dag()
+dagify(y ~ x + z,
+ x ~~ z) %>%
+ node_canonical() %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
+ geom_dag_point() +
+ geom_dag_edges_diagonal() +
+ geom_dag_text() +
+ theme_dag()
There are also geoms based on those in ggrepel for inserting text and labels, and a special geom called geom_dag_collider_edges() that highlights any biasing pathways opened by adjusting for collider nodes. See the vignette introducing DAGs for more info.
@@ -298,9 +302,8 @@
-
diff --git a/docs/articles/intro-to-ggdag_files/figure-html/ggdag_adjustment_-1.png b/docs/articles/intro-to-ggdag_files/figure-html/ggdag_adjustment_-1.png
index 222dc2c1..75cffa10 100644
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diff --git a/docs/articles/intro-to-ggdag_files/figure-html/ggdag_path-1.png b/docs/articles/intro-to-ggdag_files/figure-html/ggdag_path-1.png
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diff --git a/docs/authors.html b/docs/authors.html
index f1a7ab82..0ed781a6 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -1,6 +1,6 @@
-
+
@@ -9,17 +9,17 @@
Authors • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -35,7 +35,8 @@
-
+
+
+
Analyze and Create Elegant Directed Acyclic Graphs • ggdag
-
-
-
+
+
+
-
+
-
@@ -27,14 +28,15 @@
-
+
+
-
-
-
+
+
@@ -100,110 +105,110 @@
Installation
You can install ggdag with:
-
+install.packages("ggdag")
Or you can install the development version from GitHub with:
-
+# install.packages("devtools")
+devtools::install_github("malcolmbarrett/ggdag")
Example
ggdag makes it easy to use dagitty in the context of the tidyverse. You can directly tidy dagitty objects or use convenience functions to create DAGs using a more R-like syntax:
-library(ggdag)
-
-# example from the dagitty package
-dag <- dagitty::dagitty( "dag {
- y <- x <- z1 <- v -> z2 -> y
- z1 <- w1 <-> w2 -> z2
- x <- w1 -> y
- x <- w2 -> y
- x [exposure]
- y [outcome]
- }")
-
-tidy_dag <- tidy_dagitty(dag)
-
-tidy_dag
-#> # A DAG with 7 nodes and 12 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 13 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 v 11.8 8.03 -> z1 10.4 7.77 FALSE
-#> 2 v 11.8 8.03 -> z2 12.1 6.66 FALSE
-#> 3 w1 10.2 6.85 -> x 9.95 6.28 FALSE
-#> 4 w1 10.2 6.85 -> y 11.1 6.39 FALSE
-#> 5 w1 10.2 6.85 -> z1 10.4 7.77 FALSE
-#> 6 w1 10.2 6.85 <-> w2 10.9 5.75 FALSE
-#> 7 w2 10.9 5.75 -> x 9.95 6.28 FALSE
-#> 8 w2 10.9 5.75 -> y 11.1 6.39 FALSE
-#> 9 w2 10.9 5.75 -> z2 12.1 6.66 FALSE
-#> 10 x 9.95 6.28 -> y 11.1 6.39 FALSE
-#> 11 z1 10.4 7.77 -> x 9.95 6.28 FALSE
-#> 12 z2 12.1 6.66 -> y 11.1 6.39 FALSE
-#> 13 y 11.1 6.39 <NA> <NA> NA NA FALSE
-
-# using more R-like syntax to create the same DAG
-tidy_ggdag <- dagify(y ~ x + z2 + w2 + w1,
- x ~ z1 + w1 + w2,
- z1 ~ w1 + v,
- z2 ~ w2 + v,
- w1 ~~ w2, # bidirected path
- exposure = "x",
- outcome = "y") %>% tidy_dagitty()
-
-tidy_ggdag
-#> # A DAG with 7 nodes and 12 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 13 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 v 9.30 13.4 -> z1 9.74 12.1 FALSE
-#> 2 v 9.30 13.4 -> z2 7.96 13.0 FALSE
-#> 3 w1 8.74 11.0 -> x 8.86 11.6 FALSE
-#> 4 w1 8.74 11.0 -> y 7.68 11.5 FALSE
-#> 5 w1 8.74 11.0 -> z1 9.74 12.1 FALSE
-#> 6 w1 8.74 11.0 <-> w2 8.00 12.0 FALSE
-#> 7 w2 8.00 12.0 -> x 8.86 11.6 FALSE
-#> 8 w2 8.00 12.0 -> y 7.68 11.5 FALSE
-#> 9 w2 8.00 12.0 -> z2 7.96 13.0 FALSE
-#> 10 x 8.86 11.6 -> y 7.68 11.5 FALSE
-#> 11 z1 9.74 12.1 -> x 8.86 11.6 FALSE
-#> 12 z2 7.96 13.0 -> y 7.68 11.5 FALSE
-#> 13 y 7.68 11.5 <NA> <NA> NA NA FALSE
+library(ggdag)
+
+# example from the dagitty package
+dag <- dagitty::dagitty( "dag {
+ y <- x <- z1 <- v -> z2 -> y
+ z1 <- w1 <-> w2 -> z2
+ x <- w1 -> y
+ x <- w2 -> y
+ x [exposure]
+ y [outcome]
+ }")
+
+tidy_dag <- tidy_dagitty(dag)
+
+tidy_dag
+#> # A DAG with 7 nodes and 12 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 13 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 v 11.8 8.03 -> z1 10.4 7.77 FALSE
+#> 2 v 11.8 8.03 -> z2 12.1 6.66 FALSE
+#> 3 w1 10.2 6.85 -> x 9.95 6.28 FALSE
+#> 4 w1 10.2 6.85 -> y 11.1 6.39 FALSE
+#> 5 w1 10.2 6.85 -> z1 10.4 7.77 FALSE
+#> 6 w1 10.2 6.85 <-> w2 10.9 5.75 FALSE
+#> 7 w2 10.9 5.75 -> x 9.95 6.28 FALSE
+#> 8 w2 10.9 5.75 -> y 11.1 6.39 FALSE
+#> 9 w2 10.9 5.75 -> z2 12.1 6.66 FALSE
+#> 10 x 9.95 6.28 -> y 11.1 6.39 FALSE
+#> 11 z1 10.4 7.77 -> x 9.95 6.28 FALSE
+#> 12 z2 12.1 6.66 -> y 11.1 6.39 FALSE
+#> 13 y 11.1 6.39 <NA> <NA> NA NA FALSE
+
+# using more R-like syntax to create the same DAG
+tidy_ggdag <- dagify(y ~ x + z2 + w2 + w1,
+ x ~ z1 + w1 + w2,
+ z1 ~ w1 + v,
+ z2 ~ w2 + v,
+ w1 ~~ w2, # bidirected path
+ exposure = "x",
+ outcome = "y") %>% tidy_dagitty()
+
+tidy_ggdag
+#> # A DAG with 7 nodes and 12 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 13 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 v 9.30 13.4 -> z1 9.74 12.1 FALSE
+#> 2 v 9.30 13.4 -> z2 7.96 13.0 FALSE
+#> 3 w1 8.74 11.0 -> x 8.86 11.6 FALSE
+#> 4 w1 8.74 11.0 -> y 7.68 11.5 FALSE
+#> 5 w1 8.74 11.0 -> z1 9.74 12.1 FALSE
+#> 6 w1 8.74 11.0 <-> w2 8.00 12.0 FALSE
+#> 7 w2 8.00 12.0 -> x 8.86 11.6 FALSE
+#> 8 w2 8.00 12.0 -> y 7.68 11.5 FALSE
+#> 9 w2 8.00 12.0 -> z2 7.96 13.0 FALSE
+#> 10 x 8.86 11.6 -> y 7.68 11.5 FALSE
+#> 11 z1 9.74 12.1 -> x 8.86 11.6 FALSE
+#> 12 z2 7.96 13.0 -> y 7.68 11.5 FALSE
+#> 13 y 7.68 11.5 <NA> <NA> NA NA FALSE
ggdag also provides functionality for analyzing DAGs and plotting them in ggplot2:
-
-
-
-
+
+
+ggdag_adjustment_set(tidy_ggdag, node_size = 14) +
+ theme(legend.position = "bottom")
+
As well as geoms and other functions for plotting them directly in ggplot2:
-dagify(m ~ x + y) %>%
- tidy_dagitty() %>%
- node_dconnected("x", "y", controlling_for = "m") %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend, shape = adjusted, col = d_relationship)) +
- geom_dag_edges(aes(end_cap = ggraph::circle(10, "mm"))) +
- geom_dag_collider_edges() +
- geom_dag_point() +
- geom_dag_text(col = "white") +
- theme_dag() +
- scale_adjusted() +
- expand_plot(expand_y = expand_scale(c(0.2, 0.2))) +
- scale_color_hue(name = "d-relationship", na.value = "grey75")
-
+dagify(m ~ x + y) %>%
+ tidy_dagitty() %>%
+ node_dconnected("x", "y", controlling_for = "m") %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend, shape = adjusted, col = d_relationship)) +
+ geom_dag_edges(aes(end_cap = ggraph::circle(10, "mm"))) +
+ geom_dag_collider_edges() +
+ geom_dag_point() +
+ geom_dag_text(col = "white") +
+ theme_dag() +
+ scale_adjusted() +
+ expand_plot(expand_y = expand_scale(c(0.2, 0.2))) +
+ scale_color_hue(name = "d-relationship", na.value = "grey75")
+
And common structures of bias:
-
-
-
-
+
+
+
+ggdag_butterfly_bias(edge_type = "diagonal")
+
@@ -212,11 +217,11 @@
Links
-- Download from CRAN at
https:// cloud.r-project.org/ package=ggdag
+ - Download from CRAN at
https://cloud.r-project.org/package=ggdag
-- Browse source code at
https:// github.com/ malcolmbarrett/ ggdag
+ - Browse source code at
https://github.com/malcolmbarrett/ggdag
-- Report a bug at
https:// github.com/ malcolmbarrett/ ggdag/ issues
+ - Report a bug at
https://github.com/malcolmbarrett/ggdag/issues
@@ -231,7 +236,7 @@ License
Developers
-
-Malcolm Barrett
Author, maintainer
+Malcolm Barrett
Author, maintainer 
@@ -253,13 +258,12 @@ Dev status
-
-
+
diff --git a/docs/news/index.html b/docs/news/index.html
new file mode 100644
index 00000000..dfd03113
--- /dev/null
+++ b/docs/news/index.html
@@ -0,0 +1,167 @@
+
+
+
+
+
+
+
+
+Changelog • ggdag
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Changelog
+ Source: NEWS.md
+
+
+
+
+ggdag 0.2.0 Unreleased
+
+
+- Fixed join bug in
node_equivalent_class() that didn’t account for the way dagitty returns DAGs with no direction
+- Fixed join bug in
node_equivalent_class() that didn’t check to node
+- Implemented
is_false() to avoid dependency on R 3.5.0
+- improved edge lengths
+- add
{} to adjustment set names to reflect convention
+- Set nodes to be unstyled by default
+- Changed default themes and scales to be more like base ggplot2
+- Added a
NEWS.md file to track changes to the package.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
diff --git a/docs/pkgdown.css b/docs/pkgdown.css
index 6ca2f37a..c03fb08d 100644
--- a/docs/pkgdown.css
+++ b/docs/pkgdown.css
@@ -58,9 +58,14 @@ img {
max-width: 100%;
}
+/* Fix bug in bootstrap (only seen in firefox) */
+summary {
+ display: list-item;
+}
+
/* Typographic tweaking ---------------------------------*/
-.contents h1.page-header {
+.contents .page-header {
margin-top: calc(-60px + 1em);
}
@@ -136,10 +141,9 @@ a.anchor {
.ref-index th {font-weight: normal;}
.ref-index td {vertical-align: top;}
+.ref-index .icon {width: 40px;}
.ref-index .alias {width: 40%;}
-.ref-index .title {width: 60%;}
-
-.ref-index .alias {width: 40%;}
+.ref-index-icons .alias {width: calc(40% - 40px);}
.ref-index .title {width: 60%;}
.ref-arguments th {text-align: right; padding-right: 10px;}
diff --git a/docs/pkgdown.js b/docs/pkgdown.js
index de9bd724..eb7e83d2 100644
--- a/docs/pkgdown.js
+++ b/docs/pkgdown.js
@@ -25,9 +25,13 @@
for (var i = 0; i < links.length; i++) {
if (links[i].getAttribute("href") === "#")
continue;
- var path = paths(links[i].pathname);
+ // Ignore external links
+ if (links[i].host !== location.host)
+ continue;
+
+ var nav_path = paths(links[i].pathname);
- var length = prefix_length(cur_path, path);
+ var length = prefix_length(nav_path, cur_path);
if (length > max_length) {
max_length = length;
pos = i;
@@ -52,13 +56,14 @@
return(pieces);
}
+ // Returns -1 if not found
function prefix_length(needle, haystack) {
if (needle.length > haystack.length)
- return(0);
+ return(-1);
// Special case for length-0 haystack, since for loop won't run
if (haystack.length === 0) {
- return(needle.length === 0 ? 1 : 0);
+ return(needle.length === 0 ? 0 : -1);
}
for (var i = 0; i < haystack.length; i++) {
@@ -78,9 +83,9 @@
element.setAttribute('data-original-title', tooltipOriginalTitle);
}
- if(Clipboard.isSupported()) {
+ if(ClipboardJS.isSupported()) {
$(document).ready(function() {
- var copyButton = "";
+ var copyButton = "";
$(".examples, div.sourceCode").addClass("hasCopyButton");
@@ -91,7 +96,7 @@
$('.btn-copy-ex').tooltip({container: 'body'});
// Initialize clipboard:
- var clipboardBtnCopies = new Clipboard('[data-clipboard-copy]', {
+ var clipboardBtnCopies = new ClipboardJS('[data-clipboard-copy]', {
text: function(trigger) {
return trigger.parentNode.textContent;
}
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 5b243ff0..82542de3 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,11 +1,8 @@
-pandoc: 2.1.3
-pkgdown: 1.1.0.9000
-pkgdown_sha: 98bfe0fdfd59b33ef1a88ef6896cd60f805f0e81
+pandoc: 2.7.3
+pkgdown: 1.3.0
+pkgdown_sha: ~
articles:
bias-structures: bias-structures.html
intro-to-dags: intro-to-dags.html
intro-to-ggdag: intro-to-ggdag.html
-urls:
- reference: https://malco.io/ggdag//reference
- article: https://malco.io/ggdag//articles
diff --git a/docs/reference/activate_collider_paths.html b/docs/reference/activate_collider_paths.html
index 362a0afd..de0af5ee 100644
--- a/docs/reference/activate_collider_paths.html
+++ b/docs/reference/activate_collider_paths.html
@@ -1,6 +1,6 @@
-
+
@@ -9,17 +9,17 @@
Activate paths opened by stratifying on a collider — activate_collider_paths • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Covariate Adjustment Sets — Covariate Adjustment Sets • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Convert a <code>tidy_dagitty</code> object to data.frame — as.data.frame.tidy_dagitty • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Convert a <code>tidy_dagitty</code> object to tbl — as.tbl.tidy_daggity • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Convert DAGS to tidygraph — as_tbl_graph • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Canonicalize a DAG — Canonicalize DAGs • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -41,7 +41,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Find colliders — Colliders • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Adjust for variables and activate any biasing paths that result — Adjust for variables • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Manipulate DAG coordinates — coordinates • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
D-relationship between variables — Assess d-separation between variables • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -44,7 +44,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Create a dagitty DAG — dag • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Create a dagitty DAG using R-like syntax — dagify • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -41,7 +41,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Dplyr verb methods for <code>tidy_dagitty</code> objects — dplyr • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Generating Equivalent Models — Equivalent DAGs and Classes • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -44,7 +44,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Find Exogenous Variables — Exogenous Variables • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Quickly scale the size of a ggplot — expand_plot • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Generate expansion vector for scales. — expand_scale • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -43,7 +43,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Fortify a <code>tidy_dagitty</code> object for <code>ggplot2</code> — fortify • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Edges for paths activated by stratification on colliders — geom_dag_collider_edges • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -39,7 +39,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Directed DAG edges — DAG Edges • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Directed and bidirected DAG edges — geom_dag_edges • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Node text — geom_dag_text • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Quickly plot a DAG in ggplot2 — ggdag • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Quickly plot a DAG in ggplot2 — ggdag_classic • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -39,7 +39,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Create a new ggplot — ggplot.tidy_dagitty • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -38,7 +38,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Function reference • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -35,7 +35,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Find Instrumental Variables — Instrumental Variables • ggdag
-
+
-
+
-
+
-
+
-
+
@@ -40,7 +40,8 @@
-
+
+
-
+
@@ -9,17 +9,17 @@
Test for object class for tidy_dagitty — is.tidy_dagitty • ggdag
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Detecting colliders in DAGs — Test if Variable Is Collider • ggdag
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DAG labels — DAG Labels • ggdag
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DAG Nodes — Nodes • ggdag
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Pipe operator — %>% • ggdag
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Familial relationships between variables — Assess familial relationships between variables • ggdag
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An Introduction to Directed Acyclic Graphs
Malcolm Barrett
-2018-08-23
+2019-09-11
Source:vignettes/intro-to-dags.Rmd
intro-to-dags.Rmd2018-08-23
A quick note on terminology: I use the terms confounding and selection bias below, the terms of choice in epidemiology. The terms, however, depend on the field. In some fields, confounding is referred to as omitted variable bias or selection bias. Selection bias also sometimes refers to variable selection bias, a related issue that refers to misspecified models.
- +Directed Acyclic Graphs
A DAG displays assumptions about the relationship between variables (often called nodes in the context of graphs). The assumptions we make take the form of lines (or edges) going from one node to another. These edges are directed, which means to say that they have a single arrowhead indicating their effect. Here’s a simple DAG where we assume that x affects y:
- +
You also sometimes see edges that look bi-directed, like this:
- +
But this is actually shorthand for an unmeasured cause of the two variables (in other words, unmeasured confounding):
-# canonicalize the DAG: Add the latent variable in to the graph
-dagify(y ~~ x) %>%
- ggdag_canonical() # canonicalize the DAG: Add the latent variable in to the graph
+dagify(y ~~ x) %>%
+ ggdag_canonical()
A DAG is also acyclic, which means that there are no feedback loops; a variable can’t be its own descendant. The above are all DAGs because they are acyclic, but this is not:
- +
Relationships between variables
Let’s say we’re looking at the relationship between smoking and cardiac arrest. We might assume that smoking causes changes in cholesterol, which causes cardiac arrest:
-smoking_ca_dag <- dagify(cardiacarrest ~ cholesterol,
- cholesterol ~ smoking + weight,
- smoking ~ unhealthy,
- weight ~ unhealthy,
- labels = c("cardiacarrest" = "Cardiac\n Arrest",
- "smoking" = "Smoking",
- "cholesterol" = "Cholesterol",
- "unhealthy" = "Unhealthy\n Lifestyle",
- "weight" = "Weight"),
- latent = "unhealthy",
- exposure = "smoking",
- outcome = "cardiacarrest")
-
-ggdag(smoking_ca_dag, text = FALSE, use_labels = "label")smoking_ca_dag <- dagify(cardiacarrest ~ cholesterol,
+ cholesterol ~ smoking + weight,
+ smoking ~ unhealthy,
+ weight ~ unhealthy,
+ labels = c("cardiacarrest" = "Cardiac\n Arrest",
+ "smoking" = "Smoking",
+ "cholesterol" = "Cholesterol",
+ "unhealthy" = "Unhealthy\n Lifestyle",
+ "weight" = "Weight"),
+ latent = "unhealthy",
+ exposure = "smoking",
+ outcome = "cardiacarrest")
+
+ggdag(smoking_ca_dag, text = FALSE, use_labels = "label")
The path from smoking to cardiac arrest is directed: smoking causes cholesterol to rise, which then increases risk for cardiac arrest. Cholesterol is an intermediate variable between smoking and cardiac arrest. Directed paths are also chains, because each is causal on the next. Let’s say we also assume that weight causes cholesterol to rise and thus increases risk of cardiac arrest. Now there’s another chain in the DAG: from weight to cardiac arrest. However, this chain is indirect, at least as far as the relationship between smoking and cardiac arrest goes.
We also assume that a person who smokes is more likely to be someone who engages in other unhealthy behaviors, such as overeating. On the DAG, this is portrayed as a latent (unmeasured) node, called unhealthy lifestyle. Having a predilection towards unhealthy behaviors leads to both smoking and increased weight. Here, the relationship between smoking and weight is through a forked path (weight <- unhealthy lifestyle -> smoking) rather than a chain; because they have a mutual parent, smoking and weight are associated (in real life, there’s probably a more direct relationship between the two, but we’ll ignore that for simplicity).
@@ -157,11 +161,11 @@There are also common ways of describing the relationships between nodes: parents, children, ancestors, descendants, and neighbors (there are a few others, as well, but they refer to less common relationships). Parents and children refer to direct relationships; descendants and ancestors can be anywhere along the path to or from a node, respectively. Here, smoking and weight are both parents of cholesterol, while smoking and weight are both children of an unhealthy lifestyle. Cardiac arrest is a descendant of an unhealthy lifestyle, which is in turn an ancestor of all nodes in the graph.
So, in studying the causal effect of smoking on cardiac arrest, where does this DAG leave us? We only want to know the directed path from smoking to cardiac arrest, but there also exists an indirect, or back-door, path. This is confounding. Judea Pearl, who developed much of the theory of causal graphs, said that confounding is like water in a pipe: it flows freely in open pathways, and we need to block it somewhere along the way. We don’t necessarily need to block the water at multiple points along the same back-door path, although we may have to block more than one path. We often talk about confounders, but really we should talk about confounding, because it is about the pathway more than any particular node along the path.
Chains and forks are open pathways, so in a DAG where nothing is conditioned upon, any back-door paths must be one of the two. In addition to the directed pathway to cardiac arrest, there’s also an open back-door path through the forked path at unhealthy lifestyle and on from there through the chain to cardiac arrest:
- +ggdag_paths(smoking_ca_dag, text = FALSE, use_labels = "label", shadow = TRUE)
We need to account for this back-door path in our analysis. There are many ways to go about that–stratification, including the variable in a regression model, matching, inverse probability weighting–all with pros and cons. But each strategy must include a decision about which variables to account for. Many analysts take the strategy of putting in all possible confounders. This can be bad news, because adjusting for colliders and mediators can introduce bias, as we’ll discuss shortly. Instead, we’ll look at minimally sufficient adjustment sets: sets of covariates that, when adjusted for, block all back-door paths, but include no more or no less than necessary. That means there can be many minimally sufficient sets, and if you remove even one variable from a given set, a back-door path will open. Some DAGs, like the first one in this vignette (x -> y), have no back-door paths to close, so the minimally sufficient adjustment set is empty (sometimes written as “{}”). Others, like the cyclic DAG above, or DAGs with important variables that are unmeasured, can not produce any sets sufficient to close back-door paths.
For the smoking-cardiac arrest question, there is a single set with a single variable: {weight}. Accounting for weight will give us an unbiased estimate of the relationship between smoking and cardiac arrest, assuming our DAG is correct. We do not need to (or want to) control for cholesterol, however, because it’s an intermediate variable between smoking and cardiac arrest; controlling for it blocks the path between the two, which will then bias our estimate (see below for more on mediation).
- +ggdag_adjustment_set(smoking_ca_dag, text = FALSE, use_labels = "label", shadow = TRUE)
More complicated DAGs will produce more complicated adjustment sets; assuming your DAG is correct, any given set will theoretically close the back-door path between the outcome and exposure. Still, one set may be better to use than the other, depending on your data. For instance, one set may contain a variable known to have a lot of measurement error or with a lot of missing observations. It may, then, be better to use a set that you think is going to be a better representation of the variables you need to include. Including a variable that doesn’t actually represent the node well will lead to residual confounding.
What about controlling for multiple variables along the back-door path, or a variable that isn’t along any back-door path? Even if those variables are not colliders or mediators, it can still cause a problem, depending on your model. Some estimates, like risk ratios, work fine when non-confounders are included. This is because they are collapsible: risk ratios are constant across the strata of non-confounders. Some common estimates, though, like the odds ratio and hazard ratio, are non-collapsible: they are not necessarily constant across strata of non-confounders and thus can be biased by their inclusion. There are situations, like when the outcome is rare in the population (the so-called rare disease assumption), or when using sophisticated sampling techniques, like incident-density sampling, when they approximate the risk ratio. Otherwise, including extra variables may be problematic.
@@ -171,29 +175,29 @@Colliders and collider-stratification bias
In a path that is an inverted fork (x -> m <- y), the node where two or more arrowheads meet is called a collider (because the paths collide there). An inverted fork is not an open path; it is blocked at the collider. That is to say, we don’t need to account for m to assess for the causal effect of x on y; the back-door path is already blocked by m.
Let’s consider an example. Influenza and chicken pox are independent; their causes (influenza viruses and the varicella-zoster virus, respectively) have nothing to do with each other. In real life, there may be some confounders that associate them, like having a depressed immune system, but for this example we’ll assume that they are unconfounded. However, both the flu and chicken pox cause fevers. The DAG looks like this:
-fever_dag <- collider_triangle(x = "Influenza",
- y = "Chicken Pox",
- m = "Fever")
-
-ggdag(fever_dag, text = FALSE, use_labels = "label")fever_dag <- collider_triangle(x = "Influenza",
+ y = "Chicken Pox",
+ m = "Fever")
+
+ggdag(fever_dag, text = FALSE, use_labels = "label")
If we want to assess the causal effect of influenza on chicken pox, we do not need to account for anything. In the terminology used by Pearl, they are already d-separated (direction separated), because there is no effect on one by the other, nor are there any back-door paths:
- +ggdag_dseparated(fever_dag, text = FALSE, use_labels = "label")
However, if we control for fever, they become associated within strata of the collider, fever. We open a biasing pathway between the two, and they become d-connected:
- +ggdag_dseparated(fever_dag, controlling_for = "m",
+ text = FALSE, use_labels = "label")
This can be counter-intuitive at first. Why does controlling for a confounder reduce bias but adjusting for a collider increase it? It’s because whether or not you have a fever tells me something about your disease. If you have a fever, but you don’t have the flu, I now have more evidence that you have chicken pox. Pearl presents it like algebra: I can’t solve y = 10 + m. But when I know that m = 1, I can solve for y.
Unfortunately, there’s a second, less obvious form of collider-stratification bias: adjusting on the descendant of a collider. That means that a variable downstream from the collider can also cause this form of bias. For example, with our flu-chicken pox-fever example, it may be that having a fever leads to people taking a fever reducer, like acetaminophen. Because fever reducers are downstream from fever, controlling for it induces downstream collider-stratification bias:
-dagify(fever ~ flu + pox,
- acetaminophen ~ fever,
- labels = c("flu" = "Influenza",
- "pox" = "Chicken Pox",
- "fever" = "Fever",
- "acetaminophen" = "Acetaminophen")) %>%
-ggdag_dseparated(from = "flu", to = "pox", controlling_for = "acetaminophen",
- text = FALSE, use_labels = "label")dagify(fever ~ flu + pox,
+ acetaminophen ~ fever,
+ labels = c("flu" = "Influenza",
+ "pox" = "Chicken Pox",
+ "fever" = "Fever",
+ "acetaminophen" = "Acetaminophen")) %>%
+ggdag_dseparated(from = "flu", to = "pox", controlling_for = "acetaminophen",
+ text = FALSE, use_labels = "label")
Collider-stratification bias is responsible for many cases of bias, and it is often not dealt with appropriately. Selection bias, missing data, and publication bias can all be thought of as collider-stratification bias. It becomes trickier in more complicated DAGs; sometimes colliders are also confounders, and we need to either come up with a strategy to adjust for the resulting bias from adjusting the collider, or we need to pick the strategy that’s likely to result in the least amount of bias. See the vignette on common structures of bias for more.
Mediation
Controlling for intermediate variables may also induce bias, because it decomposes the total effect of x on y into its parts. Depending on the research question, that may be exactly what you want, in which case you should use mediation analysis, e.g. via SEM, which can estimate direct, indirect, and total effects. Let’s return to the smoking example. Here, we only care about how smoking affects cardiac arrest, not the pathways through cholesterol it may take. Moreover, since cholesterol (at least in our DAG) intercepts the only directed pathway from smoking to cardiac arrest, controlling for it will block that relationship; smoking and cardiac arrest will appear unassociated (note that I’m not including the paths opened by controlling for a collider in this plot for clarity):
-ggdag_dseparated(smoking_ca_dag, controlling_for = c("weight", "cholesterol"),
- text = FALSE, use_labels = "label", collider_lines = FALSE)ggdag_dseparated(smoking_ca_dag, controlling_for = c("weight", "cholesterol"),
+ text = FALSE, use_labels = "label", collider_lines = FALSE)
Now smoking and cardiac arrest are d-separated. Since our question is about the total effect of smoking on cardiac arrest, our result is now going to be biased.
Resources
-- Judea Pearl also has a number of texts on the subject of varying technical difficulty. A friendly start is his recently released Book of Why, as well as his article summarizing the book: The Seven Tools of Causal Inference with Reflections on Machine Learning. A more technical introduction is Causal Inference in Statistics: A Primer. See also his article with Sander Greenland and James Robins on collapsibility: Confounding and Collapsibility in Causal Inference.
+- Judea Pearl also has a number of texts on the subject of varying technical difficulty. A friendly start is his recently released Book of Why, as well as his article summarizing the book: The Seven Tools of Causal Inference with Reflections on Machine Learning. A more technical introduction is Causal Inference in Statistics: A Primer. See also his article with Sander Greenland and James Robins on collapsibility: Confounding and Collapsibility in Causal Inference.
- Miguel Hernán, who has written extensively on the subject of causal inference and DAGs, has an accessible course on edx that teaches the use of DAGs for causal inference: Causal Diagrams: Draw Your Assumptions Before Your Conclusions. Also see his article The Hazard of Hazard Ratios for more on issues with hazard ratios in causal inference.
- Julia Rohrer has a very readable paper introducing DAGs, mostly from the perspective of psychology: Thinking Clearly About Correlations and Causation: Graphical Causal Models for Observational Data
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An Introduction to ggdag
Malcolm Barrett
-2018-08-23
+2019-09-11
Source:vignettes/intro-to-ggdag.Rmd
intro-to-ggdag.Rmd
Creating Directed Acyclic Graphs
If you already use dagitty, ggdag can tidy your DAG directly.
library(dagitty)
-library(ggdag)
-
-dag <- dagitty("dag{y <- z -> x}")
-tidy_dagitty(dag)
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # A tibble: 4 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 z 28.5 23.3 -> x 28.5 24.4 FALSE
-#> 2 z 28.5 23.3 -> y 28.5 22.1 FALSE
-#> 3 x 28.5 24.4 <NA> <NA> NA NA FALSE
-#> 4 y 28.5 22.1 <NA> <NA> NA NA FALSElibrary(dagitty)
+library(ggdag)
+
+dag <- dagitty("dag{y <- z -> x}")
+tidy_dagitty(dag)
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # A tibble: 4 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 z 28.5 23.3 -> x 28.5 24.4 FALSE
+#> 2 z 28.5 23.3 -> y 28.5 22.1 FALSE
+#> 3 x 28.5 24.4 <NA> <NA> NA NA FALSE
+#> 4 y 28.5 22.1 <NA> <NA> NA NA FALSENote that, while dagitty supports a number of graph types, ggdag currently only supports DAGs.
dagitty uses a syntax similar to the dot language of graphviz. This syntax has the advantage of being compact, but ggdag also provides the ability to create a dagitty object using a more R-like formula syntax through the dagify() function. dagify() accepts any number of formulas to create a DAG. It also has options for declaring which variables are exposures, outcomes, or latent, as well as coordinates and labels for each node.
dagified <- dagify(x ~ z,
- y ~ z,
- exposure = "x",
- outcome = "y")
-tidy_dagitty(dagified)
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 4 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 z 23.6 20.4 -> x 23.6 21.5 FALSE
-#> 2 z 23.6 20.4 -> y 23.6 19.2 FALSE
-#> 3 x 23.6 21.5 <NA> <NA> NA NA FALSE
-#> 4 y 23.6 19.2 <NA> <NA> NA NA FALSEdagified <- dagify(x ~ z,
+ y ~ z,
+ exposure = "x",
+ outcome = "y")
+tidy_dagitty(dagified)
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 4 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 z 23.6 20.4 -> x 23.6 21.5 FALSE
+#> 2 z 23.6 20.4 -> y 23.6 19.2 FALSE
+#> 3 x 23.6 21.5 <NA> <NA> NA NA FALSE
+#> 4 y 23.6 19.2 <NA> <NA> NA NA FALSECurrently, ggdag supports directed (x ~ y) and bi-directed (a ~~ b) relationships
tidy_dagitty() uses layout functions from ggraph and igraph for coordinates if none are provided, which can be specified with the layout argument. Objects of class tidy_dagitty or dagitty can be plotted quickly with ggdag(). If the DAG is not yet tidied, ggdag() and most other quick plotting functions in ggdag do so internally.
ggdag(dag, layout = "circle")
A tidy_dagitty object is just a list with a tbl_df, called data, and the dagitty object, called dag:
tidy_dag <- tidy_dagitty(dagified)
-str(tidy_dag)
-#> List of 2
-#> $ data:Classes 'tbl_df', 'tbl' and 'data.frame': 4 obs. of 8 variables:
-#> ..$ name : chr [1:4] "z" "z" "x" "y"
-#> ..$ x : num [1:4] 23.3 23.3 22.9 23.7
-#> ..$ y : num [1:4] 25.5 25.5 26.6 24.4
-#> ..$ direction: Factor w/ 3 levels "<-","->","<->": 2 2 NA NA
-#> ..$ to : chr [1:4] "x" "y" NA NA
-#> ..$ xend : num [1:4] 22.9 23.7 NA NA
-#> ..$ yend : num [1:4] 26.6 24.4 NA NA
-#> ..$ circular : logi [1:4] FALSE FALSE FALSE FALSE
-#> $ dag : 'dagitty' Named chr "dag {\nx [exposure]\ny [outcome]\nz\nz -> x\nz -> y\n}\n"
-#> - attr(*, "class")= chr "tidy_dagitty"tidy_dag <- tidy_dagitty(dagified)
+str(tidy_dag)
+#> List of 2
+#> $ data:Classes 'tbl_df', 'tbl' and 'data.frame': 4 obs. of 8 variables:
+#> ..$ name : chr [1:4] "z" "z" "x" "y"
+#> ..$ x : num [1:4] 23.3 23.3 22.9 23.7
+#> ..$ y : num [1:4] 25.5 25.5 26.6 24.4
+#> ..$ direction: Factor w/ 3 levels "<-","->","<->": 2 2 NA NA
+#> ..$ to : chr [1:4] "x" "y" NA NA
+#> ..$ xend : num [1:4] 22.9 23.7 NA NA
+#> ..$ yend : num [1:4] 26.6 24.4 NA NA
+#> ..$ circular : logi [1:4] FALSE FALSE FALSE FALSE
+#> $ dag : 'dagitty' Named chr "dag {\nx [exposure]\ny [outcome]\nz\nz -> x\nz -> y\n}\n"
+#> - attr(*, "class")= chr "tidy_dagitty"Working with DAGs
Most of the analytic functions in dagitty have extensions in ggdag and are named dag_*() or node_*(), depending on if they are working with specific nodes or the entire DAG. A simple example is node_parents(), which adds a column to the to the tidy_dagitty object about the parents of a given variable:
node_parents(tidy_dag, "x")
-#> # A DAG with 3 nodes and 2 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 4 x 9
-#> name x y direction to xend yend circular parent
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <fct>
-#> 1 z 23.3 25.5 -> x 22.9 26.6 FALSE parent
-#> 2 z 23.3 25.5 -> y 23.7 24.4 FALSE parent
-#> 3 x 22.9 26.6 <NA> <NA> NA NA FALSE child
-#> 4 y 23.7 24.4 <NA> <NA> NA NA FALSE <NA>node_parents(tidy_dag, "x")
+#> # A DAG with 3 nodes and 2 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 4 x 9
+#> name x y direction to xend yend circular parent
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <fct>
+#> 1 z 23.3 25.5 -> x 22.9 26.6 FALSE parent
+#> 2 z 23.3 25.5 -> y 23.7 24.4 FALSE parent
+#> 3 x 22.9 26.6 <NA> <NA> NA NA FALSE child
+#> 4 y 23.7 24.4 <NA> <NA> NA NA FALSE <NA>Or working with the entire DAG to produce a tidy_dagitty that has all pathways between two variables:
bigger_dag <- dagify(y ~ x + a + b,
- x ~ a + b,
- exposure = "x",
- outcome = "y")
-# automatically searches the paths between the variables labelled exposure and
-# outcome
-dag_paths(bigger_dag)
-#> # A DAG with 4 nodes and 15 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 20 x 11
-#> set name x y direction to xend yend circular path type
-#> <chr> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <ch> <lgl>
-#> 1 1 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 2 1 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 3 1 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 4 1 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 5 1 x 16.8 18.2 -> y 17.7 18.2 FALSE ope… NA
-#> 6 1 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 7 2 a 17.3 19.2 -> x 16.8 18.2 FALSE ope… NA
-#> 8 2 a 17.3 19.2 -> y 17.7 18.2 FALSE ope… NA
-#> 9 2 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 10 2 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 11 2 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 12 2 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 13 2 x 16.8 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 14 3 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
-#> 15 3 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 16 3 b 17.3 17.2 -> x 16.8 18.2 FALSE ope… NA
-#> 17 3 b 17.3 17.2 -> y 17.7 18.2 FALSE ope… NA
-#> 18 3 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
-#> 19 3 y 17.7 18.2 <NA> <NA> NA NA FALSE ope… NA
-#> 20 3 x 16.8 18.2 <NA> <NA> NA NA FALSE ope… NAbigger_dag <- dagify(y ~ x + a + b,
+ x ~ a + b,
+ exposure = "x",
+ outcome = "y")
+# automatically searches the paths between the variables labelled exposure and
+# outcome
+dag_paths(bigger_dag)
+#> # A DAG with 4 nodes and 15 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 20 x 11
+#> set name x y direction to xend yend circular path type
+#> <chr> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl> <chr> <lgl>
+#> 1 1 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 2 1 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 3 1 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 4 1 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 5 1 x 16.8 18.2 -> y 17.7 18.2 FALSE open… NA
+#> 6 1 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 7 2 a 17.3 19.2 -> x 16.8 18.2 FALSE open… NA
+#> 8 2 a 17.3 19.2 -> y 17.7 18.2 FALSE open… NA
+#> 9 2 b 17.3 17.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 10 2 b 17.3 17.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 11 2 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 12 2 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 13 2 x 16.8 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 14 3 a 17.3 19.2 -> x 16.8 18.2 FALSE <NA> NA
+#> 15 3 a 17.3 19.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 16 3 b 17.3 17.2 -> x 16.8 18.2 FALSE open… NA
+#> 17 3 b 17.3 17.2 -> y 17.7 18.2 FALSE open… NA
+#> 18 3 x 16.8 18.2 -> y 17.7 18.2 FALSE <NA> NA
+#> 19 3 y 17.7 18.2 <NA> <NA> NA NA FALSE open… NA
+#> 20 3 x 16.8 18.2 <NA> <NA> NA NA FALSE open… NAggdag also supports piping of functions and includes the pipe internally (so you don’t need to load dplyr or magrittr). Basic dplyr verbs are also supported (and anything more complex can be done directly on the data object).
library(dplyr)
-# find how many variables are in between x and y in each path
-bigger_dag %>%
- dag_paths() %>%
- group_by(set) %>%
- filter(!is.na(path) & !is.na(name)) %>%
- summarize(n_vars_between = n() - 1L)
-#> # A tibble: 3 x 2
-#> set n_vars_between
-#> <chr> <int>
-#> 1 1 1
-#> 2 2 3
-#> 3 3 3library(dplyr)
+# find how many variables are in between x and y in each path
+bigger_dag %>%
+ dag_paths() %>%
+ group_by(set) %>%
+ filter(!is.na(path) & !is.na(name)) %>%
+ summarize(n_vars_between = n() - 1L)
+#> # A tibble: 3 x 2
+#> set n_vars_between
+#> <chr> <int>
+#> 1 1 1
+#> 2 2 3
+#> 3 3 3Plotting DAGs
Most dag_*() and node_*() functions have corresponding ggdag_*() for quickly plotting the results. They call the corresponding dag_*() or node_*() function internally and plot the results in ggplot2.
ggdag_paths(bigger_dag)
ggdag_parents(bigger_dag, "x")
# quickly get the miniminally sufficient adjustment sets to adjust for when
-# analyzing the effect of x on y
-ggdag_adjustment_set(bigger_dag)# quickly get the miniminally sufficient adjustment sets to adjust for when
+# analyzing the effect of x on y
+ggdag_adjustment_set(bigger_dag)
Plotting directly in ggplot2
ggdag() and friends are, by and large, fairly thin wrappers around included ggplot2 geoms for plotting nodes, text, and edges to and from variables. For example, ggdag_parents() can be made directly in ggplot2 like this:
bigger_dag %>%
- node_parents("x") %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend, color = parent)) +
- geom_dag_point() +
- geom_dag_edges() +
- geom_dag_text(col = "white") +
- theme_dag() +
- scale_color_hue(breaks = c("parent", "child")) # ignores NA in legendbigger_dag %>%
+ node_parents("x") %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend, color = parent)) +
+ geom_dag_point() +
+ geom_dag_edges() +
+ geom_dag_text(col = "white") +
+ theme_dag() +
+ scale_color_hue(breaks = c("parent", "child")) # ignores NA in legend
The heavy lifters in ggdag are geom_dag_node()/geom_dag_point(), geom_dag_edges(), geom_dag_text(), theme_dag(), and scale_adjusted(). geom_dag_node() and geom_dag_text() plot the nodes and text, respectively, and are only modifications of geom_point() and geom_text(). geom_dag_node() is slightly stylized (it has an internal white circle), while geom_dag_point() looks more like geom_point() with a larger size. theme_dag() removes all axes and ticks, since those have little meaning in a causal model, and also makes a few other changes. expand_plot() is a convenience function that makes modifications to the scale of the plot to make them more amenable to nodes with large points and text scale_adjusted() provides defaults that are common in analyses of DAGs, e.g. setting the shape of adjusted variables to a square.
geom_dag_edges() is also a convenience function that plots directed and bi-directed edges with different geoms and arrows. Directed edges are straight lines with a single arrow head, while bi-directed lines, which are a shorthand for a latent parent variable between the two bi-directed variables (e.g. a <- L -> b), are plotted as an arc with arrow heads on either side.
You can also call edge functions directly, particularly if you only have directed edges. Much of ggdag’s edge functionality comes from ggraph, with defaults (e.g. arrow heads, truncated lines) set with DAGs in mind. Currently, ggdag has four type of edge geoms: geom_dag_edges_link(), which plots straight lines, geom_dag_edges_arc(), geom_dag_edges_diagonal(), and geom_dag_edges_fan().
dagify(y ~ x,
- m ~ x + y) %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
- geom_dag_point() +
- geom_dag_edges_arc() +
- geom_dag_text() +
- theme_dag()dagify(y ~ x,
+ m ~ x + y) %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
+ geom_dag_point() +
+ geom_dag_edges_arc() +
+ geom_dag_text() +
+ theme_dag()
If you have bi-directed edges but would like to plot them as directed, node_canonical() will automatically insert the latent variable for you.
dagify(y ~ x + z,
- x ~~ z) %>%
- node_canonical() %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
- geom_dag_point() +
- geom_dag_edges_diagonal() +
- geom_dag_text() +
- theme_dag()dagify(y ~ x + z,
+ x ~~ z) %>%
+ node_canonical() %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
+ geom_dag_point() +
+ geom_dag_edges_diagonal() +
+ geom_dag_text() +
+ theme_dag()
There are also geoms based on those in ggrepel for inserting text and labels, and a special geom called geom_dag_collider_edges() that highlights any biasing pathways opened by adjusting for collider nodes. See the vignette introducing DAGs for more info.
Installation
You can install ggdag with:
install.packages("ggdag")Or you can install the development version from GitHub with:
- +# install.packages("devtools")
+devtools::install_github("malcolmbarrett/ggdag")Example
ggdag makes it easy to use dagitty in the context of the tidyverse. You can directly tidy dagitty objects or use convenience functions to create DAGs using a more R-like syntax:
library(ggdag)
-
-# example from the dagitty package
-dag <- dagitty::dagitty( "dag {
- y <- x <- z1 <- v -> z2 -> y
- z1 <- w1 <-> w2 -> z2
- x <- w1 -> y
- x <- w2 -> y
- x [exposure]
- y [outcome]
- }")
-
-tidy_dag <- tidy_dagitty(dag)
-
-tidy_dag
-#> # A DAG with 7 nodes and 12 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 13 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 v 11.8 8.03 -> z1 10.4 7.77 FALSE
-#> 2 v 11.8 8.03 -> z2 12.1 6.66 FALSE
-#> 3 w1 10.2 6.85 -> x 9.95 6.28 FALSE
-#> 4 w1 10.2 6.85 -> y 11.1 6.39 FALSE
-#> 5 w1 10.2 6.85 -> z1 10.4 7.77 FALSE
-#> 6 w1 10.2 6.85 <-> w2 10.9 5.75 FALSE
-#> 7 w2 10.9 5.75 -> x 9.95 6.28 FALSE
-#> 8 w2 10.9 5.75 -> y 11.1 6.39 FALSE
-#> 9 w2 10.9 5.75 -> z2 12.1 6.66 FALSE
-#> 10 x 9.95 6.28 -> y 11.1 6.39 FALSE
-#> 11 z1 10.4 7.77 -> x 9.95 6.28 FALSE
-#> 12 z2 12.1 6.66 -> y 11.1 6.39 FALSE
-#> 13 y 11.1 6.39 <NA> <NA> NA NA FALSE
-
-# using more R-like syntax to create the same DAG
-tidy_ggdag <- dagify(y ~ x + z2 + w2 + w1,
- x ~ z1 + w1 + w2,
- z1 ~ w1 + v,
- z2 ~ w2 + v,
- w1 ~~ w2, # bidirected path
- exposure = "x",
- outcome = "y") %>% tidy_dagitty()
-
-tidy_ggdag
-#> # A DAG with 7 nodes and 12 edges
-#> #
-#> # Exposure: x
-#> # Outcome: y
-#> #
-#> # A tibble: 13 x 8
-#> name x y direction to xend yend circular
-#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
-#> 1 v 9.30 13.4 -> z1 9.74 12.1 FALSE
-#> 2 v 9.30 13.4 -> z2 7.96 13.0 FALSE
-#> 3 w1 8.74 11.0 -> x 8.86 11.6 FALSE
-#> 4 w1 8.74 11.0 -> y 7.68 11.5 FALSE
-#> 5 w1 8.74 11.0 -> z1 9.74 12.1 FALSE
-#> 6 w1 8.74 11.0 <-> w2 8.00 12.0 FALSE
-#> 7 w2 8.00 12.0 -> x 8.86 11.6 FALSE
-#> 8 w2 8.00 12.0 -> y 7.68 11.5 FALSE
-#> 9 w2 8.00 12.0 -> z2 7.96 13.0 FALSE
-#> 10 x 8.86 11.6 -> y 7.68 11.5 FALSE
-#> 11 z1 9.74 12.1 -> x 8.86 11.6 FALSE
-#> 12 z2 7.96 13.0 -> y 7.68 11.5 FALSE
-#> 13 y 7.68 11.5 <NA> <NA> NA NA FALSElibrary(ggdag)
+
+# example from the dagitty package
+dag <- dagitty::dagitty( "dag {
+ y <- x <- z1 <- v -> z2 -> y
+ z1 <- w1 <-> w2 -> z2
+ x <- w1 -> y
+ x <- w2 -> y
+ x [exposure]
+ y [outcome]
+ }")
+
+tidy_dag <- tidy_dagitty(dag)
+
+tidy_dag
+#> # A DAG with 7 nodes and 12 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 13 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 v 11.8 8.03 -> z1 10.4 7.77 FALSE
+#> 2 v 11.8 8.03 -> z2 12.1 6.66 FALSE
+#> 3 w1 10.2 6.85 -> x 9.95 6.28 FALSE
+#> 4 w1 10.2 6.85 -> y 11.1 6.39 FALSE
+#> 5 w1 10.2 6.85 -> z1 10.4 7.77 FALSE
+#> 6 w1 10.2 6.85 <-> w2 10.9 5.75 FALSE
+#> 7 w2 10.9 5.75 -> x 9.95 6.28 FALSE
+#> 8 w2 10.9 5.75 -> y 11.1 6.39 FALSE
+#> 9 w2 10.9 5.75 -> z2 12.1 6.66 FALSE
+#> 10 x 9.95 6.28 -> y 11.1 6.39 FALSE
+#> 11 z1 10.4 7.77 -> x 9.95 6.28 FALSE
+#> 12 z2 12.1 6.66 -> y 11.1 6.39 FALSE
+#> 13 y 11.1 6.39 <NA> <NA> NA NA FALSE
+
+# using more R-like syntax to create the same DAG
+tidy_ggdag <- dagify(y ~ x + z2 + w2 + w1,
+ x ~ z1 + w1 + w2,
+ z1 ~ w1 + v,
+ z2 ~ w2 + v,
+ w1 ~~ w2, # bidirected path
+ exposure = "x",
+ outcome = "y") %>% tidy_dagitty()
+
+tidy_ggdag
+#> # A DAG with 7 nodes and 12 edges
+#> #
+#> # Exposure: x
+#> # Outcome: y
+#> #
+#> # A tibble: 13 x 8
+#> name x y direction to xend yend circular
+#> <chr> <dbl> <dbl> <fct> <chr> <dbl> <dbl> <lgl>
+#> 1 v 9.30 13.4 -> z1 9.74 12.1 FALSE
+#> 2 v 9.30 13.4 -> z2 7.96 13.0 FALSE
+#> 3 w1 8.74 11.0 -> x 8.86 11.6 FALSE
+#> 4 w1 8.74 11.0 -> y 7.68 11.5 FALSE
+#> 5 w1 8.74 11.0 -> z1 9.74 12.1 FALSE
+#> 6 w1 8.74 11.0 <-> w2 8.00 12.0 FALSE
+#> 7 w2 8.00 12.0 -> x 8.86 11.6 FALSE
+#> 8 w2 8.00 12.0 -> y 7.68 11.5 FALSE
+#> 9 w2 8.00 12.0 -> z2 7.96 13.0 FALSE
+#> 10 x 8.86 11.6 -> y 7.68 11.5 FALSE
+#> 11 z1 9.74 12.1 -> x 8.86 11.6 FALSE
+#> 12 z2 7.96 13.0 -> y 7.68 11.5 FALSE
+#> 13 y 7.68 11.5 <NA> <NA> NA NA FALSEggdag also provides functionality for analyzing DAGs and plotting them in ggplot2:
ggdag_adjustment_set(tidy_ggdag, node_size = 14) +
+ theme(legend.position = "bottom")
As well as geoms and other functions for plotting them directly in ggplot2:
dagify(m ~ x + y) %>%
- tidy_dagitty() %>%
- node_dconnected("x", "y", controlling_for = "m") %>%
- ggplot(aes(x = x, y = y, xend = xend, yend = yend, shape = adjusted, col = d_relationship)) +
- geom_dag_edges(aes(end_cap = ggraph::circle(10, "mm"))) +
- geom_dag_collider_edges() +
- geom_dag_point() +
- geom_dag_text(col = "white") +
- theme_dag() +
- scale_adjusted() +
- expand_plot(expand_y = expand_scale(c(0.2, 0.2))) +
- scale_color_hue(name = "d-relationship", na.value = "grey75")
dagify(m ~ x + y) %>%
+ tidy_dagitty() %>%
+ node_dconnected("x", "y", controlling_for = "m") %>%
+ ggplot(aes(x = x, y = y, xend = xend, yend = yend, shape = adjusted, col = d_relationship)) +
+ geom_dag_edges(aes(end_cap = ggraph::circle(10, "mm"))) +
+ geom_dag_collider_edges() +
+ geom_dag_point() +
+ geom_dag_text(col = "white") +
+ theme_dag() +
+ scale_adjusted() +
+ expand_plot(expand_y = expand_scale(c(0.2, 0.2))) +
+ scale_color_hue(name = "d-relationship", na.value = "grey75")
And common structures of bias:
- -
+ggdag_butterfly_bias(edge_type = "diagonal")
Links
-- Download from CRAN at
https:// cloud.r-project.org/ package=ggdag
+ - Download from CRAN at
https://cloud.r-project.org/package=ggdag
-- Browse source code at
https:// github.com/ malcolmbarrett/ ggdag
+ - Browse source code at
https://github.com/malcolmbarrett/ggdag
-- Report a bug at
https:// github.com/ malcolmbarrett/ ggdag/ issues
+ - Report a bug at
https://github.com/malcolmbarrett/ggdag/issues
@@ -231,7 +236,7 @@ License
Developers
-
-Malcolm Barrett
Author, maintainer
+Malcolm Barrett
Author, maintainer
Links
-
-
- Download from CRAN at
https:// cloud.r-project.org/ package=ggdag + - Download from CRAN at
https://cloud.r-project.org/package=ggdag
- - Browse source code at
https:// github.com/ malcolmbarrett/ ggdag + - Browse source code at
https://github.com/malcolmbarrett/ggdag
- - Report a bug at
https:// github.com/ malcolmbarrett/ ggdag/ issues + - Report a bug at
https://github.com/malcolmbarrett/ggdag/issues
Author, maintainer
Author, maintainer
Dev status
- - + diff --git a/docs/news/index.html b/docs/news/index.html new file mode 100644 index 00000000..dfd03113 --- /dev/null +++ b/docs/news/index.html @@ -0,0 +1,167 @@ + + + + + + + + +Changelog
+ Source:NEWS.md
+ +ggdag 0.2.0 Unreleased +
+-
+
- Fixed join bug in
node_equivalent_class()that didn’t account for the way dagitty returns DAGs with no direction
+ - Fixed join bug in
node_equivalent_class()that didn’t checktonode
+ - Implemented
is_false()to avoid dependency on R 3.5.0
+ - improved edge lengths +
- add
{}to adjustment set names to reflect convention
+ - Set nodes to be unstyled by default +
- Changed default themes and scales to be more like base ggplot2 +
- Added a
NEWS.mdfile to track changes to the package.
+