Directed Acyclic Graphs (DAGs)

class: left, middle, inverse, title-slide

.title[
# Directed Acyclic Graphs (DAGs)
]
.subtitle[
## Gentle introduction
]
.author[
### Mabel Carabali
]
.institute[
### EBOH, McGill University
]
.date[
### 2023/08/30 (updated: 2024-09-11)
]

---

class: middle
##Objectives
1. Operationalize Directed Acyclic Graphs (DAGs)

2. Appreciate the insights into confounding and selection bias provided by DAGs

3. Examples to appreciate the importance of DAGs (and their encoded substantive knowledge) on the road to causal inference

**Felix, qui potuit rerum cognoscere causa - Vigil (29BC)**

_“Fortunate is he, who is able to know the causes of things”_

.purple[Included modified notes from Dr. Jay Brophy]

---
class: middle
##Conventional statistics & causal inference 
- “The object of statistical methods is the reduction of data” (Fisher 1922)

- Provides a parsimonious mathematical description of the joint distribution of observed variables

- Good statistical processes can describe the data

- But say nothing about the data generating process and **can’t answer causal questions**

---
class: middle
##DAGs and causal inference
- **DAGs (AKA causal diagrams)** characterize causal structures compatible with the observations & assist in drawing logical conclusions about the statistical relations 
 
- Help understanding: confounding, selection bias, covariate selection, over adjustment, instrumental variable analyses & avoid making errors about the statistical relations (much of this associated with Judea Pearl's work)

- **Potential Outcome (counterfactual)** framework provides another approach to causal inference, building on the work on RCTs from the 1920s by Fisher and Neyman (much of this associated with Donals Rubin's work)

**.purple[These frameworks are largely complementary]**

---
class: middle
##Current statistical approach
- Vague research question with some available relevant data    
- “Let the data speak” (If the data are speaking to you...)     
- Add all the variables and let multiple regression sort it out     
- Regression models alone insufficient no distinction between causes, confounders, mediators and colliders
- Residual confounding, measurement error & missing data are often ignored            
- Often model selection chosen via Akaike Information Criterion (AIC = 2K -2ln(logLikelihood)) where K is the number of model parameters        
- Provides the best predictive but not the causally correct model `$\to$` **doesn't provide causal statements**

---
class: middle
### Canons of causal inference
- Every causal inference task must rely on judgmental, extra-data assumptions (or experiments)

- Ways of encoding those assumptions mathematically and test their implications exist

- DAGs encode qualitatively _a priori_ subject matter knowledge

- Consideration of the causal model combined with data provides clarity in interpreting statistical coefficients and causal inferences

**.red[Assumption - free causal inference doesn’t exist]**

---
class: middle
###DAGs - Help identifying causal effects

.pull-left[
<img src="images/L3dag0.png" width="100%" style="display: block; margin: auto;" />
]

.pull-right[
1. **Treatment/intervention/exposure (T)**: the main cause.
2. **Outcome (O):** the main effect.
3. **Mediator (M):** caused by the treatment which in turn
causes the outcome.
4. **Confounder (C):** common cause of the treatment and
outcome.
5. **Collider (E):** common effect of any two variables on a
backdoor path.*
6. **Instrument (I):** only causes the treatment (and not the
outcome).

.small[*Non-causal path from the treatment to the outcome.]
]

---
class: middle
###DAGs - Help identifying causal effects
 
<img src="images/L3dag0.png" width="50%" style="display: block; margin: auto;" />

- **Variables** are depicted as **nodes** and connected by **arrows** 
- Acyclic (the future can’t predict the past) 
- Missing lines strongest assumption, implies variable independence 
- Include all common causes of any 2 variables & all variables involved in data generation (observed or unobserved) 
- Contain both causal and non-causal pathways 
- **Help identify causal effects by deriving testable implications of a causal model**

---
class: middle
##DAGs Between Two Variables

---
class: middle
**[Directed acyclic graphs: a tool for causal studies in paediatrics](https://www.nature.com/articles/s41390-018-0071-3)**
<img src="images/L3dagpeds.png" width="55%" style="display: block; margin: auto;" />

--
.small[
- a.Screen time (the exposure) **causes** obesity (the outcome). 
- b. Screen time acts on obesity through the **.purple[mediator]** of physical activity. 
- c. Low parental education increases both screen time and obesity, and is therefore a **.red[confounder]**.
- d. Self-harm is a **.brown[collider]** in the path from screen time to obesity.
]

---
class: middle
### More DAG terminology

- Path is a sequence of non-intersecting adjacent edges **X->T->C** or **U2->Y<-C<-T** 
- Causal path a path in which all arrows point away from T to outcome Y; **T->C->Y** 
- Total causal effect of a treatment on an outcome consists of all causal paths connecting them 
- Non-causal path connecting T and Y with at least one arrow against flow of time **T<-X->Y** 
- Descendants of a node: all nodes directly or indirectly caused by the node; **desc(T) = {C,Y}** 
- Children of a node: all nodes directly caused by the node; **child(T) = {C}** 
- Ancestors of a node: all nodes directly or indirectly causing the node; **an(T) = {X, U1, U2}** 
- Collider variable along a path with 2 arrows pointing in **U->X<-U2**

---
class: middle
**More DAG terminology**
<img src="images/DAG_std.jpg" width="40%" style="display: block; margin: auto;" />
- “Blocked” (d-separated) paths don’t transmit associations 
- “Unblocked” (d-connected) paths may transmit association 
Three blocking criteria
 - Conditioning on a non-collider blocks a path 
 - Conditioning on a collider, or a descendent of a collider, unblocks a path 
 - Not conditioning on a collider leaves a path “naturally” blocked 
 
--

**Implication:** 
- If X and Y are d-separated by Z along all paths in a DAG, then X is statistically independent of Y conditional on Z in every distribution compatible with the DAG 
- If X and Y are not d-separated by Z along all paths in the DAG, then X and Y are dependent conditional on Z in at least one distribution compatible with the DAG

---
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##Identification
The causal effect of X on Y is said to be **“identified”** if it is possible, with ideal data (infinite sample size, perfect measurement), to purge all non-causal association from the observed association between X and Y such that only the causal association remains.

One way to interpret this with DAGs, is to note that the total causal effect of `$X$` on `$Y$` is identifiable if one can condition on (“adjust for”) a set of variables {Z} that         
1. Blocks all non-causal paths between X and Y,     
2. Without blocking any causal paths between X and Y

---
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##Estimating causal effects

.pull-left[
**Backdoor criteria**
<img src="images/backdoor.png" width="40%" style="display: block; margin: auto;" />
`$Z$` is a sufficient set if: 
1. No variable in `$Z$` is a descendant of `$X$` and 
2. Every path between `$X$` and `$Y$` that contains an arrow into `$X$` is blocked by `$Z$`
]
--
.pull-right[
**Frontdoor criteria**
<img src="images/frontdoor.png" width="40%" style="display: block; margin: auto;" />
`$Z$` is a sufficient set if: 
1. `$Z$` intercepts all directed paths from `$X$` to `$Y$` 
2. No unblocked paths from `$X$` to `$Z$` 
3. All backdoor paths from `$Z$` to `$Y$` are blocked by `$X$` 
]

.small[Pearl, Judea. Causal Inference in Statistics : A Primer, John Wiley & Sons, Incorporated, 2016. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/mcgill/detail.action?docID=7104473.]

---
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## Simple DAG
What are the assumptions & statistical implications of this model?
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-9-1.svg" width="80%" style="display: block; margin: auto;" />

--
**.red[Would you believe  at least 16 assumptions and statistical implications!]**

---
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**Simple DAG ?** https://bookdown.org/jbrophy115/bookdown-clinepi/causal.html
.pull-left[
**.red[Causal implications]**
1. X & U are direct causes of Y
2. Y is a direct cause of Z
3. X is an indirect cause of Z via Y
4. X is not a cause of U and U is not a cause of X
5. U is an indirect cause of Z via Y
6. No variable causes both X and Y OR U and Y

<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-10-1.svg" width="75%" style="display: block; margin: auto;" />
]

.pull-right[
**.blue[Statistical implications]**
1. X and Y are statistically dependent
2. U and Y are statistically dependent
3. Y and Z are statistically dependent
4. X and Z are statistically dependent
5. U and Z are statistically dependent
6. X and U are statistically independent
7. X and U are statistically dependent, conditional on Y
8. X and U are statistically dependent, conditional on Z
9. X and Z are statistically independent, conditional on Y
10. U and Z are statistically independent, conditional on Y
]

---
class: middle
### What does automated statistical software do?
- Let's consider the scenario where we assess systolic blood pressure (SBP) by _.brown[race]_.
- Let's simulate data where SBP is a function of age but independent of racial group:

```r
library(tidyverse)
n <- 200; age <- runif(n, 25, 65)
#sbp is not a function of group
*sbp <- 99 + 0.1*age + exp(age/15) + rnorm(200, 0, sd = 5)
dat <- data.frame(age=age, sbp = sbp) %>%
 arrange(age) %>%
 mutate(group = case_when(
 age <40 ~ "0",
 age >= 40 ~ "1"))
dat$group <- as.factor(dat$group)
head(dat, 3)
```

```
##        age      sbp group
## 1 25.37983 102.4869     0
## 2 25.55000 106.1320     0
## 3 25.58509 105.4003     0
```
--

### .red[How would you analyze the data to assess this relationship?]
 
---
class: middle
**Traditional (Standard) approach**, OLS adjusting for _.brown[group]_:

```r
summary(lm(sbp ~ age + group, data=dat))
```

```
## 
## Call:
## lm(formula = sbp ~ age + group, data = dat)
## 
## Residuals:
## Min 1Q Median 3Q Max 
## -14.904 -5.208 -1.228 4.457 23.823 
## 
## Coefficients:
## Estimate Std. Error t value Pr(>|t|) 
## (Intercept) 42.07907 2.82467 14.897 < 2e-16 ***
## age 2.13630 0.08283 25.790 < 2e-16 ***
## group1 -12.34679 1.93724 -6.373 1.28e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.18 on 197 degrees of freedom
## Multiple R-squared: 0.8846,	Adjusted R-squared: 0.8835 
## F-statistic: 755.3 on 2 and 197 DF, p-value: < 2.2e-16
```
--

Spurious statistically difference in SBP by _.brown[group]_ is observed, yet .red[data was generated with no group exposure effect].

---
class: middle
**Visualizations and DAGs can help**
Plot the generated data

```r
myfun <- function(age) 99 + 0.1*age + exp(age/15)
g1 <- ggplot(dat, aes(age, sbp)) + geom_point() + stat_function(fun = myfun, color="red", size=1.8) +
 theme_classic() 
g2 <- ggplot(dat, aes(age, sbp, color=group)) + geom_point() + 
 stat_function(fun = myfun, color="red", size= 1.8) +
 theme_classic() 
```

.pull-left[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-14-1.svg" width="120%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-15-1.svg" width="120%" style="display: block; margin: auto;" />
]

---
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### Visualizations and DAGs can help
.pull-left[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-16-1.svg" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-17-1.svg" width="80%" style="display: block; margin: auto;" />
]

- While the DAG shows only one SBP causal pathway (Age `$\to$` SBP), 
- The automatic software also includes the **.red[spurious non-causal pathway]:**

**(Group `$\leftarrow$` Age `$\to$` SBP)**

---
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**[DAG With Omitted Objects Displayed (DAGWOOD): a framework for revealing causal assumptions in DAGs](https://doi.org/10.1016/j.annepidem.2022.01.001)**

.small[Haber NA, Wood ME, Wieten S, Breskin A. DAG With Omitted Objects Displayed (DAGWOOD): a framework for revealing causal assumptions in DAGs. Ann Epidemiol. 2022 Apr;68:64-71. https://doi.org/10.1016/j.annepidem.2022.01.001]

---
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**[DAG With Omitted Objects Displayed (DAGWOOD): a framework for revealing causal assumptions in DAGs](https://doi.org/10.1016/j.annepidem.2022.01.001)**

---
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### Understanding Selection Bias
**Let's simulate some data**

```r
set.seed(123); n = 5000
income <- rnorm(n)#simulate independent income and bp data
bp <- rnorm(n)
gg <- ggplot(data.frame(income,bp), aes(income, bp)) +
 geom_point() + geom_smooth(method='lm', formula= y~x, color="darkmagenta", size=2) +
 labs(title = "No association of bp and income in population", 
 subtitle = "Blue line is linear regression line") + theme_bw()
```

.pull-left[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-21-1.svg" width="90%" style="display: block; margin: auto;" />
]

.pull-right[
**Plot the data**
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-22-1.svg" width="90%" style="display: block; margin: auto;" />
]

---

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### Understanding Selection Bias
**.purple[What happens if "condition" on the common effect, i.e analyzing only visit=1]**

Let's simulate some data

```r
library(tidyverse)
logitVisit <- -2 + 2*income + 2*bp # simulate visit = f(income, bp)
pVisit <- 1/(1+exp(-logitVisit)); visit <- rbinom(n, 1, pVisit); 
dPop <- data.table::data.table(income, bp, visit)
# sample of those with a visit
*dSample <- dPop[visit == 1]
```

.pull-left[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-24-1.svg" width="80%" style="display: block; margin: auto;" />
]

.pull-right[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-25-1.svg" width="80%" style="display: block; margin: auto;" />
]

**.red[In this conditioned sample there is now an association between BP and income]**
---
class: middle
**Understanding selection bias**

.red[Standard (Naive) approach]

```r
summary (lm(bp~income, 
*           data=dSample))
```

```
## 
## Call:
## lm(formula = bp ~ income, data = dSample)
## 
## Residuals:
## Min 1Q Median 3Q Max 
## -2.72029 -0.52177 -0.04242 0.52481 2.81769 
## 
## Coefficients:
## Estimate Std. Error t value Pr(>|t|) 
## (Intercept) 1.01151 0.02748 36.80 <2e-16 ***
## income -0.36229 0.02457 -14.74 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7842 on 1353 degrees of freedom
## Multiple R-squared: 0.1384,	Adjusted R-squared: 0.1378 
## F-statistic: 217.4 on 1 and 1353 DF, p-value: < 2.2e-16
```
.red[Remember p-values will not pick the causally correct model!]

---
class: middle
**Understanding selection bias**

.purple[Model using all the data, which is not always available!]

```r
summary (lm(bp~income, 
*           data=dPop))
```

```
## 
## Call:
## lm(formula = bp ~ income, data = dPop)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8533 -0.6793 -0.0089  0.6924  3.8474 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.004177   0.014183  -0.295    0.768
## income      -0.006029   0.014261  -0.423    0.672
## 
## Residual standard error: 1.003 on 4998 degrees of freedom
## Multiple R-squared:  3.576e-05,	Adjusted R-squared:  -0.0001643 
## F-statistic: 0.1787 on 1 and 4998 DF,  p-value: 0.6725
```
.red[Remember p-values will not pick the causally correct model!]

---
class: middle
# .red[Star DAGs]

[medium.com](https://medium.com/causality-in-data-science/what-are-causal-graphs-abdb50354c8a)

---
class: middle
**Selection bias in RCTs**
1. Can occur on entry if no blinding      
2. .red[Bigger issue is lost to follow-up]   
- Consider Rx (A) randomized but if (A=1); `$\uparrow$` dropouts due to adverse drug effects (ADE). - Alcohol abuse (C=1) also more likely to drop out of the study and more likely to experience acute liver failure (Y=1). 
- At baseline no association between A & C due to randomization

- However, conditioning on those who do not drop out **creates a spurious backdoor negative correlation between A and C**      
- Will make patients (A=1) to be protective against acute liver failure when no causal association exists.

---
class: middle
**Selection bias in RCTs**
<img src="images/L3dagrct.png" width="75%" style="display: block; margin: auto;" />

**[Directed acyclic graphs: a tool for causal studies in paediatrics](https://www.nature.com/articles/s41390-018-0071-3)**

---
class: middle
##Summary collider vs. confounder

|                 |   **Confounder**   |     **Collider**  |
|:---------------:|:-------------------|:-----------------:|
|Main attribute   | Common cause       | Common Effect     |
|Association | Contributes to the association between its effects| Does not contribute to the association od its effects|
|Type of path| Open path | Blocked path|
|Effect of conditioning | Blocks the path | Opens the path|
|Bias before conditioning? | Yes, confounding | No|
|Bias after conditioning? | No | Yes, Collider stratification Bias|

---
class: middle
##Ever wonder about risk factor paradoxes?

Well established risk factors in general population reverse their impact in these selected .red[index] populations???

---
class: middle
### What's going on?
Editors like the word “paradox” and its mention increases likelihood of publication - novel, controversial findings, easy to invent hypothetical explanations 
- But is this a causal or non-biological explanation? 
--
<img src="images/rheum_bell.png" width="100%" style="display: block; margin: auto;" />

Remember stratifying on a collider `$\to$` spurious negative association among those risk factors in indexed (stratified) populations as the most likely explanation with an index event

**.red[ When you see the word paradox, think first about Index event (collider stratification) bias]**

---
**An egregious example (with a dose response!)**

The following was published in [JAMA](https://jamanetwork.com/journals/jama/fullarticle/1104631)
<img src="images/jama_bad.png" width="80%" style="display: block; margin: auto;" />

Should we encourage post MI patients to increase their smoking, weight, cholesterol, BP and diabetes?... And ideally do all of the above simultaneously **.Large[.red[REALLY!?]]**

---
class: middle
###DAGs with R

---
class: middle
###DAGs with R

```r
library(ggdag) # help(package="ggdag)
l3dag1<- dagify(S ~ A + C, Y ~ C) %>% #dagify() creates dagitty DAGs using a R-like syntax.
 tidy_dagitty() %>% 
 node_dconnected("A", "C", controlling_for = "S") %>%
 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 = expansion(c(0.2, 0.2))) +
 scale_color_viridis_d(
 name = "d-relationship", 
 na.value = "grey85", 
 begin = .35 ) +
 labs(caption = "A = Rx, C = alcohol abuse, Y = acute liver failure, 
 S = patients remaining in study")
l3dag1
```

---
### DAGs with R
Key functions are `dagify()` in `ggdag` package          
Consider the model: `smoking` causes `cancer` and `addictive` behaviour cases both `coffee` drinking and `smoking` but `coffee` does not cause `cancer`        
.pull-left[
**Create the dagitty object with `dagify`**

```r
coffee_cancer_dag <- ggdag::dagify(
 cancer ~ smoking,
 smoking ~ addictive,
 coffee ~ addictive,
 exposure = "coffee",
 outcome = "cancer",
 labels = c("coffee" = "Coffee", 
 "cancer" = "Lung cancer", 
 "smoking" = "Smoking", 
 "addictive" = "Addictive Behavior"
 )) 
class(coffee_cancer_dag )
```

```
## [1] "dagitty"
```
]
.pull-right[

```r
coffee_cancer_dag 
```

```
## dag {
## addictive
## cancer [outcome]
## coffee [exposure]
## smoking
## addictive -> coffee
## addictive -> smoking
## smoking -> cancer
## }
```
]

---
Class: middle
### Plot the daggity object
Use  `ggdag()` in `ggdag` package

```r
ggdag(coffee_cancer_dag) +
  #geom_dag_edges(aes(end_cap = ggraph::circle(14, "mm"))) +
  ggdag::geom_dag_node(color="grey60", size = 20) +
  geom_dag_point(color="grey60") +
  geom_dag_text(col = "darkred") +
  theme_dag() 
```

---
### Open pathways
Can be determined automatically with `ggdag_paths()`

```r
coffee_cancer_dag %>% 
  ggdag_paths() +
  #ggdag::geom_dag_node(color="grey60", size = 20) +
  #geom_dag_text(col = "darkred") +
  theme_dag() 
```

---
##Closing backdoor paths
- Randomization, regression, stratification, weighting, matching     
- Identifying variable for adjusting with `R`

```r
ggdag_adjustment_set(coffee_cancer_dag, use_labels = "label", text = FALSE)+ theme_dag() 
```

---
class: middle
### A more complicated DAG

**How to determine the causal effect of X on Y1?**

---
class: middle
### A more complicated DAG

```r
dag <- ggdag::dagify(Y1 ~ X + Z1 + Z0 + U + P,
 Y0 ~ Z0 + U,
 X ~ Y0 + Z1 + Z0 + P,
 Z1 ~ Z0,
 P ~ Y0 + Z1 + Z0,
 exposure = "X",
 outcome = "Y1")
dag_plot <- dag %>% 
 ggdag::tidy_dagitty(layout = "auto", seed = 12345) %>%
 arrange(name) %>% 
 ggplot(aes(x = x, y = y, xend = xend, yend = yend)) +
 geom_dag_point() +
 geom_dag_edges() +
 geom_dag_text(parse = TRUE, label = c("P", "U", "X",
 expression(Y[0]), expression(Y[1]), expression(Z[0]), expression(Z[1]))) +
 theme_dag() +
 geom_dag_node(color="darkmagenta") + geom_dag_text(color="white")

dag_plot
```

**How to determine the causal effect of X on Y1?**

---
class: middle

##R can help 
.pull-left[
Questions arising from this DAG. 
1. How many paths are there from X to Y1? 
2. How many of those paths are spurious (backdoor) paths? 
3. How many of those backdoor paths are open? 
4. What is the minimal set of variables to block these spurious pathways? 
]
.pull-right[
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-43-1.svg" width="100%" style="display: block; margin: auto;" />
]

**Questions theoretically answerable by careful attention to DAG but easier with `dagitty` built-in functions**

---
class: middle
##R can help ...

```r
g <- dagitty::paths(dag, "X", "Y1")
a <- paste0("There are ", length(g$paths), 
 " pathways from X to Y1 and all are backdoor except for 1") 
b <- paste0("Of these backdoor pathways ", 
 sum(g$open=="TRUE"), " are open") 
c <- paste0("The minimum adjustment sets are ", 
 adjustmentSets(dag, "X", "Y1", type = "minimal"))

print(c(a,b,c))
```

```
## [1] "There are 43 pathways from X to Y1 and all are backdoor except for 1"
## [2] "Of these backdoor pathways 25 are open"                              
## [3] "The minimum adjustment sets are c(\"P\", \"U\", \"Z0\", \"Z1\")"     
## [4] "The minimum adjustment sets are c(\"P\", \"Y0\", \"Z0\", \"Z1\")"
```

---
class: middle

### "Incomplete" Adjustment

```r
ggdag_adjust(dag, var = c("Z1", "P"))+ theme_dag() 
```

---
class: middle

### "Complete" Adjustment

```r
ggdag_adjust(dag, var = c("Z1", "Z0", "P", "Y0"))+ theme_dag() 
```

---
class: middle
### "Complete" Adjustment (but 'U' was not labeled as 'latent')

```r
ggdag_adjust(dag, var = c("Z1", "Z0", "P", "U"))+ theme_dag() 
```

---
class: middle
### Labelling the 'U' as latent
.pull-left[

```r
dag0 <- ggdag::dagify(Y1 ~ X + Z1 + Z0 + U + P,
 Y0 ~ Z0 + U,
 X ~ Y0 + Z1 + Z0 + P,
 Z1 ~ Z0,
 P ~ Y0 + Z1 + Z0,
 exposure = "X",
 outcome = "Y1",
* latent = "U")
dag_plot0 <- dag0 %>% 
 ggdag::tidy_dagitty(layout = "auto", 
 seed = 12345) %>%
 arrange(name) %>% 
 ggplot(aes(x = x, y = y, 
 xend = xend, yend = yend)) +
 geom_dag_point() +
 geom_dag_edges() +
 geom_dag_text(parse = TRUE, 
 label = c("P", "U", "X",
 expression(Y[0]), expression(Y[1]), expression(Z[0]), expression(Z[1]))) +
 theme_dag() +
 geom_dag_node(color="darkmagenta") + 
 geom_dag_text(color="white") 
```
]

.pull-right[
**Does not change the DAG**
<img src="L3_EPIB704_DAG_intro_files/figure-html/unnamed-chunk-49-1.svg" width="80%" style="display: block; margin: auto;" />

]

---
class: middle

**But the revised DAG has a revised  "Complete" Adjustment set**
.pull-left[

```r
ggdag_adjust(dag0, 
             var = c("Z1", "Z0", "P", "U"))+ 
  theme_dag() 
```

]
.pull-right[

```r
adjustmentSets(dag0, "X", "Y1", type = "minimal")
```

```
## { P, Y0, Z0, Z1 }
```

```r
ggdag_adjust(dag0, 
             var = c("Z1", "Z0", "P", "Y0"))+ 
  theme_dag() 
```

]

---

class: middle
###Conclusion
DAGs can be super useful on the road to causal inference

**References**
- Williams, T.C., Bach, C.C., Matthiesen, N.B. et al. Directed acyclic graphs: a tool for causal studies in paediatrics. Pediatr Res 84, 487–493 (2018). https://doi.org/10.1038/s41390-018-0071-3
- Haber NA, Wood ME, Wieten S, Breskin A. DAG With Omitted Objects Displayed (DAGWOOD): a framework for revealing causal assumptions in DAGs. Ann Epidemiol. 2022 Apr;68:64-71. https://doi.org/10.1016/j.annepidem.2022.01.001 
- Piccininni, M., Konigorski, S., Rohmann, J.L. et al. Directed acyclic graphs and causal thinking in clinical risk prediction modeling. BMC Med Res Methodol 20, 179 (2020). https://doi.org/10.1186/s12874-020-01058-z
- Pearl J. An introduction to causal inference. Int J Biostat. 2010 Feb 26;6(2):Article 7. doi: 10.2202/1557-4679.1203. PMID: 20305706; PMCID: PMC2836213.
- Causal Inference with R (https://www.r-causal.org/chapters/05-dags)
- Causal Diagrams website: https://causaldiagrams.org/

---

##Extra Resources:
- https://dagitty.net/
- [dagshub.com](https://dagshub.com/blog/an-introduction-to-directed-acyclic-graphs-dags-for-data-scientists/)
- [medium.com](https://medium.com/causality-in-data-science/what-are-causal-graphs-abdb50354c8a)
- [Causal Inference Ch-5](https://www.r-causal.org/chapters/05-dags)
- Pearl, Judea. Causal Inference in Statistics : A Primer, John Wiley & Sons, Incorporated, 2016. ProQuest Ebook Central, https://ebookcentral.proquest.com/lib/mcgill/detail.action?docID=7104473.

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class: middle

###  QUESTIONS?

## COMMENTS?

# RECOMMENDATIONS?