Week 3, Session 3 — DAGs with dagitty and ggdag

Course 3 — #courses

R. Heller

Note

Workflow lab using the variant template: Goal → Approach → Execution → Check → Report.

Learning objectives

  • Express a causal scenario as a directed acyclic graph (DAG).
  • Identify confounders, mediators, and colliders from a DAG.
  • Use dagitty::adjustmentSets() to find sufficient adjustment sets.

Prerequisites

Conceptual knowledge of confounding.

Background

A DAG is a set of variables joined by arrows that encode assumed causal directions. The graph distinguishes three kinds of third variable on a path between exposure and outcome: a confounder is a common cause; a mediator lies on the causal path from exposure to outcome; a collider is a common effect of two variables on the path. The practical upshot is that adjusting for a confounder reduces bias, adjusting for a mediator removes part of the effect you are trying to estimate, and adjusting for a collider creates bias where none existed.

dagitty and ggdag let you declare a DAG in text, visualise it, and then query it for adjustment sets — the minimal variable sets that block all back-door paths from exposure to outcome without opening new ones. The right adjustment set depends on the question. For the total effect of X on Y, you want to close all back-door paths but leave mediators alone; for the direct effect, you also block mediators.

M-bias is the classic example of collider adjustment: conditioning on a variable that is a common effect of an unmeasured cause of X and an unmeasured cause of Y opens a path and biases the estimate. This is why “adjust for everything” is bad advice.

Setup

library(tidyverse)
library(dagitty)
library(ggdag)
set.seed(42)
theme_set(theme_minimal(base_size = 12))

1. Goal

Write a confounder, mediator, and collider scenario as DAGs; ask dagitty which variables to adjust for.

2. Approach

dag1 <- dagitty('dag {
  X -> Y
  C -> X
  C -> Y
  X [exposure]
  Y [outcome]
}')

dag2 <- dagitty('dag {
  X -> M -> Y
  X -> Y
  X [exposure]
  Y [outcome]
}')

dag3 <- dagitty('dag {
  X -> Z
  Y -> Z
  X -> Y
  X [exposure]
  Y [outcome]
}')

ggdag(dag1) + theme_dag()

ggdag(dag2) + theme_dag()

ggdag(dag3) + theme_dag()

3. Execution

adjustmentSets(dag1, exposure = "X", outcome = "Y",
               effect = "total")
{ C }
# Total vs direct effect when a mediator exists
adjustmentSets(dag2, exposure = "X", outcome = "Y",
               effect = "total")
 {}
adjustmentSets(dag2, exposure = "X", outcome = "Y",
               effect = "direct")
{ M }
# Collider: do not adjust for Z
adjustmentSets(dag3, exposure = "X", outcome = "Y")
 {}

4. Check

Simulate dag1 and verify that adjusting for C recovers the true effect while failing to adjust biases it.

n  <- 2000
c_ <- rnorm(n)
x  <- 0.6 * c_ + rnorm(n)
y  <- 0.4 * x + 0.7 * c_ + rnorm(n)
df <- tibble(c_, x, y)

coef(lm(y ~ x,        data = df))["x"]
        x 
0.7042359 
coef(lm(y ~ x + c_,   data = df))["x"]
        x 
0.3866581

The unadjusted coefficient is inflated; the adjusted one is close to 0.4 as simulated.

5. Report

A directed acyclic graph is a compact, testable statement of causal assumptions. Dagitty identified the confounder C as the required adjustment set in the first DAG; the collider Z in the third DAG is explicitly not in any adjustment set, and conditioning on it would introduce selection bias.

Common pitfalls

  • Listing “every variable we measured” as the adjustment set.
  • Adjusting for a mediator and calling the result a total effect.
  • Using automated variable selection on observational data without a DAG.
  • Drawing the DAG after the analysis.

Further reading

  • Textor J et al. (2016), Robust causal inference using directed acyclic graphs: the R package ‘dagitty’.
  • Hernán MA, Robins JM. Causal Inference: What If.
  • Greenland S, Pearl J, Robins JM (1999), Causal diagrams for epidemiologic research.

Session info

sessionInfo()
R version 4.4.1 (2024-06-14)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.4 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3 
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so;  LAPACK version 3.12.0

locale:
 [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
 [4] LC_COLLATE=C.UTF-8     LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
 [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
[10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   

time zone: UTC
tzcode source: system (glibc)

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] ggdag_0.2.13    dagitty_0.3-4   lubridate_1.9.5 forcats_1.0.1  
 [5] stringr_1.6.0   dplyr_1.2.1     purrr_1.2.2     readr_2.2.0    
 [9] tidyr_1.3.2     tibble_3.3.1    ggplot2_4.0.3   tidyverse_2.0.0

loaded via a namespace (and not attached):
 [1] viridis_0.6.5      generics_0.1.4     stringi_1.8.7      hms_1.1.4         
 [5] digest_0.6.39      magrittr_2.0.5     evaluate_1.0.5     grid_4.4.1        
 [9] timechange_0.4.0   RColorBrewer_1.1-3 fastmap_1.2.0      jsonlite_2.0.0    
[13] ggrepel_0.9.8      gridExtra_2.3      viridisLite_0.4.3  scales_1.4.0      
[17] tweenr_2.0.3       cli_3.6.6          graphlayouts_1.2.3 rlang_1.2.0       
[21] polyclip_1.10-7    tidygraph_1.3.1    cachem_1.1.0       withr_3.0.2       
[25] yaml_2.3.12        otel_0.2.0         tools_4.4.1        tzdb_0.5.0        
[29] memoise_2.0.1      boot_1.3-30        curl_7.1.0         vctrs_0.7.3       
[33] R6_2.6.1           lifecycle_1.0.5    V8_8.2.0           htmlwidgets_1.6.4 
[37] MASS_7.3-60.2      ggraph_2.2.2       pkgconfig_2.0.3    pillar_1.11.1     
[41] gtable_0.3.6       glue_1.8.1         Rcpp_1.1.1-1.1     ggforce_0.5.0     
[45] xfun_0.57          tidyselect_1.2.1   knitr_1.51         farver_2.1.2      
[49] htmltools_0.5.9    igraph_2.3.1       labeling_0.4.3     rmarkdown_2.31    
[53] compiler_4.4.1     S7_0.2.2