Directed acyclic graphs in choosing covariates for multivariable model of observational study_West China Medical Journal

Authors：

CAO Yuzi ^1,2 , YUAN Chi ^1,2,3 , LIU Gang ⁴ , SUN Feng ⁵ ,  LI Sheyu ^1,2

1. Department of Endocrinology and Metabolism, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, P. R. China;
2. MAGIC China Center, Chinese Evidence-based Medicine Center, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, P. R. China;
3. Department of Pediatric Surgery, West China Hospital, Sichuan University, Chengdu, Sichuan 610041, P. R. China;
4. School of Public Health, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, Hubei 430030, P. R. China;
5. Department of Epidemiology and Biostatistics, School of Public Health, Peking University, Beijing 100091, P. R. China;

Corresponding?author：

LI Sheyu, Email: lisheyu@gmail.com

Keywords：

Directed acyclic graph; confounder; covariate selection; causal inference

DOI：

10.7507/1002-0179.202504241

Video：

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In observational studies, multivariable analysis is commonly used to control confounding and reduce bias in the estimation of causal effect between exposure and outcome. However, in clinical problems with complex causal relationships, researchers select covariates for adjustment through clinical intuition and data-driven methods, which may lead to biased results. In recent years, directed acyclic graphs (DAGs) have become a popular method for visualizing causal relationships between variables. An appropriately constructed DAG can help researchers identify confounders, intermediate variables and other non-confounding variables, thereby improving covariates selection for multivariable analysis. In practice, researchers should incorporate clinical knowledge, systematic methods and transparent reporting to fully utilize DAG in causal inference, and support more reliable clinical decisions.

Citation： CAO Yuzi, YUAN Chi, LIU Gang, SUN Feng, LI Sheyu. Directed acyclic graphs in choosing covariates for multivariable model of observational study. West China Medical Journal, 2025, 40(12): 2045-2052. doi: 10.7507/1002-0179.202504241 Copy

1.	Stovitz SD, Shrier I. Causal inference for clinicians. BMJ Evid Based Med, 2019, 24(3): 109-112.
2.	Hernán MA, Robins JM. Causal inference: what if. Boca Raton: Chapman & Hall/CRC, 2024.
3.	Hernán MA, Robins JM. Estimating causal effects from epidemiological data. J Epidemiol Community Health, 2006, 60(7): 578-586.
4.	Katz MH. Multivariable analysis: a primer for readers of medical research. Ann Intern Med, 2003, 138(8): 644-650.
5.	袁馳, 周祎靈, 曹雨滋, 等. 基于真實世界數據的觀察性研究因果推斷——目標試驗模擬實施要點及案例分析. 中國胸心血管外科臨床雜志, 2024, 31(12): 1743-1752.
6.	Fletcher RH, Fletcher SW, Fletcher GS. Clinical epidemiology: the essentials. 5 ed. Philadelphia: Lippincott Williams & Wilkins, 2012.
7.	Pearl J. Causal diagrams for empirical research. Biometrika, 1995, 82(4): 669-688.
8.	Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology, 1999, 10(1): 37-48.
9.	Rothman KJ, Greenland S, Lash TL. Modern epidemiology. Philadelphia: Lippincott Williams & Wilkins, 2008.
10.	VanderWeele TJ. Principles of confounder selection. Eur J Epidemiol, 2019, 34(3): 211-219.
11.	VanderWeele TJ. On the distinction between interaction and effect modification. Epidemiology, 2009, 20(6): 863-871.
12.	Bours MJL. Tutorial: A nontechnical explanation of the counterfactual definition of effect modification and interaction. J Clin Epidemiol, 2021, 134: 113-124.
13.	Hernán MA, Robins JM. Instruments for causal inference: an epidemiologist’s dream?. Epidemiology, 2006, 17(4): 360-372.
14.	Ding P, VanderWeele TJ, Robins JM. Instrumental variables as bias amplifiers with general outcome and confounding. Biometrika, 2017, 104(2): 291-302.
15.	Hernán MA, Hernández-Díaz S, Robins JM. A structural approach to selection bias. Epidemiology, 2004, 15(5): 615-625.
16.	Sauer B, Brookhart MA, Roy JA, et al. Covariate selection// Velentgas P, Dreyer NA, Nourjah P, et al. Developing a protocol for observational comparative effectiveness research: a user’s guide. Rockville (MD): Agency for Healthcare Research and Quality (US), 2013.
17.	安康, 秦懇, 李舍予, 等. 肥胖與絕經期女性居民骨密度的相關性研究. 四川大學學報(醫學版), 2017, 48(1): 23-27.
18.	秦懇, 何敏, 曹曉濤, 等. 肥胖與 50 歲以上男性骨質疏松的相關性研究. 四川大學學報(醫學版), 2017, 48(1): 17-22.
19.	Biondi-Zoccai G, Romagnoli E, Agostoni P, et al. Are propensity scores really superior to standard multivariable analysis?. Contemp Clin Trials, 2011, 32(5): 731-740.
20.	Li G, Prior JC, Leslie WD, et al. Frailty and risk of fractures in patients with type 2 diabetes. Diabetes Care, 2019, 42(4): 507-513.
21.	Shen Y, Shi Q, Zou X, et al. Time-dependent risk of fracture in adults with type 2 diabetes receiving anti-diabetic drug: a one-stage network meta-analysis. Diabetes Metab Res Rev, 2024, 40(2): e3780.
22.	鄒昕雨, 李舍予. 時間-事件結局證據合成中時間的效應修飾作用. 中國循證醫學雜志, 2024, 24(3): 364-372.
23.	Rutter GA, Chimienti F. SLC30A8 mutations in type 2 diabetes. Diabetologia, 2015, 58(1): 31-36.
24.	Sladek R, Rocheleau G, Rung J, et al. A genome-wide association study identifies novel risk loci for type 2 diabetes. Nature, 2007, 445(7130): 881-885.
25.	Emdin CA, Khera AV, Kathiresan S. Mendelian randomization. JAMA, 2017, 318(19): 1925-1926.
26.	Concato J, Feinstein AR, Holford TR. The risk of determining risk with multivariable models. Ann Intern Med, 1993, 118(3): 201-210.
27.	Greenland S, Pearce N. Statistical foundations for model-based adjustments. Annu Rev Public Health, 2015, 36: 89-108.
28.	Greenland S, Daniel R, Pearce N. Outcome modelling strategies in epidemiology: traditional methods and basic alternatives. Int J Epidemiol, 2016, 45(2): 565-575.
29.	Weinberg CR. Toward a clearer definition of confounding. Am J Epidemiol, 1993, 137(1): 1-8.
30.	Walter S, Tiemeier H. Variable selection: current practice in epidemiological studies. Eur J Epidemiol, 2009, 24(12): 733-736.
31.	Talbot D, Massamba VK. A descriptive review of variable selection methods in four epidemiologic journals: there is still room for improvement. Eur J Epidemiol, 2019, 34(8): 725-730.
32.	Staerk C, Byrd A, Mayr A. Recent methodological trends in epidemiology: no need for data-driven variable selection?. Am J Epidemiol, 2024, 193(2): 370-376.
33.	Ramspek CL, Steyerberg EW, Riley RD, et al. Prediction or causality? A scoping review of their conflation within current observational research. Eur J Epidemiol, 2021, 36(9): 889-898.
34.	Rassen JA, Glynn RJ, Brookhart MA, et al. Covariate selection in high-dimensional propensity score analyses of treatment effects in small samples. Am J Epidemiol, 2011, 173(12): 1404-1413.
35.	Hernán MA, Hernández-Díaz S, Werler MM, et al. Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. Am J Epidemiol, 2002, 155(2): 176-184.
36.	Greenland S. Modeling and variable selection in epidemiologic analysis. Am J public Health, 1989, 79(3): 340-349.
37.	Greenland S, Neutra R. Control of confounding in the assessment of medical technology. Int J Epidemiol, 1980, 9(4): 361-367.
38.	Talbot D, Diop A, Lavigne-Robichaud M, et al. The change in estimate method for selecting confounders: a simulation study. Stat Methods Med Res, 2021, 30(9): 2032-2044.
39.	Ferguson KD, McCann M, Katikireddi SV, et al. Evidence synthesis for constructing directed acyclic graphs (ESC-DAGs): a novel and systematic method for building directed acyclic graphs. Int J Epidemiol, 2020, 49(1): 322-329.
40.	Rubin DB. Should observational studies be designed to allow lack of balance in covariate distributions across treatment groups?. Stat Med, 2009, 28(9): 1420-1423.
41.	Rubin DB. For objective causal inference, design trumps analysis. Ann Appl Stat, 2008, 2(3): 808-840.
42.	Textor J, Van Der Zander B, Gilthorpe MS, et al. Robust causal inference using directed acyclic graphs: the R package ‘dagitty’. Int J Epidemiol, 2016, 45(6): 1887-1894.
43.	Shrier I, Platt RW. Reducing bias through directed acyclic graphs. BMC Med Res Methodol, 2008, 8: 70.
44.	Howards PP, Schisterman EF, Poole C, et al. “Toward a clearer definition of confounding” revisited with directed acyclic graphs. Am J Epidemiol, 2012, 176(6): 506-511.
45.	Tennant PWG, Murray EJ, Arnold KF, et al. Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations. Int J Epidemiol, 2021, 50(2): 620-632.
46.	Rueegg CS. Directed acyclic graphs to foster transparency and scientific dialogue. Lancet Oncol, 2024, 25(6): 693-694.
47.	Armond ACV, Cobey KD, Moher D. Key concepts in clinical epidemiology: research integrity definitions and challenges. J Clin Epidemiol, 2024, 171: 111367.
48.	Richardson TS, Robins JM. Single world intervention graphs: a primer//Second UAI workshop on causal structure Learning. Bellevue, Washington, 2013.
49.	Ocampo A, Bather JR. Single-world intervention graphs for defining, identifying, and communicating estimands in clinical trials. Stat Med, 2023, 42(21): 3892-3902.
50.	Breskin A, Cole SR, Hudgens MG. A practical example demonstrating the utility of single-world intervention graphs. Epidemiology, 2018, 29(3): e20-e21.
51.	Didelez V. Invited commentary: where do the causal DAGS come from?. Am J Epidemiol, 2024, 193(8): 1075-1078.
52.	Petersen AH, Ekstr?m CT, Spirtes P, et al. Constructing causal life-course models: comparative Study of data-driven and theory-driven approaches. Am J Epidemiol, 2023, 192(11): 1917-1927.

1. Stovitz SD, Shrier I. Causal inference for clinicians. BMJ Evid Based Med, 2019, 24(3): 109-112.
2. Hernán MA, Robins JM. Causal inference: what if. Boca Raton: Chapman & Hall/CRC, 2024.
3. Hernán MA, Robins JM. Estimating causal effects from epidemiological data. J Epidemiol Community Health, 2006, 60(7): 578-586.
4. Katz MH. Multivariable analysis: a primer for readers of medical research. Ann Intern Med, 2003, 138(8): 644-650.
5. 袁馳, 周祎靈, 曹雨滋, 等. 基于真實世界數據的觀察性研究因果推斷——目標試驗模擬實施要點及案例分析. 中國胸心血管外科臨床雜志, 2024, 31(12): 1743-1752.
6. Fletcher RH, Fletcher SW, Fletcher GS. Clinical epidemiology: the essentials. 5 ed. Philadelphia: Lippincott Williams & Wilkins, 2012.
7. Pearl J. Causal diagrams for empirical research. Biometrika, 1995, 82(4): 669-688.
8. Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology, 1999, 10(1): 37-48.
9. Rothman KJ, Greenland S, Lash TL. Modern epidemiology. Philadelphia: Lippincott Williams & Wilkins, 2008.
10. VanderWeele TJ. Principles of confounder selection. Eur J Epidemiol, 2019, 34(3): 211-219.
11. VanderWeele TJ. On the distinction between interaction and effect modification. Epidemiology, 2009, 20(6): 863-871.
12. Bours MJL. Tutorial: A nontechnical explanation of the counterfactual definition of effect modification and interaction. J Clin Epidemiol, 2021, 134: 113-124.
13. Hernán MA, Robins JM. Instruments for causal inference: an epidemiologist’s dream?. Epidemiology, 2006, 17(4): 360-372.
14. Ding P, VanderWeele TJ, Robins JM. Instrumental variables as bias amplifiers with general outcome and confounding. Biometrika, 2017, 104(2): 291-302.
15. Hernán MA, Hernández-Díaz S, Robins JM. A structural approach to selection bias. Epidemiology, 2004, 15(5): 615-625.
16. Sauer B, Brookhart MA, Roy JA, et al. Covariate selection// Velentgas P, Dreyer NA, Nourjah P, et al. Developing a protocol for observational comparative effectiveness research: a user’s guide. Rockville (MD): Agency for Healthcare Research and Quality (US), 2013.
17. 安康, 秦懇, 李舍予, 等. 肥胖與絕經期女性居民骨密度的相關性研究. 四川大學學報(醫學版), 2017, 48(1): 23-27.
18. 秦懇, 何敏, 曹曉濤, 等. 肥胖與 50 歲以上男性骨質疏松的相關性研究. 四川大學學報(醫學版), 2017, 48(1): 17-22.
19. Biondi-Zoccai G, Romagnoli E, Agostoni P, et al. Are propensity scores really superior to standard multivariable analysis?. Contemp Clin Trials, 2011, 32(5): 731-740.
20. Li G, Prior JC, Leslie WD, et al. Frailty and risk of fractures in patients with type 2 diabetes. Diabetes Care, 2019, 42(4): 507-513.
21. Shen Y, Shi Q, Zou X, et al. Time-dependent risk of fracture in adults with type 2 diabetes receiving anti-diabetic drug: a one-stage network meta-analysis. Diabetes Metab Res Rev, 2024, 40(2): e3780.
22. 鄒昕雨, 李舍予. 時間-事件結局證據合成中時間的效應修飾作用. 中國循證醫學雜志, 2024, 24(3): 364-372.
23. Rutter GA, Chimienti F. SLC30A8 mutations in type 2 diabetes. Diabetologia, 2015, 58(1): 31-36.
24. Sladek R, Rocheleau G, Rung J, et al. A genome-wide association study identifies novel risk loci for type 2 diabetes. Nature, 2007, 445(7130): 881-885.
25. Emdin CA, Khera AV, Kathiresan S. Mendelian randomization. JAMA, 2017, 318(19): 1925-1926.
26. Concato J, Feinstein AR, Holford TR. The risk of determining risk with multivariable models. Ann Intern Med, 1993, 118(3): 201-210.
27. Greenland S, Pearce N. Statistical foundations for model-based adjustments. Annu Rev Public Health, 2015, 36: 89-108.
28. Greenland S, Daniel R, Pearce N. Outcome modelling strategies in epidemiology: traditional methods and basic alternatives. Int J Epidemiol, 2016, 45(2): 565-575.
29. Weinberg CR. Toward a clearer definition of confounding. Am J Epidemiol, 1993, 137(1): 1-8.
30. Walter S, Tiemeier H. Variable selection: current practice in epidemiological studies. Eur J Epidemiol, 2009, 24(12): 733-736.
31. Talbot D, Massamba VK. A descriptive review of variable selection methods in four epidemiologic journals: there is still room for improvement. Eur J Epidemiol, 2019, 34(8): 725-730.
32. Staerk C, Byrd A, Mayr A. Recent methodological trends in epidemiology: no need for data-driven variable selection?. Am J Epidemiol, 2024, 193(2): 370-376.
33. Ramspek CL, Steyerberg EW, Riley RD, et al. Prediction or causality? A scoping review of their conflation within current observational research. Eur J Epidemiol, 2021, 36(9): 889-898.
34. Rassen JA, Glynn RJ, Brookhart MA, et al. Covariate selection in high-dimensional propensity score analyses of treatment effects in small samples. Am J Epidemiol, 2011, 173(12): 1404-1413.
35. Hernán MA, Hernández-Díaz S, Werler MM, et al. Causal knowledge as a prerequisite for confounding evaluation: an application to birth defects epidemiology. Am J Epidemiol, 2002, 155(2): 176-184.
36. Greenland S. Modeling and variable selection in epidemiologic analysis. Am J public Health, 1989, 79(3): 340-349.
37. Greenland S, Neutra R. Control of confounding in the assessment of medical technology. Int J Epidemiol, 1980, 9(4): 361-367.
38. Talbot D, Diop A, Lavigne-Robichaud M, et al. The change in estimate method for selecting confounders: a simulation study. Stat Methods Med Res, 2021, 30(9): 2032-2044.
39. Ferguson KD, McCann M, Katikireddi SV, et al. Evidence synthesis for constructing directed acyclic graphs (ESC-DAGs): a novel and systematic method for building directed acyclic graphs. Int J Epidemiol, 2020, 49(1): 322-329.
40. Rubin DB. Should observational studies be designed to allow lack of balance in covariate distributions across treatment groups?. Stat Med, 2009, 28(9): 1420-1423.
41. Rubin DB. For objective causal inference, design trumps analysis. Ann Appl Stat, 2008, 2(3): 808-840.
42. Textor J, Van Der Zander B, Gilthorpe MS, et al. Robust causal inference using directed acyclic graphs: the R package ‘dagitty’. Int J Epidemiol, 2016, 45(6): 1887-1894.
43. Shrier I, Platt RW. Reducing bias through directed acyclic graphs. BMC Med Res Methodol, 2008, 8: 70.
44. Howards PP, Schisterman EF, Poole C, et al. “Toward a clearer definition of confounding” revisited with directed acyclic graphs. Am J Epidemiol, 2012, 176(6): 506-511.
45. Tennant PWG, Murray EJ, Arnold KF, et al. Use of directed acyclic graphs (DAGs) to identify confounders in applied health research: review and recommendations. Int J Epidemiol, 2021, 50(2): 620-632.
46. Rueegg CS. Directed acyclic graphs to foster transparency and scientific dialogue. Lancet Oncol, 2024, 25(6): 693-694.
47. Armond ACV, Cobey KD, Moher D. Key concepts in clinical epidemiology: research integrity definitions and challenges. J Clin Epidemiol, 2024, 171: 111367.
48. Richardson TS, Robins JM. Single world intervention graphs: a primer//Second UAI workshop on causal structure Learning. Bellevue, Washington, 2013.
49. Ocampo A, Bather JR. Single-world intervention graphs for defining, identifying, and communicating estimands in clinical trials. Stat Med, 2023, 42(21): 3892-3902.
50. Breskin A, Cole SR, Hudgens MG. A practical example demonstrating the utility of single-world intervention graphs. Epidemiology, 2018, 29(3): e20-e21.
51. Didelez V. Invited commentary: where do the causal DAGS come from?. Am J Epidemiol, 2024, 193(8): 1075-1078.
52. Petersen AH, Ekstr?m CT, Spirtes P, et al. Constructing causal life-course models: comparative Study of data-driven and theory-driven approaches. Am J Epidemiol, 2023, 192(11): 1917-1927.

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