efigure. Directed Acyclic Graph to Determine Whether Familial Factors Exist That Contribute to Both Eating Disorders and Suicide

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1 Supplementary Online Content Yao S, Kuja-Halkola R, Thornton LM, et al. Familial liability for eating s and suicide attempts: evidence from a population registry in Sweden. JAMA Psychiatry. Published online January 13, doi: /jamapsychiatry efigure. Directed Acyclic Graph to Determine Whether Familial Factors Exist That Contribute to Both Eating Disorders and Suicide etable 1. Odds Ratio of Suicide Attempts and Death by Suicide in Individuals With Eating Disorders, Adjusted for Different Comorbid Conditions etable 2. Test if Sex Modifies the Association Between Eating Disorders and Suicide Attempts and Death by Suicide etable 3. Odds Ratio of Suicide Attempts Among Individuals With at Least One Relative With Eating Disorders, Adjusted for Their Own Eating Disorders etable 4. Odds Ratio of Suicide Attempts Among Individuals With at Least One Relative With Eating Disorders, Adjusted for Their Own Comorbidities etable 5. Odds Ratio of Suicide Attempts Among Individuals With at least One Relative With Eating Disorders, Adjusted for Comorbidities in Relatives This supplementary material has been provided by the authors to give readers additional information about their work American Medical Association. All rights reserved. 1

2 efigure. Directed Acyclic Graph to determine whether familial factors exist that contribute to both eating s and suicide efigure illustrates the underlying mechanisms between eating s and suicide attempts in a Directed Acyclic Graph (DAG). 1 To simplify the exposition, here we restrict attention to pairs of relatives; the arguments carry over to familial clusters of arbitrary size. In efigure1, ED j and SCD j represent eating s and suicide attempts, respectively, for individual j in a given pair; j = 1, 2. U ED represents common causes for ED 1 and ED 2, and U SCD represents common causes for SCD 1 and SCD 2. U j represents common causes (confounders) for ED j and SCD j that may vary within the pair, and C represents common causes (confounders) for ED j and SCD j that are constant within the pair. The (set of) variable(s) C can be thought of as representing familial liability to both eating s and suicide attempts. Thus, the research question is to what extent C exists. We addressed this question by exploring the association between SCD 1 and ED 2, without and with adjusting for ED 1 (analyses generating Table 3 and etable 2, respectively). (Individual 1 is referred to as the index individual in the main manuscript). To motivate these analyses, consider the paths ED 2 C SCD 1 ED 2 C ED 1 SCD 1 and ED 2 U ED ED 1 SCD 1. In the analysis that does not adjust for ED 1, all these paths are open and may contribute to a statistical association between SCD 1 and ED 2. Thus, the observed positive association between SCD 1 and ED 2 (Table 3) could, in principle, be explained by the path ED 2 U ED ED 1 SCD 1, which does not presume the existence of C. In the analysis that adjusts for ED 1, this path and the path ED 2 C ED 1 SCD 1 are blocked; whereas path ED 2 C SCD 1 is not influenced, if C exists. However, by adjusting for ED 1 we additionally open the paths ED 2 C ED 1 U 1 SCD 1 ED 2 U ED ED 1 C SCD 1 and ED 2 U ED ED 1 U 1 SCD 1. The first two of these paths presume the existence of C, whereas the third does not. Thus, in principle, the observed adjusted (for ED 1 ) association between SCD 1 and ED 2 (etable 2) could be explained by the path ED 2 U ED ED 1 U 1 SCD 1. However, note that by symmetry U ED is most likely to affect ED 1 and ED 2 in the same direction. That is, if high levels of U ED are associated with high levels of ED 1, then high levels of U ED are also associated with high levels of ED 2. Regarding U 1, it is easy to think of confounders that could affect ED 1 and SCD 1 in the same direction, e.g. a genetic vulnerability or a deplorable family environment. However, it is much more difficult to think of confounders that would affect ED 1 and SCD 1 in opposite directions. Thus, we allege that the net effect of U 1 on ED 1 and SCD 1 is most likely in the same direction. As a consequence, adjusting for ED 1 is likely to induce a negative association between SCD American Medical Association. All rights reserved. 2

3 and ED 2. 2 Thus, the fact that the positive association between SCD 1 and ED 2 remains when we adjust for ED 1 is relatively strong evidence for the presence of path ED 2 C SCD 1, i.e., for the presence of C. ereferences 1. Greenland S, Pearl J, Robins JM. Causal diagrams for epidemiologic research. Epidemiology. 1999;10(1): Greenland S. Quantifying biases in causal models: classical confounding vs collider-stratification bias. Epidemiology. 2003;14(3): American Medical Association. All rights reserved. 3

4 etable 1. Odds ratio of suicide attempts and death by suicide in individuals with eating s, adjusted for different comorbid conditions Total population Adjust for MDD Adjust for ANX Adjust for SUD OR (95% CI) p- OR (95% CI) value Suicidal attempts p- value OR (95% CI) p- value 1.96 ( ) < ( ) < ( ) < ( ) < ( ) < ( ) <.001 Bulimia 2.11 ( ) < ( ) < ( ) <.001 Female 1.85 ( ) < ( ) < ( ) < ( ) < ( ) < ( ) <.001 Bulimia 1.96 ( ) < ( ) < ( ) <.001 Male 1.62 ( ) < ( ) < ( ) < ( ) ( ) ( ) <.001 Bulimia 3.89 ( ) < ( ) < ( ) <.001 Total population Death by suicide 2.13 ( ) < ( ) < ( ) < ( ) < ( ) < ( ) <.001 Bulimia 1.63 ( ) ( ) ( ).002 Female 2.01 ( ) < ( ) < ( ) < ( ) < ( ) < ( ) <.001 Bulimia 1.48 ( ) ( ) ( ).01 Male 2.19 ( ) ( ) ( ) ( ) ( ) < ( ) <.001 Bulimia 3.10 ( ) ( ) ( ).13 Note: MDD: major depressive ; ANX: anxiety ; SUD: substance use 2016 American Medical Association. All rights reserved. 4

5 etable 2. Test if sex modifies the association between eating s and suicide attempts and death by suicide Suicide attempts Death by suicide Crude model Adjusted model Crude model Adjusted model χ 2 p χ 2 p χ 2 p χ 2 p Bulimia American Medical Association. All rights reserved. 5

6 etable 3. Odds ratio of suicide attempts among individuals with at least one relative with an eating, adjusted for their own eating s Full Full cousin Half cousin Bulimia OR (95% CI) p-value OR (95% CI) p-value OR (95% CI) p- # Obs. value used < ( ) ( ) ( ) <.001 1,680, ( ) ( ) ( ) , ( ) ( ) ( ) , < ( ) ( ) ( ).002 1,753, ( ) ( ) ( ) ,222 Note: OR: Odds Ratio; CI: Confidence Interval. The models adjusted for birth year, sex, number of the type of relatives, family cluster effect, and the eating s in the index individual (i.e., the individual from whom we acquired information on suicide attempts and relatives eating s) American Medical Association. All rights reserved. 6

7 etable 4. Odds ratio of suicide attempts among individuals with at least one relative with eating s, adjusted for their own comorbidities Adjust for MDD Adjust for ANX Adjust for SUD OR (95% CI) p OR (95% CI) p OR (95% CI) p s Full 1.20 ( ) < ( ) < ( ) < ( ) ( ) ( ) ( ) ( ) ( ).11 Full cousin 1.08 ( ) ( ) < ( ) <.001 Half cousin 0.89 ( ) ( ) ( ).13 Full 1.04 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ).25 Full cousin 1.10 ( ) ( ) ( ).003 Half cousin 0.81 ( ) ( ) ( ).08 Bulimia Full 1.34 ( ) ( ) < ( ) < ( ) ( ) ( ) ( ) ( ) ( ).15 Full cousin 1.17 ( ) ( ) ( ).002 Half cousin 1.00 ( ) ( ) ( ).74 Note: MDD: major depressive ; ANX: anxiety ; SUD: substance use 2016 American Medical Association. All rights reserved. 7

8 etable 5. Odds ratio of suicide attempts among individuals with at least one relative with eating s, adjusted for comorbidities in relatives Adjust for MDD Adjust for ANX Adjust for SUD OR (95% CI) p OR (95% CI) p OR (95% CI) p s Full 1.06 ( ) ( ) < ( ) < ( ) ( ) ( ) ( ) ( ) ( ).20 Full cousin 1.05 ( ) ( ) ( ).001 Half cousin 0.87 ( ) ( ) ( ).09 Full 0.93 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ).25 Full cousin 1.07 ( ) ( ) ( ).009 Half cousin 0.80 ( ) ( ) ( ).04 Bulimia Full 1.11 ( ) ( ) ( ) < ( ) ( ) ( ) ( ) ( ) ( ).30 Full cousin 1.11 ( ) ( ) ( ).009 Half cousin 0.98 ( ) ( ) ( ).96 Note: MDD: major depressive ; ANX: anxiety ; SUD: substance use 2016 American Medical Association. All rights reserved. 8