How and why criteria defining moderators & mediators differ between the Baron & Kenny and MacArthur approaches

1. How and why criteria defining moderators & mediators differ between the Baron & Kenny and MacArthur approaches Helena C. Kraemer, PhD Michaela Kiernan, PhD Stanford Prevention Research Center Stanford University School of Medicine

2. Introduction • Why the ‘MacArthur’ approach? • Why compare approaches? • Keep in mind….

3. Objectives • Provide rationale for examining moderators and mediators • Clarify differences in criteria used to establish variables as moderators and mediators by the two approaches • Explain rationale for the modifications by the MacArthur approach • Consider implications for the design & interpretation of future studies • Discuss future directions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

4. Rationale for examining moderators & mediators in treatment RCTs • Establishing moderators of treatment response—who responds & who does not—identifies the best target of treatments. • Establishing mediators of treatment response— how a treatment works—prompts strengthening, addition or removal of certain treatment components

5. Rationale for examining moderators & mediators in risk factor research • Establishing that one risk factor moderates another risk factor suggests on whom or under what conditions the second risk factor might work • Establishing that one risk factor mediates another risk factor suggests a possible chain leading to the outcome • And, thus, where the chain might be broken for purposes of prevention

6. Need for scientific vocabulary • If the same scientific term is applied to multiple different situations, or different terms are applied to the same situation such ambiguity will lead to non-reproducible results, misunderstandings and errors • In biomedical research, lives and well-being are at stake Kraemer, Kiernan, Essex & Kupfer (2006) under review.

7. T O M T M O Both approaches use the same conceptual definitions • A variable M is a moderatorof the relationship between a target variable T and an outcome O in a particular population, if M explains for whom or under what conditionsT is related to O • A variable M is a mediatorof the relationship between T and O if M helps explain how or whyT is related to O Baron & Kenny (1986)

8. Objectives • Provide rationale for examining moderators and mediators • Clarify differences in criteria used to establish variables as moderators and mediators by the two approaches • Explain rationale for the modifications by the MacArthur approach • Consider implications for the design & interpretation of future studies • Discuss future directions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

9. Eligibility and analytic criteria • 3 elements: Target (T), M, Outcome (O) • T and M always precede O • Eligibility criteria • What variable is eligible to be a moderator? A mediator? • Analytic criteria • What is needed to demonstrate that an eligible variable is a moderator of T with O? A mediator of T with O?

10. Linear model • For sake of simplicity here: • Assume that T is binary, M and O are ordinal • Use a linear model • Association between T, M, and O: • M = γ0 + γ1T + ε • O = β0 + β1T + β2M + β3TM + ε* • Variables centered Kraemer, Stice, Kazdin, & Kupfer (2001); Kraemer, Wilson, Fairburn, & Agras (2002)

11. Criteria for both approaches Baron & Kenny approach MacArthur approach M M M M moderates mediates moderates mediates T T T T Eligibility criteria Temporal precedence of either T or M [Not specified] M before T Association between T and M [Not specified] 1=0 Analytical criteria3030 Kraemer, Kiernan, Essex & Kupfer (2006) under review.

12. Criteria for both approaches Baron & Kenny approach MacArthur approach M M M M moderates mediates moderates mediates T T T T Eligibility criteria Temporal precedence of either T or M T before M T before M Association between T and M 10 10 Analytical criteria Assume Either 20 3=0;or 30 120 Kraemer, Kiernan, Essex & Kupfer (2006) under review.

13. Criteria for both approaches Baron & Kenny approach MacArthur approach M M M M moderates mediates moderates mediates T T T T Eligibility criteria Temporal precedence of either T or M [Not specified] T before M M before T T before M Association between T and M [Not specified] 10 1=0 10 Analytical criteria30 Assume 30Either 20 3=0;or 30 120 Kraemer, Kiernan, Essex & Kupfer (2006) under review.

14. Objectives • Provide rationale for examining moderators and mediators • Clarify differences in criteria used to establish variables as moderators and mediators by the two approaches • Explain rationale for the modifications by the MacArthur approach • Consider implications for the design & interpretation of future studies • Discuss future directions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

15. ‘Shocking’ differences? • MacArthur approach specifies: • For moderation, no association between M and T, and M before T. • For mediation, presence of a non-zero interaction between associated M and T can suffice

16. Statistical versus clinical significance • Baron & Kenny approach (1986) • Non-significant result does not “prove” null hypothesis. Significant result is not necessarily of clinical significance. • MacArthur approach (2000) • Effect size of T on O can be pieced apart into components related to the effects of T on M.

17. Some unavoidable mathematics Overall effect size of T on O: β1+ β2 EffectT(mean M) + β3(mean M - centered M) [V + β2β3EffectT(variance M)]1/2 Effect size of T on O conditional on M=m: β1+β3m V1/2

18. Assumptions about causality • Baron and Kenny approach • Use definitions that assume causal pathways are known • A moderator is “a third variable exhibiting statistical interaction by virtue of its being antecedent or intermediate in the causal process under study” Last (1995) • A mediator is “a variable that occurs in the causal pathway from an independent to a dependent variable. It causes variation in the dependent variable, and itself caused to vary by the independent variable” Last (1995) Kraemer, Kiernan, Essex & Kupfer (2006) under review.

19. Assumptions about causality • Baron and Kenny approach continued • Causal relationship between T and O is often simply assumed as part of the theoretical model • If data do not contradict the assumption, causal inferences are often drawn either from longitudinal observational studies or cross-sectional studies Kraemer, Kiernan, Essex & Kupfer (2006) under review.

20. Assumptions about causality • MacArthur approach • Gain understanding of possible causal processes involved • If causal processes known, no need to establish if variables are moderators or mediators • In medical research, greater reluctance to accept casual inferences from observational data • Premature causal inferences are avoided Kraemer, Kiernan, Essex & Kupfer (2006) under review.

21. Objectives • Provide rationale for examining moderators and mediators • Clarify differences in criteria used to establish variables as moderators and mediators by the two approaches • Explain rationale for the modifications by the MacArthur approach • Consider implications for the design & interpretation of future studies • Discuss future directions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

22. Implications for research design • Unique identification of moderators and mediators • Necessity for longitudinal studies Kraemer, Kiernan, Essex & Kupfer (2006) under review.

23. Clarifying ambiguities • Establishing the relationship between two variables and an outcome • Whether the relationship is moderation or mediation • Which variable is the moderator (or mediator) and which variable is being moderated (or mediated) Kraemer, Kiernan, Essex & Kupfer (2006) under review.

24. O O O O O A 1 R 1-1 B A 1-2 R 2 B What is the relationship between X1 and X2 with O? X1 X2 2 A X1 and X2 are not associated if and only if 2 =.5 R 1-2 B Kraemer, Kiernan, Essex & Kupfer (2006) under review.

25. Conclusions by approach Eligibility criteria Analytical criteria Conclusions X1 precedes X2 Association between X1 and X2 Interaction between X1 and X2 Main effect of X2 Baron & Kenny MacArthur [Yes] No No No [Yes] No No Yes [Yes] Yes No No Yes Yes No Yes [Yes] No Yes No/ Yes [Yes] Yes Yes No/ Yes

26. Conclusions by approach Eligibility criteria Analytical criteria Conclusions X1 precedes X2 Association between X1 and X2 Interaction between X1 and X2 Main effect of X2 Baron & Kenny MacArthur [Yes] No No No Neither Neither [Yes] No No Yes Neither Neither [Yes] Yes No No Neither Neither Yes Yes No Yes [Yes] No Yes No/ Yes [Yes] Yes Yes No/ Yes

27. Conclusions by approach Eligibility criteria Analytical criteria Conclusions X1 precedes X2 Association between X1 and X2 Interaction between X1 and X2 Main effect of X2 Baron & Kenny MacArthur [Yes] No No No Neither Neither [Yes] No No Yes Neither Neither [Yes] Yes No No Neither Neither Yes Yes No Yes X2 mediates X1 X2 mediates X1 [Yes] No Yes No/ Yes [Yes] Yes Yes No/ Yes

28. Conclusions by approach Eligibility criteria Analytical criteria Conclusions X1 precedes X2 Association between X1 and X2 Interaction between X1 and X2 Main effect of X2 Baron & Kenny MacArthur [Yes] No No No Neither Neither [Yes] No No Yes Neither Neither [Yes] Yes No No Neither Neither Yes Yes No Yes X2 mediates X1 X2 mediates X1 [Yes] No Yes No/ X1 moderates X2 X1 moderates X2 Yes X2 moderates X1 [Yes] Yes Yes No/ Yes

29. Conclusions by approach Eligibility criteria Analytical criteria Conclusions X1 precedes X2 Association between X1 and X2 Interaction between X1 and X2 Main effect of X2 Baron & Kenny MacArthur [Yes] No No No Neither Neither [Yes] No No Yes Neither Neither [Yes] Yes No No Neither Neither Yes Yes No Yes X2 mediates X1 X2 mediates X1 [Yes] No Yes No/ X1 moderates X2 X1 moderates X2 Yes X2 moderates X1 [Yes] Yes Yes No/ X2 mediates X1 X2 mediates X1 Yes X1 moderates X2 X2 moderates X1

30. Establishing variables as moderators or mediators • Baron & Kenny approach • ‘A priori’ assumptions about position of M and T to determine which variable is labeled a moderator (or mediator) • Same data but different researchers lead to non-replicable results • MacArthur approach • Unique and consistent conclusions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

31. O O A R B Establishing variables as moderators or mediators • MacArthur approach • Can examine the same general construct with the same measurement method; however, they are different variables Social support (Changes in) Social support (Baseline) Social support (Changes in) Kraemer, Kiernan, Essex & Kupfer (2006) under review.

32. Implications for research design • Unique identification of moderators and mediators • Necessity for longitudinal studies Kraemer, Kiernan, Essex & Kupfer (2006) under review.

33. T O M T M O Implications for research designs • To establish causal moderators and mediators, test in randomized trials • Mediation causation • To establish moderators or mediators, • Conduct longitudinal studies w/ > 3 time pts • Can conduct w/ only 2 time points, if detecting fixed markers (e.g., gender, race/ethnicity, genotype) as moderators of subsequent T or if detecting mediators of fixed markers

34. Implications for research designs • Not possible to use cross-sectional studies to establish moderators and mediators • Interaction  moderation • Useful for identifying variables for future longitudinal studies, either observational or randomized trials

35. Objectives • Provide rationale for examining moderators and mediators • Clarify differences in the criteria used to establish variables as moderators and mediators by the two approaches • Explain rationale for the modifications by the MacArthur approach • Consider implications for the design & interpretation of future studies • Discuss future directions Kraemer, Kiernan, Essex & Kupfer (2006) under review.

36. Insights from early use of approach • Recent approach • Need to establish criteria for independence • Hypothesis testing versus hypothesis generating • If a moderator M of T with O is identified, process leading from T to O (e.g., mediators) may differ in subgroups with different M Kraemer, Kiernan, Essex & Kupfer (2006), under review.

37. Some empirical examples Caspi A et al. Role of genotype in the cycle of violence in maltreated children. Science 2002;297:851-854. Essex et al. Exploring risk factors for the emergence of children’s mental health problems. Archives of Gen Psychiatry in press. The MTA Cooperative Group. Mediators and moderators of treatment response for children with attention-deficit/hyperactivity disorder. Archives of General Psychiatry 1999;56:1088-1096. Owens EB et al. Which treatment for whom for ADHD? Moderators of treatment response in the MTA. Journal of Consulting and Clinical Psychology 2003;71:540-552.

38. Resources Kraemer, H.C. Lowe, K.K., Kupfer, D.J.  To Your Health:  What Research Tells Us About Risk.  Oxford University Press.  2005. http://toyourhealthbook.com Baron R, Kenny D. The moderator-mediator variable distinction in social psychological research. JPSP 1986;51:1173-1182. Kraemer HC, Stice E, Kazdin A, Offord D, Kupfer D. How do risk factors work together? Mediators, moderators, and independent, overlapping, and proxy risk factors. American Journal of Psychiatry 2001;158:848-856. Kraemer HC, Wilson GT, Fairburn CG, Agras WS. Mediators and moderators of treatment effects in RCTs. Archives of General Psychiatry 2002;59:877-883. Kraemer HC, Kiernan M, Essex MJ, Kupfer DJ. Moderators and mediators: Comparing the Baron & Kenny and MacArthur approaches. 2006:Manuscript under review.