1. Copyright 2004, D. P. MacKinnon 1 Methods to study Treatment Mechanisms of Action David P. MacKinnon NIDA Mechanisms Conference February 26 and 27, 2004 PDefinitions PAction and Conceptual Theory PStatistical Methods PAssumptions PSupported by NIDA

2. Copyright 2004, D. P. MacKinnon 2 Preparatory Remarks “Everyone talks about the weather but nobody does anything about it.” (Mark Twain) Neil Armstrong, last man on the moon

3. Copyright 2004, D. P. MacKinnon 3 Mediators and Moderators Nursing “.. Should consider hypotheses about mediators and moderators that could provide additional information about why an observed phenomenon occurs” (Bennett, 2000). Children’s programs “.. Including even one mediator and one moderator in a program theory and testing it with the evaluation.. will yield more fruit….” (Petrosino, 2000) Child mental health “rapid progress … depends on efforts to identify moderators and mediators of treatment outcome. We recommend randomized clinical trials routinely include and report such analyses” (Kraemer et al., 2002).

4. Copyright 2004, D. P. MacKinnon 4 2, 3, 4, or more variable effects.  Two variables: X  Y, Y  X, X  Y are reciprocally related. Measures of effect include the correlation, covariance, regression coefficient, odds ratio, mean difference.  Three variables: X  M  Y, X  Y  M, Y  X  M, and all combinations of reciprocal relations. Special names for third variable effects, confounder, mediator, moderator/interaction.  Four variables: many possible relations among variables, e.g., X  Z  M  Y

5. Copyright 2004, D. P. MacKinnon 5 Mediator A variable that is intermediate in the causal process relating an independent to a dependent variable. P Child Psychotherapy induces catharsis, insight and other mediators which lead to a better outcome (Freedheim & Russ, 1981) P Psychotherapy changes attributional style which reduces depression (Hollon, Evans, & DeRubies, 1991) P Parenting programs reduce parents negative discipline which reduces symptoms among children with ADHD (Hinshaw, 2002).

6. Copyright 2004, D. P. MacKinnon 6 Single Mediator Model MEDIATOR M INDEPENDENT VARIABLE XY DEPENDENT VARIABLE ab c’

7. Copyright 2004, D. P. MacKinnon 7 More Mediator Definitions  A mediator is a variable in a chain whereby an independent variable causes the mediator which in turn causes the outcome variable (Sobel, 1990)  The generative mechanism through which the focal independent variable is able to influence the dependent variable (Baron & Kenny, 1986)  A variable that occurs in a causal pathway from an independent variable to a dependent variable. It causes variation in the dependent variable and itself is caused to vary by the independent variable (Last, 1988)

8. Copyright 2004, D. P. MacKinnon 8 Other names for Mediators and the Mediated Effect  Intervening variable is a variable that comes in between two others.  Process variable because it represents the process by which X affects Y.  Intermediate or surrogate endpoint is a variable that can used in place of an ultimate endpoint.  Indirect Effect to indicate that there is a direct effect of X on Y and there is an indirect effect of X on Y through M.  Proximal to distal variables

9. Copyright 2004, D. P. MacKinnon 9 Mediator versus Confounder  Confounder is a variable related to two variables of interest that falsely obscures or accentuates the relation between them (Meinert & Tonascia, 1986)  The definition below is also true of a confounder because a confounder also accounts for the relation but it is not intermediate in a causal sequence.  “In general, a mediator is a variable that explains how or why two variables are related.”

10. Copyright 2004, D. P. MacKinnon 10 Reasons for Mediation Analysis in Treatment Research Mediation is important for clinical science. Practical implications include reduced cost and more effective treatments. Mediation analysis is based on theory for the processes underlying treatments. Action theory corresponds to how the treatment will affect mediators—the X to M relation. Conceptual Theory focuses on how the mediators are related to the outcome variables—the M to Y relation (Chen, 1990, Lipsey, 1993).

11. Copyright 2004, D. P. MacKinnon 11 Questions about mediators selected for therapy Are these the right mediators? Are they causally related to the outcome? Is self-esteem causally related to symptoms? Conceptual Theory Can these mediators be changed? Can personality be changed? Action Theory Will the change in these mediators that we can muster with our treatment be sufficient to lead to desired change in the outcome? Do we have the resources to change self-esteem in four sessions? Both Action and Conceptual Theory.

12. Copyright 2004, D. P. MacKinnon 12 Mediation Causal Steps Test  Series of steps described in Judd & Kenny (1981) and Baron & Kenny (1986).  One of the most widely used methods to assess mediation in psychology.  Consists of a series of tests required for mediation as shown in the next slides.

13. Copyright 2004, D. P. MacKinnon 13 Step 1 MEDIATOR M INDEPENDENT VARIABLE XY DEPENDENT VARIABLE c 1.The independent variable causes the dependent variable: Y = i 1 + c X +  

14. Copyright 2004, D. P. MacKinnon 14 Step 2 MEDIATOR M INDEPENDENT VARIABLE XY DEPENDENT VARIABLE 2. The independent variable causes the potential mediator: M = i 2 + a X +   a

15. Copyright 2004, D. P. MacKinnon 15 Step 3 MEDIATOR M INDEPENDENT VARIABLE XY DEPENDENT VARIABLE a 3. The mediator must cause the dependent variable controlling for the independent variable: Y = i 3 + c’ X + b M +   b c’

16. Copyright 2004, D. P. MacKinnon 16 Mediated Effect Measures Mediated effect=ab Standard error= Mediated effect=ab=c-c’ (see MacKinnon et al., 1995 for a proof) Direct effect= c’ Total effect= ab+c’=c Test for significant mediation: z’=or compute Confidence Limits abab

17. Copyright 2004, D. P. MacKinnon 17 Results of Statistical Simulation Study (MacKinnon et al., 2002)  Substantial differences in Type I error rates and power across causal steps, difference in coefficients ( c-c’ ), and product of coefficients ( ab ) methods. Causal steps described in Baron and Kenny (1986) have low power for small effects.  A product of coefficient test has good balance of power and Type I error rates, can be easily extended to longitudinal and multiple mediators, and has clear links with action and conceptual theory.

18. Copyright 2004, D. P. MacKinnon 18 Mediation Methods Mediated effect=ab Standard error= Confidence intervals based on the distribution of the product of two random variables are more accurate than existing methods and methods in common use have low power (MacKinnon et al., 2002). Confidence intervals based on the bias-corrected bootstrap are most accurate overall (MacKinnon, Lockwood, & Williams, 2004).

19. Copyright 2004, D. P. MacKinnon 19 Approximate Sample Size for.8 Power Effect Size SobelAsymmetric CL Causal Steps Small/Small675 507 >10,000 Medium/Medium90 69405 Large/Large42 3389 Note: For a model with a direct effect of zero. For causal steps, nonzero direct effect reduces required sample size. Sample sizes are determined by empirical methods and are not exact. Effect size from Cohen (1988).

20. Copyright 2004, D. P. MacKinnon 20 Measures of Effect Size  Correlation between X and M for the a parameter. Partial correlations for b and c’. Correlation of.1,.3, and.5 correspond to small, medium, and large effects (Cohen 1988)  Standardized betas for b, c’, and a. Change in standard deviations in the dependent variable for a standard deviation change in the independent variable  Proportion mediated ab/c = 1- c’/c = ab/(ab+c’)  Ratio of mediated to direct effect ab/c’  R-squared attributable to the mediated effect

21. Copyright 2004, D. P. MacKinnon 21 Assumptions I Homogeneous effects across subgroups: It assumed that the relation from X to M and from M to Y are homogeneous across subgroups or other characteristics of participants in the study. MacArthur model emphasizes the explicit test of whether the relation between M and Y differs across levels of X. Tested as an assumption in other methods (see Judd & Kenny 1981).

22. Copyright 2004, D. P. MacKinnon 22 Mediator versus Moderator  Moderator is a variable that affects the strength or form of the relation between two variables. The variable is not intermediate in the causal sequence, so it is not a mediator.  Moderator is also an interaction, the relation between X and Y depends on a third variable. There are other more detailed definitions of a moderator.  Tested by including interaction effects in addition to main effects of X.

23. Copyright 2004, D. P. MacKinnon 23 Moderators  Moderators determine for whom the program is most effective. Could be used to match treatments.  Moderators may also include mediation, e.g., the relation between X and M differs across groups, a, M and Y differs across groups, b, or whether the mediated effect ab, differs across groups.

24. Copyright 2004, D. P. MacKinnon 24 Moderated Mediation X MY a1a1 b1b1 c1’c1’ Group 1 X MY a2a2 b2b2 c2’c2’ Group 2 Separate mediated effect in each group: a 1 b 1, a 2 b 2

25. Copyright 2004, D. P. MacKinnon 25 Assumptions II  No measurement error: use reliable measures or estimate measurement models (Hoyle & Kenny, 1999).  No omitted variables: Program of study to examine candidate explanatory variables. Measure multiple mediators.  No missing data: Use existing adjustments and investigate sources of missing data.  Normally distributed scores: Apply methods for categorical variables or use resampling methods

26. Copyright 2004, D. P. MacKinnon 26 Mediation in Psychotherapy (Freedheim & Russ, 1992) Program outcome Catharsis Correction of emotional experience Insight and emotional resolution Problem Solving and Coping

27. Copyright 2004, D. P. MacKinnon 27 Measurement -Atomic mechanisms were hypothesized for the observable processes of chemical reactions. Experiments by John Dalton and Antoine Lavoisier demonstrating that mass was conserved and proportions of original elements were identical after chemical reactions led to the conclusion that matter was composed of atoms. Now electronic microscope. -Gregor Mendel hypothesized particles or genes were the mechanisms for his studies of inheritance in pea plants. Discovery of DNA and the genome, direct measurement of the previously unobserved genes is possible. These examples demonstrate how science improves by measuring previously unobserved mediating mechanisms.

28. Copyright 2004, D. P. MacKinnon 28 Assumptions III Mediation chain is correct: Any mediation model is part of a longer mediation chain. The researcher decides what part of the micromediational chain to examine. Similar decisions must be made about outcomes. Niles (1922) and Wright (1923) agreed on this. Temporal precedence X before M before Y: Collect longitudinal experimental data. Select appropriate timing and spacing of observations, e.g., trigger and threshold models

29. Copyright 2004, D. P. MacKinnon 29 Special Topic: Longitudinal Models Mediation model implies temporal precedence such that X causes M which then causes Y. Random assignment to conditions test the relation from X to M. Longitudinal models help shed light on longitudinal relations among X, M, and Y (Cheong et al, 2003; Cole & Maxwell, 2003)

30. Copyright 2004, D. P. MacKinnon 30 Two-wave Longitudinal Model BASELINE OUTCOME BASELINE MEDIATOR POST-TEST OUTCOME POST-TEST MEDIATOR PROGRAM Mediated effect=b 4 b 5 Direct effect = b 3 b1b1 b3b3 b4b4 b5b5 b2b2

31. Copyright 2004, D. P. MacKinnon 31 Latent Growth Model (LGM) LGM model change over time by estimating an intercept and slope for change in variables. These models can be used to investigate mediation by estimating change over time for the mediator and change over time for the outcome. The relation between the change in the mediator and change in the outcome represents the b path (Cheong et al. 2003). The causal direction of correlated change is ambiguous. Another LGM estimates change in the mediator at earlier time points and relates to change in the outcome at later time points providing more evidence for temporal precedence of the mediator.

32. Copyright 2004, D. P. MacKinnon 32 a c’ b

33. Copyright 2004, D. P. MacKinnon 33 Future Directions More mediation and moderation analysis of intervention studies. Programs of research to solve the limitations of single studies including the best experiments to follow a mediation and moderation analysis. Continue work extending mediation methods in survival analysis, longitudinal growth curve modeling, and multilevel models.

34. Copyright 2004, D. P. MacKinnon 34 Workshop on Mediating Mechanisms: Hypothesized Effects NIDA Mechanisms Workshop # Studies with Med. and Mod. Analysis Interest in Med. and Mod. Analysis Norms Regarding Reporting Results of Studies Comprehension of Reasons for Med. and Mod. Analysis Beliefs About the Importance of Theory Testing