How to use the Mediation Macro for Causal Modeling

1. CCEB How to use the Mediation Macro for Causal Modeling Mark S. Cary Thomas R. TenHave Department of Biostatistics and Epidemiology Center for Clinical Epidemiology and Biostatistics University of Pennsylvania School of Medicine Philadelphia, Pennsylvania USA June 19 2009 25 slides; 15 minutes if you play it as a slide show with narration ©Trustees of the University of Pennsylvania, 2009

2. Overview • We show you how to use our Structural Mean Model (SMM) SAS® Macro to calculate the effects of a mediator • This macro also computes the traditional model based on ordinary least squares regression (OLS) • We’ll have a brief non-technical overview of the issues and then • Show the specific macro setup, • and how to read the output. • More details are in the technical papers listed in the presentation

3. Why Mediation? • Randomized controlled trials (RCT) tell us whether there is an intent-to-treat (ITT) effect for treatment, but not how the treatment works • For example, clinical trials show that psychotherapies have an effect, but there is little consensus on how psychotherapy produces its effect, even for well studied therapies like Cognitive Behavioral Therapy. • To study the “how”, we are interested in the mediating variables that are caused by the treatment and then produce the effect on the outcome • For example, in a treatment to encourage studying before a test, the actual amount of studying might be a mediating variable both impacted by encouragement and also leading to improvement on the test

4. X (Treatment) Y (Test Score) An Encouragement Design Example • Suppose we assign students to either a “Study Skills” training program or to a “Placebo” session which encourages self-esteem. • The study skills training encourages students to study, but does not force them to • Many clinical trials are encouragement designs, encouraging participants to take their prescribed medications or cooperate with a therapy program • Suppose we find that those in the study skills program have more improvement in test scores • We can ask– was this improvement due to them studying more for the test? Or, did their improvement come from some factor not measured, such as the encouragement per se?

5. The traditional “Causal” Steps Method (Baron & Kenny) Add the mediator to the regression model and see if the treatment effect disappears M (Time Studying) β ne 0 α ne 0 X (Treatment) Y (Test Score) τ’=0 We have mediation when: 1) We regress Y on X and find a significant T coefficient, and 2) We regress Y on X and the T effect disappears or attenuates, and 3) We have a significant α and β.

6. References on Traditional Approaches • Baron, R. M., & Kenny, D. A. (1986). The moderator-mediator variable distinction in social psychology research: conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173-1182. • Kazdin, A. E. (2007). Mediators and mechanisms of change in psychotherapy research. Annual Review of Clinical Psychology, 3, 1-27 • MacKinnon, D.P. (2008). Introduction to statistical mediation analysis. New York: Lawrence Erlbaum Associates. • MacKinnon, D. P., Fairchild, A. J., & Fritz, M. S. (2007). Mediation analysis. Annual Review of Psychology, 58, 565-592.

7. The Problem is Sequential Ignorability • Randomization is an “ignorable” assignment mechanism • The traditional model requires Sequential Ignorability: • the assumption that patients randomized to a level of treatment are also randomized to their level on subsequent mediators • However, the experimenter is not randomizing how much studying each student does; that is up to the student and other factors in terms of unmeasured variables (e.g., stress, sleep) The mediator is also assumed to be randomized Treatment is randomized M (Time Studying) X (Treatment) Y (Test Score)

8. How do we solve this? • We always have the chance of unknown confounders. No matter how many variables we add to the models, there still could be an unknown confounder • Other approaches • Sequential randomization, first of the treatment, and then of the mediator. • We present a Structural Mean Model approach, • See for details: Ten Have, T. R., Joffe, M. M., Lynch, K. G., Brown, G. K., Maisto, S. A., & Beck, A. T. (2007). Causal mediation analysis with rank preserving models. Biometrics, 63(3), 926-934. • There are other causal methods reviewed in • Lynch, K. G., Cary, M. S., Gallop, R., & Ten Have, T. R. (2008). Causal mediation analyses for randomized trials. Health Services & Outcomes Research Methodology, 8(2),

9. Causal Modeling Approach • We will not explain the details of causal modeling. • However, by using a Structural Mean Model (SMM) that is, more technically, a Rank Preserving Model, • we are able to estimate both the treatment and mediation effectssimultaneously without the need for assuming sequential ignorability. • However, we have to make other assumptions.

10. Causal Modeling Assumptions • SUTVA (Stable Unit Treatment Value Assumption) • All treatments are the same (no effective and ineffective pills) • Causal effects do not depend on what other patients are receiving • Randomization • The treatment groups were randomized • There is independence of observations (for standard error estimation) • No baseline variables by intermediate factor (X*R and X*M) interactions on the outcome (Y) • No interactions between intervention and mediator (R*M) on outcome (Y) • To compute accurate estimates, we need an intent-to-treat effect on the mediator that is modified by baseline covariates (ie, X*R on M) • These interactions are used as instrumental variables

11. Mediation Macro • Obtain the mediation macro files from Tom Ten Have at tenhave@mail.med.upenn.edu • Use the “Mediation_Macro_Example_1JULY2009.sas” as your template. The date on it will be changed with any further revisions /*************************************************************************** * Mediation_Macro_Example_1JULY2009.sas * Example of mediation macro with test dataset * Written by: Tom TeHave, Mark Cary Department of Biostatistics, University of Pennsylvania School of Medicine, Philadelphia, PA *****************************************************************************/ ************************************************************************** ** Include the mediation macro and the DoSMM macro that calls it **************************************************************************; %include 'M:\mcary\mediation_macro\mediation.macro.1JULY2009.sas'; %include 'M:\mcary\mediation_macro\DoSMM.macro.1JULY2009.sas'; Change the path names to your location

12. The “Mediation_Macro_Example_1JULY.sas” contains the data inline for a test • You will have a randomization variable • Mediator variable • Outcome variable • And a Baseline covariate to provide interaction needed for estimation

13. The mediation analysis is called using the DoSMM macro (i.e., Do the SMM model), which calls the underlying estimation macros. • The DoSMM calls for a number of parameters

14. The Parameters

15. The first page of output repeats the parameters • And gives the N for before and after listwise deletion • The model does not allow missing data, thus you might need to impute data in some cases

16. Next is the Intent-to-Treat (ITT) results showing that there is an effect of randomization.

17. The randomization increases the mediator variable • In this case, the model is logistic because the mediator is a binary variable

18. Then, the mediator is added to the model with randomization. The randomization effect decreases only slightly, and the mediation effect is not significant

19. Next, some assumptions for causal modeling are checked • We want no R*M on Y interaction, and do not have one.

20. We want no X*M interaction on Y, but we have one in this case

21. We want no X*R on Y interaction and do not have one

22. Finally, we do have the X*R interaction on M, that is, an interaction between the baseline covariate and the randomization on the Mediator • In this case, we use logistic regression because the mediator is binary

23. The results of the causal modeling comes next, along with the number of iterations to convergence

24. For convenience, a we print a final chart that compares the estimates from the two models • The SMM suggests no direct effect of the randomization, with a substantial mediation effect • The OLS model has the opposite suggestion

25. Summary • Mediation studies the “how” of why a treatment works • However, traditional methods have the problem of assumingsequential ignorability, which makes them susceptible to unmeasured confounders • The causal model approach does not have this limitation, but does make other assumptions which we will test with similar causal methods under development • Using both methods in a study contributes to the convergent validity of the findings