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Mediator analysis within field trials

Mediator analysis within field trials. Laura Stapleton UMBC. Session outline. Basic mediation model Comment on causality Tests of the hypothesized mediation effect Examples of mediation models for cluster randomized trials Brief preview of advanced issues and software.

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Mediator analysis within field trials

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  1. Mediator analysis within field trials Laura Stapleton UMBC

  2. Session outline • Basic mediation model • Comment on causality • Tests of the hypothesized mediation effect • Examples of mediation models for cluster randomized trials • Brief preview of advanced issues and software

  3. Basic mediation model c Treatment T Outcome Y Mediator M a b Treatment T Outcome Y c’ total effect = indirect effect + direct effect c = ab + c’

  4. Causality concerns • Because the mediator is not manipulated, causal interpretations are limited Z Mediator M a b  Treatment T Ok! Outcome Y • Possible misspecification • In future research, manipulate mediator • For now, assume or hypothesize that M causes Y

  5. Tests of the hypothesized mediation effect Mediator M a b • The estimate of the indirect effect, ab, is based on the sample • To infer that a non-zero ab exists in the population, a test of the significance of ab is needed • Several approaches have been suggested and differ in their ability to “see” a true effect (power) Treatment T Outcome Y c’

  6. Tests of the hypothesized mediation effect • z test of ab (with normal theory confidence interval) • Asymmetric confidence interval (Empirical M or distribution of the product) • Other tests not considered today: • Causal steps approach (Baron & Kenny) • Test of joint significance • Bootstrap resampling

  7. z test of ab product • seab = • Calculate z = • Compare z test value to critical values on the normal distribution • Can also calculate confidence interval around ab CI = • One of the least powerful approaches • Problem is that the ab product is not normally distributed, so critical values are inappropriate

  8. I simulated 1,000 estimates of a and 1,000 estimates of b where mean = 0 and SD=1 Distribution of path a Distribution of path b Distribution of product of axb

  9. Empirical M-test (asymmetric CI) • Determines empirical distribution of z of the ab product (not assuming normality) • Distribution is leptokurtic and symmetric when αβ=0, but is skewed if αβ > 0 or αβ < 0 • Given a, b, and their SEs, PRODCLIN determines the distribution of ab and critical values • Confidence interval limits: • If CI does not include zero, then “significant”

  10. Mediation models for cluster randomized trials • Extend basic model to situations when treatment is administered at group level • Model depends on whether mediator is measured at group or individual level • Upper-level mediation (2→2→1 Design) • Cross-level mediation (2→1→1 Design) • Cross-level and upper-level mediation (2→1 / 2→1 Design)

  11. Measured variable partitioning • First, consider that any variable may be partitioned into individual level components and cluster level components

  12. Mediation model possibilities

  13. Data Example Context • Cluster randomized trial (hierarchical design) • 14 pre-schools: ½ treatment, ½ control • Socio-emotional curriculum • Outcome is child behavior • Possible mediators: teacher attitude, child socio-emotional knowledge • Sample data are on posted handout (n=84) • Analyses with SPSS (HLM and SAS available)

  14. Total effect of treatment Before we examine mediation, let’s examine the total effect of treatment on the outcome… γ’01 Treatment CLUSTER Outcome CLUSTER Treatment Outcome Outcome INDIVIDUAL

  15. Total effect of treatment: Results MIXED Y WITH T /FIXED= T | SSTYPE(3) /RANDOM = INTERCEPT | SUBJECT(J) COVTYPE(VC) /METHOD = REML /CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1) SINGULAR(0.000000000001) HCONVERGE (0,ABSOLUTE) LCONVERGE(0,ABSOLUTE) PCONVERGE(0.000001,ABSOLUTE) /PRINT = CPS G SOLUTION TESTCOV. Given that SD of Y is 4.381, effect size of treatment is large: .97.

  16. Upper-level mediation model (2→2→1) Mediator CLUSTER γ01 γ’01 Treatment CLUSTER Outcome CLUSTER γ’02 Mediator Treatment Outcome Outcome INDIVIDUAL

  17. Upper-level mediation model: Results To estimate the a path, I ran an OLS regression is SPSS using a file from the 14 schools The estimate is .714 with a standard error of .628

  18. Upper-level mediation model: Results To estimate the b path, I ran a mixed model MIXED Y WITH T M1 /FIXED= T M1 | SSTYPE(3) /RANDOM = INTERCEPT | SUBJECT(J) COVTYPE(VC) <<remainder of syntax same as before>> The estimate is .795 with a SE of .656

  19. Upper-level mediation model: Results Mediator CLUSTER .714 .795 Treatment CLUSTER Outcome CLUSTER 3.671 Mediator Treatment Outcome Outcome INDIVIDUAL • Direct effect = 3.671 • Indirect effect = (.714)(.795) = .568 • Total effect = DE + IE = 3.671 + .568 = 4.239

  20. Upper-level mediation model: Results • Significance test of the indirect effect • PRODCLINhttp://www.public.asu.edu/~davidpm/ripl/Prodclin/

  21. Cross-level mediation model (2→1→1) Model A Model B γ01 Mediator CLUSTER γ’01 Treatment CLUSTER Treatment CLUSTER Outcome CLUSTER Mediator Mediator Treatment Treatment Outcome Mediator INDIVIDUAL Mediator INDIVIDUAL γ’10 Outcome INDIVIDUAL

  22. Cross-level mediation model: Results To estimate the a path: MIXED M2_GrandC WITH T /FIXED= T | SSTYPE(3) /RANDOM = INTERCEPT | SUBJECT(J) COVTYPE(VC) <<remainder of syntax same as before>> The estimate is 2.643 with SE of 1.195

  23. Cross-level mediation model: Results To estimate the b path: MIXED Y WITH M2_GrandC T /FIXED= M2_GrandC T | SSTYPE(3) /RANDOM = INTERCEPT | SUBJECT(J) COVTYPE(VC) <<remainder of syntax same as before>> The estimate is .592 with a SE of .143

  24. Cross-level mediation model:Results Model A Model B Mediator CLUSTER 2.643 Treatment CLUSTER Treatment CLUSTER Outcome CLUSTER 2.675 Mediator Mediator Treatment Treatment Outcome Mediator INDIVIDUAL Mediator INDIVIDUAL .592 Outcome INDIVIDUAL • Direct effect = 2.675 • Indirect effect = (2.643)(.592) = 1.564 • Total effect = 2.675 + 1.564 = 4.239

  25. Cross-level mediation model: Results • Test of the indirect effect

  26. Cross-level and upper-level mediation model (2→1 / 2→1) Model B Model A γ01 γ’02 Mediator CLUSTER Mediator CLUSTER Treatment CLUSTER Outcome CLUSTER Treatment CLUSTER γ’01 Ave. M Mediator M Treatment Treatment Outcome γ’10 Mediator INDIVIDUAL Mediator INDIVIDUAL Outcome INDIVIDUAL

  27. Cross-level and upper-level mediation model: Results Path a is the same as in the prior model. For the b paths: MIXED Y WITH M2_AVE M2_GrandC T /FIXED= M2_AVE M2_GrandC T | SSTYPE(3) /RANDOM = INTERCEPT | SUBJECT(J) COVTYPE(VC) <<remainder of syntax same as before>>

  28. Cross-level and upper-level mediation model (2→1 / 2→1) Mediator CLUSTER Mediator CLUSTER 2.643 -.041 Treatment CLUSTER Outcome CLUSTER Treatment CLUSTER 2.761 Ave. M Mediator M Treatment Treatment Outcome Mediator INDIVIDUAL Mediator INDIVIDUAL GRAND_C .600 Outcome INDIVIDUAL • Note that there are now TWO mediation paths: • abindividual = (2.643)(.600) = 1.586 • abcluster = (2.643)(-.041) = -.109

  29. Cross-level and upper-level mediation model (2→1 / 2→1) • Test of the indirect effect at the individual level:

  30. Cross-level and upper-level mediation model (2→1 / 2→1) • Test of the indirect effect at the cluster level:

  31. Mediator CLUSTER Mediator CLUSTER 2.643 .559 Treatment CLUSTER Outcome CLUSTER Treatment CLUSTER 2.761 Ave. M Mediator M Treatment Treatment Outcome Mediator INDIVIDUAL Mediator INDIVIDUAL GROUP_C .600 Outcome INDIVIDUAL Cross-level and upper-level mediation model (2→1 / 2→1) • The level-2 effect of the mediator differs with group- versus grand-mean centering: • abcluster = (2.643)(.559) = 1.477 with GROUP_C • abcluster = (2.643)(-.041) = -.109 with GRAND_C

  32. Brief preview of advanced issues • Multisite / randomized blocks (1→1 →1) • Testing mediation in 3-level models • Including multiple mediators • Examining moderated mediation • Dichotomous or polytomous outcomes • Measurement error in mediation models • Bayesian estimation of indirect effects

  33. Notes on software • SPSS • HLM • SAS (PROC MIXED) • MLwiN • Mplus

  34. stapleton@umbc.edu

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