Multilevel Mediation Analysis for Repeated Measures RCT

[pronabesh]

Hi SAS Users,

I am trying to do a multilevel mediation analysis using a 2x4 RCT design, where there are 2 conditions (control vs. experimental) and 4 time points (baseline, 1 month, 3 month and 6 month). A cut of the person-time dataset is shown below.

Obs	Idnum	cond	time	Mediator	Outcome
1	20001	1, control	0 Baseline	40	6.75
2	20001	1, control	1 month	38	6.75
3	20001	1, control	3 month	38	7.75
4	20001	1, control	6 month	20	5.50
5	20005	1, control	0 Baseline	6	3.25
6	20005	1, control	1 month	4	2.25
7	20005	1, control	3 month	2	2.50
8	20005	1, control	6 month	12	1.75
9	20006	1, control	0 Baseline	12	6.00
10	20006	1, control	1 month	14	6.00
11	20006	1, control	3 month	12	6.50
12	20006	1, control	6 month	12	5.25
13	20007	1, control	0 Baseline	10	7.75
14	20007	1, control	1 month	8	7.00
15	20007	1, control	3 month	2	7.00
16	20007	1, control	6 month	6	7.50
17	20008	2, experimental	0 Baseline	34	5.00
18	20008	2, experimental	1 month	40	7.50
19	20008	2, experimental	3 month	38	5.25
20	20008	2, experimental	6 month	40	4.25
21	20009	1, control	0 Baseline	12	3.75
22	20009	1, control	1 month	2	3.25
23	20009	1, control	3 month	20	4.75
24	20009	1, control	6 month	20	4.00
25	20010	2, experimental	0 Baseline	20	6.25
26	20010	2, experimental	1 month	20	5.75
27	20010	2, experimental	3 month	18	2.25
28	20010	2, experimental	6 month	10	4.75

The intervention cond id coded as 0 and 1; putative mediator and outcome were  measured at baseline and all follow ups.

Is there a way to evaluate mediation effects using this longitudinal data set with time varying measures?

If so, what is the best way of measuring the direct and indirect effects?

I used a random residual statement to account for within subject correlation, but the issue is that this solution of fixed effects is the marginal means. I need to evaluate the temporal effects as well, i.e., intervention -> mediates the intermediary putative mediator between 1 and 3 month -> changes outcome at 6 month.

This may be complicated but any help is much appreciated!

[SteveDenham]

Can you share the GLIMMIX/GENMOD code that you are currently using?  At least for me, it is easier to adapt what you already have in hand, rather than starting from square one.  The mediator variable intrigues me--it is a response variable, but is also a covariate of sorts.  There might be a way to use PROC PHREG, since it is set up for time-dependent covariates, but we are rapidly moving towards the edge of my experience.

Steve Denham

[pronabesh]

Steve,

The code I am tying to test is below. Also there is a correction in the post, the condition is codes 1 and 2 not 0 and 1.

/*-----------------------------------------------------*/
/* Mediation model 1                          */
/* Intervention on Outcome                 */
/*-----------------------------------------------------*/

proc glimmix data=work;
    class idnum cond time;
    model outcome = cond time cond*time / s;
    random time/ subject=idnum type=un residual;

     lsmeans cond*time;
run;

/*-----------------------------------------------------*/
/* Mediation model 2                          */
/* Intervention on Mediator                  */
/*-----------------------------------------------------*/

proc glimmix data=work;
    class idnum cond time;
    model mediator = cond time cond*time / s;
    random time/ subject=idnum type=un residual;

     lsmeans cond*time;
run;

/*-----------------------------------------------------*/
/* Mediation model 3                         */
/* Intervention and Mediator on Outcome*/
/*-----------------------------------------------------*/

proc glimmix data=work;
    class idnum cond time;
    model outcome = cond time cond*time mediator mediator*time / s;
    random time/ subject=idnum type=un residual;

     lsmeans cond*time;

     lsmeans mediator*time;
run;

I have added the interaction terms with time to test the time dependent fixed effects.

Here is the scenario: lets assume that the intervention changes the mediator at 3 months which then mediates a change in the outcome at 6 months. If I set the reference category to baseline, it is possible to test the fixed effects for these changes: (1) cond*time (where cond=experimental and time=6 month in Model 1); (2) cond*time (where cond=experimental and time=3 month in Model 2) and (3) mediator*time in Model 3.

However, it is complicated to get the direct and indirect effects from this.

[SteveDenham]

Parts 1 and 2 certainly make sense to me.  In model 3, however, we run into the problem that mediator is a continuous covariate.  Consequently, I would attack things just a bit differently.

First, since we are in GLIMMIX, I would use type=chol for the Cholesky root of the unstructured matrix--guarantees positive semidefinite G matrix.

Second, I would have the second lsmeans statement with multiple AT mediator= values, if the time by mediator interaction is significant:

lsmeans time/AT mediator=mean;

lsmeans time/AT mediator=<lowest value observed>;

lsmeans time/AT mediator=<highest value observed>;

If the time by mediator interaction is not significant, well, then I would seriously consider dropping it from the model, as now the slopes are parallel, so comparisons will not depend on the values that mediator takes on.

Steve Denham

[pronabesh]

Thank You Steve! Is there any way to get the direct and indirect effects? Otherwise, I might just have to report the betas and p-values. 

[SteveDenham]

Look at the solution vector (the betas).  Which do you consider direct?  I would say condition and time and their interaction.  To get the indirect effect, look at the change in these betas when mediator is added in (this includes all mediator and mediator interaction terms).  If this is missing your point entirely, then I think you may need to work this through a structural equation model approach (PROC CALIS for example, or PROC MODEL in SAS/ETS) that specifies direct and indirect effects more specifically.

Steve Denham

[pronabesh]

Hello Steve,

Sorry for not following up on this earlier.

I took your suggestion and tried two methods: (1) using a person time data set and modeled the time, cond and mediator interaction using GLIMMIX. I used a random residual statement to account for within subject correlation (code shown below).

/*-----------------------------------------------------*/

/* Mediation model 1                          */

/* Intervention on Outcome                 */

/*-----------------------------------------------------*/

proc glimmix data=work;

  class idnum cond time;

    model &outcome = cond|time/s;

    random time/ subject=idnum type=chol residual;

    lsmeans cond*time;

run;

/*-----------------------------------------------------*/

/* Mediation model 2                          */

/* Intervention on Mediator                  */

/*-----------------------------------------------------*/

proc glimmix data=work;

  class idnum cond time;

    model &med = cond|time / s;

    random time/ subject=idnum type=chol residual;

    lsmeans cond*time;

run;

/*-----------------------------------------------------*/

/* Mediation model 3                          */

/* Intervention and Mediator on Outcome*/

/*-----------------------------------------------------*/

proc glimmix data=work;

  class idnum cond time;

    model &outcome = cond|time|&med / s;

    random time/ subject=idnum type=chol residual;

    lsmeans cond*time;

    lsmeans time/AT &med=12.9236111 /*mean*/;

    lsmeans time/AT &med=12 /*median*/;

run;

[pronabesh]

The solution of fixed effects and type II test of fixed effects from the final model (Model 3) is shown below. The reference was set as baseline and  DASS_anxiety is the mediator.

Solutions for Fixed Effects
Effect	Condition	time	Estimate	Standard Error	DF	t Value	Pr > |t|
Intercept			4.9622	0.121	667	41.01	<.0001
cond	1, control		-0.057	0.1681	667	-0.34	0.7347
cond	2, experimental		0	.	.	.	.
time		1 month	-0.5048	0.1092	1691	-4.62	<.0001
time		3 month	-0.6054	0.127	1691	-4.77	<.0001
time		6 month	-0.8472	0.1357	1691	-6.24	<.0001
time		Baseline (reference group)	0	.	.	.	.
cond*time	1, control	1 month	0.2916	0.1501	1691	1.94	0.0522
cond*time	1, control	3 month	0.1661	0.1754	1691	0.95	0.3437
cond*time	1, control	6 month	0.5023	0.1857	1691	2.71	0.0069
cond*time	1, control	Baseline (reference group)	0	.	.	.	.
cond*time	2, experimental	1 month	0	.	.	.	.
cond*time	2, experimental	3 month	0	.	.	.	.
cond*time	2, experimental	6 month	0	.	.	.	.
cond*time	2, experimental	Baseline (reference group)	0	.	.	.	.
DASS_ANXIETY			0.03509	0.008233	1691	4.26	<.0001
DASS_ANXIETY*cond	1, control		0.0177	0.01172	1691	1.51	0.131
DASS_ANXIETY*cond	2, experimental		0	.	.	.	.
DASS_ANXIETY*time		1 month	0.01697	0.009498	1691	1.79	0.0741
DASS_ANXIETY*time		3 month	0.01906	0.01159	1691	1.64	0.1004
DASS_ANXIETY*time		6 month	0.02687	0.01274	1691	2.11	0.0352
DASS_ANXIETY*time		Baseline (reference group)	0	.	.	.	.
DASS_ANXIE*cond*time	1, control	1 month	-0.01377	0.01297	1691	-1.06	0.2886
DASS_ANXIE*cond*time	1, control	3 month	-0.01029	0.01591	1691	-0.65	0.5178
DASS_ANXIE*cond*time	1, control	6 month	-0.02023	0.01675	1691	-1.21	0.2274
DASS_ANXIE*cond*time	1, control	Baseline (reference group)	0	.	.	.	.
DASS_ANXIE*cond*time	2, experimental	1 month	0	.	.	.	.
DASS_ANXIE*cond*time	2, experimental	3 month	0	.	.	.	.
DASS_ANXIE*cond*time	2, experimental	6 month	0	.	.	.	.
DASS_ANXIE*cond*time	2, experimental	Baseline (reference group)	0	.	.	.	.
Type III Tests of Fixed Effects
Effect	Num DF	Den DF	F Value	Pr > F
cond	1	667	1.57	0.2105
time	3	1691	17.53	<.0001
cond*time	3	1691	2.89	0.0344
DASS_ANXIETY	1	1691	134.49	<.0001
DASS_ANXIETY*cond	1	1691	0.5	0.4776
DASS_ANXIETY*time	3	1691	1.73	0.1581
DASS_ANXIE*cond*time	3	1691	0.62	0.6036

Based on my understanding, if the type II tests of fixed effects for mediator*time is significant then mediation is present. The solution vectors are shown in solution for fixed effects, but for the life of me I can not figure out how best to present this finding or figure out a way to find direct/indirect effects.

[SteveDenham]

The F tests for mediator*time and mediator*condition*time are not significant, but the mediator "main effect" (which is really an intercept measure) is significant.

OK.  I am walking out on a very thin limb here, and my interpretation may not fit your field.  I would say that  I see two populations, defined by the level of dass_anxiety, and the responses over time being essentially identical for those two.  There seems to be an indication that the time course differs somewhat by condition as well.  So, in a guess as to what is going on--direct effects are time and dass_anxiety, and condition an indirect effect on the time course of the response.  Plots over time should make this apparent.

Steve Denham

[pronabesh]

Thanks for the suggestion Steve. I will try to look at the plots for interpretation. I also tried specifying line equations in proc CALIS (code shown below) which gives direct and indirect effects at each time point. The only issue is that I am not sure if I should specify a line equation for baseline as there should be no mediation at baseline in any case. However, that means baseline will be excluded from the error matrix.

ods html;

proc calis cov data=work_wide g4=1000 gconv=1e-10 all technique=levmar;

/*------------------------*/

LINEQS

outcome1_month = b1 cond + c1 mediator1_month + e11,

mediator1_month = a1 cond + e21,

outcome3_month = b2 cond + c2 mediator3_month + e12,

mediator3_month = a2 cond + e22,

outcome6_month = b3 cond + c3 mediator6_month + e13,

mediator6_month = a3 cond + e23

;

STD

cond=vartrt,

e11 = var11,

e21 = var21,

e12 = var12,

e22 = var22,

e13 = var13,

e23 = var23

;

COV

e11 e12 e13= COV1,

e21 e22 e23= COV2

;

run;

[SteveDenham]

This is a case of statistics as art.  I would fit it both ways, and hopefully find that the estimated values for mediation at baseline are zero.

And if they are NOT zero or nearly so, then I begin to wonder about "pathologies" in the data I am trying to model.

Steve Denham