# Mixed Model Versus GEE estimates and which to use

I am new to both GEE and mixed modeling, so please bare with me:

Briefly: my exposure is television viewing in childhood (tv) and I am trying to assess change in body mass index (bmisds) over 3 time (time) points - ages 4, 12 and 13 with adjustment for covariates. I first ran the analysis as a generalized estimating equation using proc genmod. When I run this analysis as a mixed effects model (with a random intercept and time treated as a random effect), I am essentially getting extremely similar/same parameter estimates to the GEE. Am I doing something wrong? This is the code I used:

proc mixed data=test;
class tv(ref="2.00") M_ID mom_gc(ref="1.00") brfed(ref="2.00")
preec(ref="0.00") gender_merged
firstborn sectioyes mat_ed activityhs4;
model bmisds=time tv time*tv mom_gc brfed preec gender_merged firstborn
sectioyes mat_ed activityhs4 GA_weeks MBMIsvkon1
maternal_age_birth weightsds_1/s corrb;
random int time/subject=M_ID;
run;


If it is right, why are the estimates so similar and which one do you recommend using? As I understand it, the GEE gives you population effects but the mixed effects model gives you both population averages and subject-specific effects, so how would I interpret an interaction for tv (2hours)*time with an estimate of 0.20 for example in the mixed effects model above? Instead of saying "children who watch TV for >2 hours had, on average, a 0.20-unit higher body mass index over time" as I might for the GEE, would I say "a child who watches >2 hours of TV has a 0.20-unit higher body mass index over time"? Where do the random effects come in? I am not seeing anything "extra" in the output of the mixed effects model over the GEE..

## 1 Answer

I wish you had mentioned whether your outcome was continuous or not or had some bizarre looking distribution or was like normal ..you know...

That said, I think you should not be surprised both gave you the same results and should give you the same estimates, except in few cases, not to risk being off topic, better left untouched.

I always liked so much, how Twisk in his "Applied Longitudinal Data Analysis for Epidemiology" explains GEE and Mixed models. I have slightly modified few lines (with your example) otherwise I am quoting from page 88 of his book.

"The interpretation of the regression coefficients of a predictor variables from a random coefficient analysis is exactly the same as the interpretation of the regression coefficients estimated with GEE analysis, so the interpretation is twofold: (1) the ‘between-subjects’ interpretation indicates that a difference between two subjects of 1 unit in, for instance, the predictor variable X2 is associated with a difference of 0.20-units (this is your beta) in the outcome variable Y; (2) the ‘within-subject’ interpretation indicates that a change within one subject of 1 unit in the predictor variable X2 is associated with a change of 0.20-unit in the outcome variable Y. Again, the ‘real’ interpretation is a combination of both relationships."

Hubbard et al, mentioned the following interpretation and along with other more reasons they argued GEE is more close to the truth than mixed models. So..

In case of a mixed effect linear relationship "Change in the mean outcome for a unit change in the associated neighborhood exposure, keeping the random effect (neighborhood) fixed"

In case of the GEE "Change in the mean outcome for a unit change in the associated neighborhood exposure across all of the neighborhoods observed"

This article might interest you. But, please careful. It is all about assumption, nothing else.

Hubbard AE, Ahern J, Fleischer NL, Van der Laan M, Lippman SA, Jewell N, et al. To GEE or not to GEE: comparing population average and mixed models for estimating the associations between neighborhood risk factors and health. Epidemiology (Cambridge, Mass). 2010;21(4):467-74.