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I'm running a logistic mixed model (in SAS) and these are my results:

proc glimmix data=ADL_logistic; 
class NEURO ID;
model ADL_bin (event="1") = NEURO LogTime  NEURO*LogTime/ dist=binary solution;
random intercept /subject=id g gcorr;
run;

fixed effects

As you can see, the standard error for NEURO is very big compared to its estimate, therefore, the effect is considered not significant. However, the difference is 1.7223 which is quite big compared to 2.9727, so it should be significant. When I plot the average evolutions of both groups, there is a big difference between them, indicating that this difference should be significant. The sample size is 54 for the "0" group and 89 for the "1" group.

enter image description here

What can be wrong?

The code I used to make the plot of the average evolutions:

data h;
do neuro=0 to 1 by 1;
    do subject=1 to 1000 by 1;
        b=sqrt(3.2988)*rannor(-1) ; *covariance parameter estimate 3.2988;
        do t=1 to 12 by 0.1;
        if neuro=0 then y=exp(2.9727 - 1.7223 + b -1*(0.6056 + 0.3607)*log(t))/(1+ exp(2.9727 + b -1*(0.6056 + 0.3607)*log(t)));
            else y=exp(2.9727 + b -0.6056*log(t))/(1+ exp(2.9727 + b -0.6056*log(t)));
        output;
        end;
    end;
end;

proc sort data=h;
by t neuro;
run;

proc means data=h;
var y;
by t neuro;
output out=out;
run;

*dm "dlgprtsetup orient=L nodisplay";
*filename fig ’c:/filename.eps’;
*goptions reset=all interpol=join  ftext=swiss device=pslepsfcgsfname=fig 
    gsfmode=replace targetdevice=winprtc;
proc gplot data=out;
plot y*t=neuro  / haxis=axis1 vaxis=axis2 legend=legend1;
axis1 label=(h=2  'LogTime') value=(h=1.5) order=(0 to 14 by 1)minor=none;
axis2 label=(h=2 A=90 'P(Y=1)') value=(h=1.5) order=(0 to 1 by 0.1) minor=none;
legend1 label=(h=1.5 'Neuro: ') value=(h=1.5 '0' '1');
title h=2.5 'Marginal average evolutions';
symbol1 c=red i=join w=20 l=1 mode=include;
symbol2 c=blue i=join w=20 l=1 mode=include;
where _stat_='MEAN';
run;quit;run;
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1 Answer 1

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The output looks perfectly fine to me - your estimate divided by its standard error (-1.7223/1.2) is -1.44, which gives you the non-significant result you obtained. The ratio of the estimate of NEURO to the estimate for the intercept has nothing to do with the significance of NEURO. Also, in plots, differences can look important although they are not. If you add confidence intervals to your plot, it might become more clear that the uncertainty associated with NEURO is too high to obtain a significant result.

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