## How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

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# How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

I have data on approximately 50 people who were treated for drug abuse with a novel treatment.  At baseline and at 5 equally spaced follow ups, they were evaluated for various problems on continuous scales.  I want to test the hypothesis that there was an improvement from baseline to 3 months and then no retreat from that improvement.

I know I can do equivalence testing on pairs of follow up points, but I am thinking of some sort of spline effect in MIXED or GLIMMIX. But I haven't quite figured out how to code it.

Any hints appreciated.

Using SAS 9.4.

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Solution
‎02-17-2016 06:29 AM
Super Contributor
Posts: 301

## Re: How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

[ Edited ]

What a funny question. I think I have a kind of solution, but its not perfect.

I suggest to make a model with a natural cubic spline. In the second model I suggest making a variable that is minimum of time and 3, and then make a natural cubic spline on that one. Then test from the first model to the second model. It is not perfect, because the second model has a non-differentiabable point at time=3. So it is neccessary to allow the same in the first model if the second model should be contained in the first model.

Secondly, it is very difficult to test that the change in the interval from 0 to 3 should be positive (improvement). The method here only test that there is a spline up to time=3, and constant for time>3.

Here is the code:

``````
data mydata;
do i=1 to 500;
time=6*ranuni(-1);
time2=min(time,3);
effekt=mod(i,2);
y=2+time+rannor(-1);
output;
end;
run;

*The test is seen it the type3 tests;
proc glimmix data=mydata;
effect spline1 = spline(time / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5) );
effect spline2 = spline(time2 / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5) );
model y=effekt effekt*spline1 effekt*spline2 /dist=normal ;
store out=model1;
run;
proc glimmix data=mydata;
effect spline2 = spline(time2 / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5) );
model y=effekt  effekt*spline2 /dist=normal ;
store out=model2;
run;

data template;
do effekt=0 to 1;
do time=0 to 6 by 0.01;
time2=min(time,3);

output;
end;
end;
ruN;
proc plm restore=model1;
score data=template out=pred1;
run;
proc plm restore=model2;
score data=template out=pred2;
run;

data pred;
merge pred1(rename=(predicted=pred1)) pred2(rename=(predicted=pred2));
by effekt time;
run;
symbol1 c=black i=none v=dot;
symbol2 c=red i=none v=dot;
proc gplot data=pred(where=(effekt));
plot (pred1 pred2 )*time/overlay;
run;``````

and here is the figure:

All Replies
Solution
‎02-17-2016 06:29 AM
Super Contributor
Posts: 301

## Re: How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

[ Edited ]

What a funny question. I think I have a kind of solution, but its not perfect.

I suggest to make a model with a natural cubic spline. In the second model I suggest making a variable that is minimum of time and 3, and then make a natural cubic spline on that one. Then test from the first model to the second model. It is not perfect, because the second model has a non-differentiabable point at time=3. So it is neccessary to allow the same in the first model if the second model should be contained in the first model.

Secondly, it is very difficult to test that the change in the interval from 0 to 3 should be positive (improvement). The method here only test that there is a spline up to time=3, and constant for time>3.

Here is the code:

``````
data mydata;
do i=1 to 500;
time=6*ranuni(-1);
time2=min(time,3);
effekt=mod(i,2);
y=2+time+rannor(-1);
output;
end;
run;

*The test is seen it the type3 tests;
proc glimmix data=mydata;
effect spline1 = spline(time / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5,3,3.5,4,4.5,5,5.5) );
effect spline2 = spline(time2 / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5) );
model y=effekt effekt*spline1 effekt*spline2 /dist=normal ;
store out=model1;
run;
proc glimmix data=mydata;
effect spline2 = spline(time2 / NATURALCUBIC  knotmethod=list(0.5,1,1.5,2,2.5) );
model y=effekt  effekt*spline2 /dist=normal ;
store out=model2;
run;

data template;
do effekt=0 to 1;
do time=0 to 6 by 0.01;
time2=min(time,3);

output;
end;
end;
ruN;
proc plm restore=model1;
score data=template out=pred1;
run;
proc plm restore=model2;
score data=template out=pred2;
run;

data pred;
merge pred1(rename=(predicted=pred1)) pred2(rename=(predicted=pred2));
by effekt time;
run;
symbol1 c=black i=none v=dot;
symbol2 c=red i=none v=dot;
proc gplot data=pred(where=(effekt));
plot (pred1 pred2 )*time/overlay;
run;``````

and here is the figure:

Frequent Contributor
Posts: 140

## Re: How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

Thanks!  That looks like a good approach

Posts: 2,655

## Re: How can I test a nonlinear hypothesis in MIXED or GLIMMIX?

[ Edited ]

I really like Jacob's approach.

Here is something a little simpler, along the lines of a Helmert contrast.  You do have to expand this out, as I have only put in the time coefficients, so this would be for the first treatment arm:

``````LSMESTIMATE time*treatment 'pre vs all follow' -5 1 1 1 1 1 divisor 5,
'time 1 vs follow' 0 -4 1 1 1 1 divisor 4,
'time 2 vs follow' 0 0 -3 1 1 1 divisor 3,
'time 3 vs follow' 0 0 0 -2 1 1 divisor 2,
'time 4 vs follow' 0 0 0 0 -1 1/joint;``````

Steve Denham

☑ This topic is solved.