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I have data from a study for a "device". Subjects receive an implant and are followed for 5 years, with a checkup every year. A "disability score" is calculated from a survey every visit. The implant comes in different "sizes". Also, every year the "device condition" is evaluated. What I'm trying to do is see if "device condition" is associated with "disability score" while controlling for implant size/time/subject.

The Data:

I have the subject id, implant (A and B for sizes and is a static/baseline variable), the timepoint (12, 24, 36, 48, 60 months), implant condition (ordinal scale where 0 is best condition and can change timepoint to timepoint within each subject) and the disability score (dependent quantitative variable).

Example shown below

data modelling;
    input sid $ implant $ timepoint condition disability_score;
    cards;
    1 A 12 0 8
    1 A 24 0 9
    1 A 36 1 9.5
    1 A 48 1 8
    1 A 60 2 9
    2 B 12 1 7
    2 B 24 2 6
    2 B 36 2 7
    2 B 48 3 8
    2 B 60 4 9
    .....
    15 A 12 0 8
    15 A 24 0 9
    15 A 36 1 9.5
    15 A 48 1 8
    15 A 60 2 9
    ;
run;

I'm using proc mixed, but I'm not sure which syntax would be most appropriate for this question. My initial inkling is this is a repeated measures situation and used this:

proc mixed data=modelling plots=none;
    class sid implant timepoint condition;
    model disability_score = implant condition timepoint condition*timepoint;
    repeated timepoint / subject=sid;
run;

However, one thing I'm concerned with is if timepoint needs/should be a quantitative value, and if this is truly a repeated measures situation. When I run this, the condition and implant seem to be significant, and timepoint is not.

I also tried using the random statement with the subject id instead and using timepoint as quantitative

proc mixed data=modelling plots=none;
    class sid implant condition;
    model disability_score = implant condition timepoint condition*timepoint;
    random sid;
run;

When I do this, I get vastly different results, with timepoint being significant and both implant and condition no longer significant.

Really, I'm not 100% sure which is the correctly specified model, and am looking for some validation and/or guidance to the correctly specified model for this question.

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1 Answer 1

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The main difference between these models is that you are treating timepoint as categorical in the first model:

proc mixed data=modelling plots=none;
    class sid implant timepoint condition;
    model disability_score = implant condition timepoint condition*timepoint;
    repeated timepoint / subject=sid;
run;

....and as numeric/continuous in the second:

proc mixed data=modelling plots=none;
    class sid implant condition;
    model disability_score = implant condition timepoint condition*timepoint;
    random sid;
run;

In both cases, you are specifying a "variance components" (VC) structure. This is the default in PROC MIXED and also the simplest, where the correlations of errors within a subject are presumed to be 0. As I said, this is the default in PROC MIXED, but is not a reasonable choice for most repeated measures designs because we expect there to be correlations within subjects. This is not be the reason you obtain different results, but it is something that should be addressed in your modelling. AR(1) and Unstructured should be explored.

The likely cause of the differences you see is the treatment of the timepoint variable. When you use it as continuous the software estimates a single estimate for the effect and that estimate is a linear effect. When you treat the variable as categorical this allows for nonlinear effects as it estimates a separate parameter for each level of timepoint. Without access to your data it is very hard to say more, but I believe this should be the first thing to look at.

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