Linear Regression for Repeated Measures across Multiple Subjects

[SPSSforBME]

Hello,

I hope that someone might be able to help me with a Regression Analysis on Repeated Measures data. I have a data set from a biomechanics study and am trying to determine if there is a difference in the path of motion in a joint when it is treated with two different surgeries. I would like to determine the average regression line across my 8 specimens for the two different surgical repairs and then compare these two regression lines to see if they are statistically different. However, I am unsure how to determine these regression models let alone statistically test them.

My data is structures as follows. I have 8 specimens which were repaired using one technique and then each was tested using a protocol which produced 15 X,Y coordinate pairs. Each specimen was then repaired using the second technique and another set of 15 X,Y pairs was recorded. How would I go about getting an overall regression for each of these two repairs across all 8 specimens? One last thing, in some specimens not all 15 points could be recorded as the points were taken at set X-values and they did not reach that value (ie did not translate that far because they were more stable).

Any help would be greatly appreciated.

Thank you

[Maguin, Eugene]

I think there might be some interesting clarifications needed. 1) 8 subjects (animals, persons?? Just curious) or 16 subjects. 2) Experimental injury?? Assumed randomly equal across subjects? 3) A predefined set of 'x' positions at which the maximal 'y' dimension movement is measured? 4) was single 'y' dimension measure obtained at each 'x' position or were multiple 'y' measurements taken at each 'x' position (a single time point is assumed)?? 5) So, really two data vectors for each intervention: a) was each 'x' positions attainted (Yes/No) and b) maximal 'y' measurement attained at each 'x' position but missing if 'x' position was not attained?? 6) Can we assume that 'x' ranges from some minimal value to some maximal value and if x(i) is not attained then x(i+1) through x(n) also will not be attained. 7) How much missing data at an worst 'x' position for the poorest performing treatment?

 Gene Maguin



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of SPSSforBME
Sent: Tuesday, November 20, 2012 2:15 PM
To: [hidden email]
Subject: Linear Regression for Repeated Measures across Multiple Subjects

Hello,

I hope that someone might be able to help me with a Regression Analysis on Repeated Measures data. I have a data set from a biomechanics study and am trying to determine if there is a difference in the path of motion in a joint when it is treated with two different surgeries. I would like to determine the average regression line across my 8 specimens for the two different surgical repairs and then compare these two regression lines to see if they are statistically different. However, I am unsure how to determine these regression models let alone statistically test them.

My data is structures as follows. I have 8 specimens which were repaired using one technique and then each was tested using a protocol which produced
15 X,Y coordinate pairs. Each specimen was then repaired using the second technique and another set of 15 X,Y pairs was recorded. How would I go about getting an overall regression for each of these two repairs across all 8 specimens? One last thing, in some specimens not all 15 points could be recorded as the points were taken at set X-values and they did not reach that value (ie did not translate that far because they were more stable).

Any help would be greatly appreciated.

Thank you




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[SPSSforBME]

I hope that I can provide you the necessary information.

1) 8 human cadaverous specimens which had two repairs performed on them in a repeated measures manner
2) yes, it is an experimentally created injury which has been shown to been shown to be repeatable
3&4)the data is extracted from motion pathways so the y value is a single value taken when the predefined x value is reached
5)yes, X was either attained or not and if it was not then no y value was recorded for that x,y pair
6)yes, once one x value is not attained no subsequent ones were attained
7)in the worst case there could be as many as 7 missing pairs

Thanks

[Maguin, Eugene]

Since the same subject cadaver serves as the subject for both treatments, I'd guess you'd have to expect there to be some correlation in the response between treatment A and treatment B.  I think the data have to be viewed as two data vectors per cadaver per treatment condition (one is dichotomous Y/N on 'x' position attainment; the other is 'y' position attained either missing or a number). I think that the data fit the description of a two part model. In a social science context, suppose persons are asked, "Over the past 7 days, how many drinks did you have on <day(i) of the 7 day period)". Some people will have 7 "never drank"; other will have drank some amount every day. I think your data fit that structure. However, a two part model requires bigger sample sizes to estimate. You don't have that. The x data have no missing data and perhaps you could fit a double repeated measures model to the data using GenLinMixed. I don't have experience with that. Perhaps someone else !
 on the list does and could reply.  Alternatively, I wonder if you could rank subjects on the number of 'x' positions attained. I'd guess that you expect a between treatment difference on the average rank. Given the rank data, I think it would be useful to investigate permutation tests.

You can't treat the y data as a repeated measures model because of the missing data. You could try fitting a mixed model using Mixed. I think the models would be

Level 1: Y(I,j) = B0(i) + B1*xposition(i) + e(I,j).
Level 2: B0(i) = G0 + G1*arm(j) + f(j).

However, this ignores the likely between treatment correlation. I'm not sure how to include that.

I'd guess that this experimental design-data structure is not so uncommon in medical research. I see that you are at London and I'm wondering if you've been through the biostats resources there.

Gene Maguin

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of SPSSforBME
Sent: Tuesday, November 20, 2012 4:02 PM
To: [hidden email]
Subject: Re: Linear Regression for Repeated Measures across Multiple Subjects

I hope that I can provide you the necessary information.

1) 8 human cadaverous specimens which had two repairs performed on them in a repeated measures manner
2) yes, it is an experimentally created injury which has been shown to been shown to be repeatable 3&4)the data is extracted from motion pathways so the y value is a single value taken when the predefined x value is reached 5)yes, X was either attained or not and if it was not then no y value was recorded for that x,y pair 6)yes, once one x value is not attained no subsequent ones were attained 7)in the worst case there could be as many as 7 missing pairs

Thanks



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[SPSSforBME]

Thank you for your suggestions. I will look into these areas further. As of yet I have not met with someone in my institution's statistics department as I supposed this forum would be faster (which you have proven to be the case) but I will certainly go down that path if I can't properly implement your suggestions.

Thank you again,
Josh