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Reapeated measures linear regression

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Reapeated measures linear regression

Hi everybody,

I would like to perform a linear regression with repeated measurements: 20 patients with 4 measurements for each.

Do you have an idea how to take into account the correlated data?

I thought to random coefficient/intercept models using PROC MIXED. What do you think about this approach?

Thanking you in advance for your answer.

Regards,


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‎05-28-2013 04:20 PM
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Posts: 152

Re: Reapeated measures linear regression

Plots of results comparing two methods are good.  Whether the R-square statistic is good is another story because, with only two variables, the R-squared statistic is only the square of the Pearson's correlation coefficient between the two variables.  Sometimes, the value of the Pearson's correlation coefficient (and its partner, the R-squared statistic) can be misleading when comparing two methods because the values from the two methods can be strongly correlated but the values from each of the methods can differ quite markedly.

The simple Bland-Altman scatter plot of differences between paired measurements (on the Y-axis) vs. the mean of the paired measurements (on the X-axis) is one way to depict the relationship between the two methods to detect possible biases and outlying measurements (although it does not account for repeated within-individual paired measurements).

Various statistical methods and measures have been suggested to compare two methods--intraclass correlations, Deming regression (both methods are subject to measurement error so that neither method is a "gold standard"), structural equation modelling (for measurement error models), etc.  Even though you should produce the graphs that your colleagues want, it would be worthwhile for you in the future to read up more on the statistical methods relating to method comparisons.  Besides books and Google Scholar, you might also look at Lex Jansen's Internet site about SAS articles from conference proceedings that discuss methods comparisons to see how you might use SAS to implement these models.

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Trusted Advisor
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Re: Reapeated measures linear regression

PROC GLIMMIX or PROC GLM is definitely the way to go.

Contributor
Posts: 57

Re: Reapeated measures linear regression

Thanks a lot for your answer.

Contributor
Posts: 57

Re: Reapeated measures linear regression

Hi,

I would need to estimate the R-square and the p-value for the slope for this model. As I have to quantitative data, linear regression using PROC GLM is quite simple omitting CLASS statement.

Example:

proc glm data=RAW;

     model VALUE_A = VALUE_B;

run;

Now, I have some difficulties to add the REPEATED statement to specify that measures is repeated on patients (replicates).

Do you have any idea?

Thanks in advance

Regular Contributor
Posts: 152

Re: Reapeated measures linear regression

Go to the SAS Internet site, http://support.sas.com/documentation/, to read the PROC MIXED example on repeated measures.  Aligning your study with this example should allow you to analyze your data appropriately.

Generally, with mixed models and repeated measures, the R-squared measure is less useful than with ordinary least-squares regression because the interest is in modelling correctly the variance-covariance matrix among the repeated measures and in estimating the direction and the size of the model independent variable parameters rather than in estimating the proportion of the variance of the dependent variable "explained" by the independent variables.

Contributor
Posts: 57

Re: Reapeated measures linear regression

Thanks a lot 1zmm.

I completely agree with your advices. I used to use PROC mixed for similar problematics. In this particular case (method comparison using X subjects with Y replicates for each), my colleagues want to provide a plot with the results of the linear regression (method A vs method B and corresponding fit) and indicate the R-square.

I do not know if it is feasible/relevant.

Thanks

Solution
‎05-28-2013 04:20 PM
Regular Contributor
Posts: 152

Re: Reapeated measures linear regression

Plots of results comparing two methods are good.  Whether the R-square statistic is good is another story because, with only two variables, the R-squared statistic is only the square of the Pearson's correlation coefficient between the two variables.  Sometimes, the value of the Pearson's correlation coefficient (and its partner, the R-squared statistic) can be misleading when comparing two methods because the values from the two methods can be strongly correlated but the values from each of the methods can differ quite markedly.

The simple Bland-Altman scatter plot of differences between paired measurements (on the Y-axis) vs. the mean of the paired measurements (on the X-axis) is one way to depict the relationship between the two methods to detect possible biases and outlying measurements (although it does not account for repeated within-individual paired measurements).

Various statistical methods and measures have been suggested to compare two methods--intraclass correlations, Deming regression (both methods are subject to measurement error so that neither method is a "gold standard"), structural equation modelling (for measurement error models), etc.  Even though you should produce the graphs that your colleagues want, it would be worthwhile for you in the future to read up more on the statistical methods relating to method comparisons.  Besides books and Google Scholar, you might also look at Lex Jansen's Internet site about SAS articles from conference proceedings that discuss methods comparisons to see how you might use SAS to implement these models.

Contributor
Posts: 57

Re: Reapeated measures linear regression

Thanks one more time 1zmm for all your detailed advices.

Best,

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