## Longitudinal Analysis with a Small Sample

Regular Contributor
Posts: 180

# Longitudinal Analysis with a Small Sample

[ Edited ]

Hello all,

I have a samll data (N=7) with a longitudinal nature, and I am not sure how to analyze it. I am interested in a practical solution as well as an understanding of the correct one in case I had a larger sample.

My DV of interest is blood pressure. It is measured for each subject at baseline, and at several other time points post-treatment. There is only one group (one arm study).

My variables are: ID, Pressure (continuous), Time (categorical), Pressure at Baseline (I copied the values of the first time point into a column). The data is in long format, like SAS "likes it".

The differences between baseline and post treatment time points are relatively high (at the first time point the mean of difference is around 17, with a SD of 7). A simle Wilcoxon signed rank test is significant, despite the small sample.

Assuming that I had more data, what would be the correct way of analyzing this data ? My dilemma is which model is the best one. I wish to eventually compare the time points, each one to each one, but with a priority on comparing each time point to baseline.

The questions are:

1. If I put the pressure as a DV, and the Time as IV, it will include the baseline in it. Should I, or can I, enter the pressure at baseline as another covariate, or is it problematic? If I can't, how do I control for different baseline levels ?

2. Is it legal to enter the pressure change from baseline as a DV (after I calculate this variable) ? Now obviousaly I wish to test if the mean at any time point is not 0, how do I do that ?

3. What is the SAS code for models 1 and 2 ? I assume it will be either PROC MIXED or PROC GENMOD ( I am using SAS 9.4 but do not have the new PROC GEE yet) ?

4. In the case of a sample sample, how bad is it to simple to a paired t-test of Wilcoxson signed rank test for each time point vs. Baseline ?

Posts: 2,655

## Re: Longitudinal Analysis with a Small Sample

First, take a look at Frank Harrell's website here:

http://biostat.mc.vanderbilt.edu/wiki/Main/ManuscriptChecklist

Using that as a guideline, i'll try to answer the four questions you pose.

1. If I put the pressure as a DV, and the Time as IV, it will include the baseline in it. Should I, or can I, enter the pressure at baseline as another covariate, or is it problematic? If I can't, how do I control for different baseline levels ?

I would use the baseline as a covariate for comparisons of the post baseline lsmeans.  If comparison of these to the baseline is what you want, then an RMANOVA is in order.

2. Is it legal to enter the pressure change from baseline as a DV (after I calculate this variable) ? Now obviousaly I wish to test if the mean at any time point is not 0, how do I do that ?

I would NOT do this.  See Harrell's comments.

3. What is the SAS code for models 1 and 2 ? I assume it will be either PROC MIXED or PROC GENMOD ( I am using SAS 9.4 but do not have the new PROC GEE yet) ?

``````/* RMANOVA */
proc mixed data=yourdata;
class time subject_id;
model bp = time / ddfm=kr;
repeated time / subject = subject_id type=<choose from ar(1), arh(1), sp(pow) depending on spacing and homogeneity of variance across time>;
run;

/ *RMANCOVA */
/* Here time excludes the baseline point */
proc mixed data=yourdata;
class time subject_id;
model bp = time baseline_bp / ddfm=kr;
repeated time / subject = subject_id type=<choose from ar(1), arh(1), sp(pow) depending on spacing and homogeneity of variance across time>;
run;
``````

4. In the case of a sample sample, how bad is it to simple to a paired t-test of Wilcoxson signed rank test for each time point vs. Baseline ?

My opinion--this assumes a perfect correlation of all the timepoints with the baseline, plus there is no adjustment for the multiple comparisons.  This equals "bad idea" in my book.

Steve Denham

Discussion stats