Hi Nicolas

The "common random effects design matrix" expression  means that all subjects in your prospective study are expected in advance to have the same random effects design matrix (Zi). If you assume a linear trajectory over time and a two-year study with repeated measurements every six months then this matrix can be:

1  0
1  0.5
1  1
1  1.5
1  2


In this case you are considering both intercept and time as random effects. ZiCol
is the column of the above matrix that you are interested in (usually column 2, slope of change over time).

To compute sample size you also need estimates of the random effects covariance matrix (Dhat), within-subject measurement error, effect size, and drop-out rate. If your study is about Alzheimer-related hippocampal volume or cortical thickness variations you can use our sample ADNI data to compute those values (ADNI791_Hipp_and_Entorh.mat). Eg.

lme_plannedSampleSize(Zi,2,total_hipp_vol_stats.Dhat,total_hipp_vol_stats.phisqhat,1,.2,.8,0.05)

Alternatively, you can perform a pilot longitudinal study with a small sample or you can use information from previous studies that are similar to the study that you are planning to run, or you can even analyse some  public available longitudinal data with lme to compute those values.

We performed sample size estimations for the study described in our paper in the wiki page:

http://surfer.nmr.mgh.harvard.edu/fswiki/LinearMixedEffectsModels


It may be useful for you to take a look at it.

Best
-Jorge