Is it possible to adjust paired data for the RNA quality measure 3'bias, percent of mRNA bases or simply RIN value? My supervisor insists on including some technical factors (at least a RIN)

Sample  PairID  Timepoint   PCT_INTRONIC_BASES  MEDIAN_3PRIME_BIAS  PCT_MRNA_BASES  RIN
1a  1   1   6.7873  0.270976    77.0604 8.4
1b  1   2   8.1872  0.231357    70.9168 6.8
2a  2   1   10.046  0.202588    72.0392 8.1
2b  2   2   7.6429  0.223535    72.0397 7.4
3a  3   1   8.9779  0.197612    69.0031 6.9
3b  3   2   5.2497  0.551641    71.607  7.6
4a  4   1   5.4145  0.683045    66.9346 7.4
4b  4   2   7.3759  0.274229    75.4435 7.5

design <- model.matrix( ~ pairID + RIN + Timepoint) ```

Yes, the design matrix you have created will work.

I would not recommend it however. Including the technical variables has the effect of using up part of your data. You have four pairs and now one of those pairs will be used to estimate the RIN coefficients. There is no strong evidence that small variations in RIN have a strong and consistent effect on gene expression. Routine adjustment for technical effects works better for experiments with lots of samples.

For a paired design, it is only the difference in RIN and Timepoint between the two members of the same pair that makes any difference.