Hi all.
I am testing a drug in an animal experiment. Animals get either the drug or
placebo (saline) and a couple of weeks later they get sacrificed to measure
expression of some genes (mRNA levels via PCR).
So, there is a Tx variable (drug or placebo) and a continuous Y variable
(mRNA quantity).
Treatment might affect the number of cells (neurons) in the target tissue.
With fewer (more) cells, we'd expect less (more) mRNA, and that would have
nothing to do with the treatment effect on gene expression. Hence, we would
want to control for this additional variable X (number of cells). For
example, we might want to fit a model
Y = b0 + b1*X + b2*Tx
Problem:
There is not sufficient tissue to do the assays for both X and Y on the
same animal. We can either measure the number of cells or the quantity of
mRNA (but not both). So, some animals have (Tx,X) measurements and some
have (Tx,Y) measurements, but no animal has (Tx,X,Y).
All animals have measurements of an additional covariate Z (which
correlates only weakly with X and/or Y).
I am stumped as to how to attack this (it seems intractable). I have the
marginal distributions of X and Y, but no clue as to their covariance,
since I have no observations where both X and Y are measured. I do have Z,
so I can try to link X and Y through their associations with Z, but that
seems unsatisfactory (given Z is not a particularly good correlate of either).
Any advice?
Thank you.
Constantine
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________________________________________________________________
Constantine Daskalakis, ScD
Assistant Professor,
Biostatistics Section, Thomas Jefferson University,
211 S. 9th St. #602, Philadelphia, PA 19107
Tel: 215-955-5695
Fax: 215-503-3804
Email: [email protected]
Webpage: http://www.jefferson.edu/medicine/pharmacology/bio/
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