How to construct a regression model with two inter-dependent dependent variables?

Let's work through a concrete (if somewhat impractical) example:

I'm a medical researcher who has reason to investigate a possible trend in a dataset of tissue samples from the human lung and human brain. We are interested in the number of viral cells of type A found in these tissue samples (measured as a discrete count).

The dataset could look something like this:

patientA_brain_virus_counts patientA_lung_virus_counts age brain_tissue_total_cells lung_tissue_total_cells gender ethnicity
239                         5783                       67    139218   1323494    M    A
2313                        3528                       72    225815   2328554    F    A
15                          356                        38    535291   5341823    F    O
4829                        13458                      81    371234   3351732    F    T


The trend noticed within the data is that there is a greater proportion of lung_virus_countsversus brain_virus_counts. However, I need to model this in order to quantify this effect.

How does one model two dependent variables in this fashion? If there was one dependent variable, I would use something like a Poisson GLM model.

Are there statistical packages (e.g. in R) which allows one to perform this?

• Why not use lung_virus_counts \ brain_virus_counts as dependent variable in Gamma GLM? – Łukasz Deryło Jul 3 '17 at 9:56
• @ŁukaszDeryło That's certainly possible. Why would you choose Gamma in this case? – ShanZhengYang Jul 3 '17 at 16:50
• It is defined in positive numbers only and skewed, just like ratios of positive numbers (usually) are. – Łukasz Deryło Jul 4 '17 at 5:42