# Model the effect of treatment on mutation burden

I am struggling a bit to model the following problem. Basically, I would like to model tumor mutation burden (mutations per megabase, a continuous) as a function of treatment (categorical). The following is an example of how data looks like

patient-id therapy-1 therapy-2 therapy-3 cancer-type TMB
PID-1      1         NA        1         CT-1        1.3
PID-2      0         0         1         CT-1        0.14
PID-3      NA        0         1         CT-2        5
PID-4      1.        1         NA        CT-3        2.3
PID-5      1         1         NA        CT-3        10
...
...


1 - treated; 0 - not treated; NA - No information

I was trying multiple linear regression, but in most cases one patient got multiple therapies. This is where I am confused on how to interpret the results of linear regression. So far, I haven't included the cancer-type information into the model. However, IMO, including cancer-type into model will yield specific treatment effects in specific cancer type? Or is it over-expectation of what we can achieve from linear model?

Also, is there a better way to address the problem to get reasonable associations between treatment and TMB in this case?

Thank you for the help. Stay safe!

• Could you post your model is it something like TMB ~ cancer-type*patient-id ?
– llrs
Sep 29, 2020 at 8:26

## 1 Answer

Depends how you consider "linear regression", if you mean Pearsons, Spearman's analysis then general linear modelling (GLM) is a far better approach if you have continuous data. I don't really understand TMB, but that is a critical output then GLM will work. Logistic regression is an alternative approach data type depending. You have to perform a Q-Q plot and the residual against against any transformations you make (you might need to transform TMB). The lower the residual the better, the straight the Q-Q plot the better.

To explain how GLM works long hair and height correlate in a straight regression analysis. The implication is if you want to be tall - cut your hair! Of once you account for gender and send it through a GLM then gender and hairlength will correlate far stronger than hair length and height.

Mac OSX has a very easy to use pointy clicky, but highly professional, GLM package on its AppStore called Wizzard (bit expensive). It doesn't do general linear mixed modelling however. Everything does GLM of course, its just this package is really easy to use and you can figure out GLM by trial and error.