# How to specify a risk model?

I'm reading this article. The authors indicated that for a random sample of 12 characteristics and 3600 patients affected in two arms (control and treatment arm), they fitted a risk model consisting of all 12 characteristics in the patients in the control arm only, as well as in the whole sample, blinded to treatment. But, they don't give a mathematical formula.

1. Does the risk model fitted in the patients in the control arm only have the following form?

$$\pi = \beta_1*x_1+... +\beta_{12}*x_{12}$$, $$(1)$$

1. Does the risk model fitted in the whole sample blinded to treatment have the following form?

$$\pi = \beta_1*x_1+... +\beta_{12}*x_{12} + \gamma*Trt$$, $$(2)$$

or this form without treatment effect ($$\gamma*Trt$$) like $$(1)$$:

$$\pi = \beta_1*x_1+... +\beta_{12}*x_{12}$$, $$(1)$$

The models you show as $$\pi = \beta_1 x_1 + \ldots$$ are additive risk models. Which is interesting because they perform so badly with even modest numbers of covariates.